Search

Quantum sensors are now universally acknowledged as one of the most promising near-term quantum technologies. The traditional formulation of quantum sensing introduces a concrete bound on ultimate precision through the so-called local sensing framework, in which a significant knowledge of prior information about the unknown parameter value is implicitly assumed. Moreover, the framework provides a systematic approach for optimizing the sensing protocol. In contrast, the paradigm of global sensing aims to find a precision bound for parameter estimation in the absence of such prior information. In recent years, vigorous research has been pursued to describe the contours of global quantum estimation. Here, we review some of these emerging developments. These developments are both in the realm of finding ultimate precision bounds with respect to appropriate figures of merit in the global sensing paradigm, as well as in the search for algorithms that achieve these bounds. We categorize these developments into two largely mutually exclusive camps; one employing Bayesian updating and the other seeking to generalize the frequentist picture of local sensing towards the global paradigm. In the first approach, in order to achieve the best performance, one has to optimize the measurement settings adaptively. In the second approach, the measurement setting is fixed, however the challenge is to identify this fixed measurement optimally., Comment: Review article, 12 pages, feedback is very welcome

Wannier-Stark localization has been proven to be a resource for quantum-enhanced sensitivity with super-Heisenberg scaling. An extremely promising feature of such probes are their ability to showcase such enhanced scaling even dynamically with system size, on top of the quadratic scaling in time. In this work, we address the issue of decoherence that occurs during evolution and characterize how that affects the sensing performance. We determine the parameter domains in which the enhancement is sustained under dephasing dynamics. As the open system dynamics is closely connected to evolution under an effective non-Hermitian Hamiltonian, we consider two such scenarios that can be engineered in an experiment. The first one is a trace-preserving dynamical description and shows the existence of quantum-enhanced sensitivity. The second one considers a non-Hermitian lattice where the presence of super-Heisenberg sensitivity further proves that quantum advantages of the Stark probes indeed can be sustained during noisy dynamics., Comment: 4.5 pages, 3 figures. Comments are welcome

Spin-orbit coupling plays an important role in both fundamental physics and technological applications. Precise estimation of the spin-orbit coupling is necessary for accurate designing across various physical setups such as solid state devices and quantum hardware. Here, we exploit quantum features in a 1D quantum wire for estimating the Rashba spin-orbit coupling with enhanced sensitivity beyond the capability of classical probes. The Heisenberg limited enhanced precision is achieved across a wide range of parameters and does not require fine tuning. Such advantage is directly related to the gap-closing nature of the probe across the entire relevant range of parameters. This provides clear advantage over conventional criticality-based quantum sensors in which quantum enhanced sensitivity can only be achieved through fine-tuning around the phase transition point. We have demonstrated quantum enhanced sensitivity for both single particle and interacting many-body probes. In addition to extending our results to thermal states and the multi-parameter scenario, we have provided an measurement basis to perform close to the ultimate precision., Comment: 6 pages, 5 figures. Comments are welcome

Discrete time crystals (DTC) exhibit a special non-equilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization and destroys the coherence required for the existence of DTC. In this letter, we devise a mechanism for establishing a stable DTC with period-doubling oscillations in an open quantum system that is governed by a properly tailored non-Hermitian Hamiltonian. We find a specific class of non-reciprocal couplings in our non-Hermitian dynamics which prevents thermalization through eigenstate ordering. Such choice of non-Hermitian dynamics, significantly enhances the stability of the DTC against imperfect pulses. Through a comprehensive analysis, we determine the phase diagram of the system in terms of pulse imperfection., Comment: Comments are welcome!

Quantum sensors based on critical many-body systems are known to exhibit enhanced sensing capability. Such enhancements typically scale algebraically with the probe size. Going beyond algebraic advantage and reaching exponential scaling has remained elusive when all the resources, such as the preparation time, are taken into account. In this work, we show that systems with first order quantum phase transitions can indeed achieve exponential scaling of sensitivity, thanks to their exponential energy gap closing. Remarkably, even after considering the preparation time using local adiabatic driving, the exponential scaling is sustained. Our results are demonstrated through comprehensive analysis of three paradigmatic models exhibiting first order phase transitions, namely Grover, $p$-spin, and biclique models. We show that this scaling survives moderate decoherence during state preparation and also can be optimally measured in experimentally available basis., Comment: 9 pages, 7 figures. Comments are welcome

Conventional formulation of quantum sensing has been mostly developed in the context of local estimation, where the unknown parameter is roughly known. In contrast, global sensing, where the prior information is incomplete and the unknown parameter is only known to lie within a broad interval, is practically more engaging but has received far less theoretical attention. Available formulations of global sensing rely on adaptive Bayesian strategies or minimizing average uncertainty. These methods either rely on challenging adaptive measurements or provide unsaturable bounds. Here, we provide an operationally motivated approach to global sensing in the frequentist picture. Our scheme yields a saturable bound on average uncertainty and allows for optimizing the measurement as well as the probe preparation simultaneously. We illustrate the implications for Gaussian single-mode sensing tasks like thermometry and phase estimation by showing that the optimal measurement indeed changes from homodyne, for local sensing, towards heterodyne, for global sensing. Depending on the task, this transformation can be gradual or sudden., Comment: 4.5 pages + 3 figs, Comments/suggestions welcome

The main power of quantum sensors is achieved when the probe is composed of several particles. In this situation, quantum features such as entanglement contribute in enhancing the precision of quantum sensors beyond the capacity of classical sensors. Originally, quantum sensing was formulated for non-interacting particles which are prepared in a special form of maximally entangled states. These probes are extremely sensitive to decoherence and any interaction between particles is detrimental to their performance. An alternative framework for quantum sensing has been developed exploiting quantum many-body systems, where the interaction between particles plays a crucial role. In this review, we investigate different aspects of the latter approach for quantum metrology and sensing. Many-body probes have been used in both equilibrium and non-equilibrium scenarios. Quantum criticality has been identified as a resource for achieving quantum enhanced sensitivity in both scenarios. In equilibrium, various types of criticalities, such as first order, second order, topological, and localization phase transitions have been exploited for sensing purposes. In non-equilibrium scenarios, quantum enhanced sensitivity has been discovered for Floquet, dissipative, and time crystal phase transitions. While each type of these criticalities has its own characteristics, the presence of one feature is crucial for achieving quantum enhanced sensitivity: the energy/quasi-energy gap closing. In non-equilibrium quantum sensing, time is another parameter which can affect the sensitivity of the probe. Typically, the sensitivity enhances as the probe evolves in time. In general, a more complete understanding of resources for non-equilibrium quantum sensors is now rapidly evolving. In this review, we provide an overview of recent progress in quantum metrology and sensing using many-body systems., Comment: Review article. Newly added Section in v2: Optimal control and machine learning strategies for quantum sensing. Several new references added. Feedback is highly appreciated!

Entanglement has been extensively used to characterize the structure of strongly correlated many-body systems. Most of these analyses focus on either spatial properties of entanglement or its temporal behavior. Negativity, as an entanglement measure, quantifies entanglement between different non-complementary blocks of a many-body system. Here, we consider a combined spatial-temporal analysis of entanglement negativity in a strongly correlated many-body system to characterize complex formation of correlations through non-equilibrium dynamics of such systems. A bond defect is introduced through a local quench at one of the boundaries of a uniform Heisenberg spin chain. Using negativity and entanglement entropy, computed by the time-dependent density matrix renormalization group, we analyze the extension of entanglement in the model as a function of time. We find that an entanglement cloud is formed, detached from the boundary spin and composed of spins with which it is highly entangled. The cloud travels ballistically in the chain until it reaches the other end where it reflects back and the cycle repeats. The revival dynamics exhibits an intriguing contraction (expansion) of the cloud as it moves away from (towards) the boundary spin.

We introduce MindSpore Quantum, a pioneering hybrid quantum-classical framework with a primary focus on the design and implementation of noisy intermediate-scale quantum (NISQ) algorithms. Leveraging the robust support of MindSpore, an advanced open-source deep learning training/inference framework, MindSpore Quantum exhibits exceptional efficiency in the design and training of variational quantum algorithms on both CPU and GPU platforms, delivering remarkable performance. Furthermore, this framework places a strong emphasis on enhancing the operational efficiency of quantum algorithms when executed on real quantum hardware. This encompasses the development of algorithms for quantum circuit compilation and qubit mapping, crucial components for achieving optimal performance on quantum processors. In addition to the core framework, we introduce QuPack, a meticulously crafted quantum computing acceleration engine. QuPack significantly accelerates the simulation speed of MindSpore Quantum, particularly in variational quantum eigensolver (VQE), quantum approximate optimization algorithm (QAOA), and tensor network simulations, providing astonishing speed. This combination of cutting-edge technologies empowers researchers and practitioners to explore the frontiers of quantum computing with unprecedented efficiency and performance.

We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling behaviors in two different phases, namely localized and extended. Our results provide a quantitative ansatz for quantum Fisher information in terms of time, probe size, and the number of excitations. In the long-time regime, the quantum Fisher information is a quadratic function of time, touching the Heisenberg limit. The system size scaling drastically depends on the phase changing from super-Heisenberg scaling in the extended phase to size-independent behavior in the localized phase. Furthermore, increasing the number of excitations always enhances the precision of the probe, although, in the interacting systems the enhancement becomes less eminent than the non-interacting probes. This is due to the induced localization by increasing the interaction between the excitations.

Current quantum simulators are primarily qubit-based, making them naturally suitable for simulating 2-level quantum systems. However, many systems in nature are inherently $d$-level, including higher spins, bosons, vibrational modes, and itinerant electrons. To simulate $d$-level systems on qubit-based quantum simulators, an encoding method is required to map the $d$-level system onto a qubit basis. Such mapping may introduce illegitimate states in the Hilbert space which makes the simulation more sophisticated. In this paper, we develop a systematic method to address the illegitimate states. In addition, we compare two different mappings, namely binary and symmetry encoding methods, and compare their performance through variational simulation of the ground state and time evolution of various many-body systems. While binary encoding is very efficient with respect to the number of qubits it cannot easily incorporate the symmetries of the original Hamiltonian in its circuit design. On the other hand, the symmetry encoding facilitates the implementation of symmetries in the circuit design, though it comes with an overhead for the number of qubits. Our analysis shows that the symmetry encoding significantly outperforms the binary encoding, despite requiring extra qubits. Their advantage is indicated by requiring fewer two-qubit gates, converging faster, and being far more resilient to Barren plateaus. We have performed variational ground state simulations of spin-1, spin-3/2, and bosonic systems as well as variational time evolution of spin-1 systems. Our proposal can be implemented on existing quantum simulators and its potential is extendable to a broad class of physical models., Comment: 15 pages, 8 figures, 2 tables

Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal phase in a disorder-free many-body system with indefinite persistent oscillations even in finite-size systems. Then we explore the sensing capability of this system to measure the spin exchange coupling. The results show strong quantum-enhanced sensitivity throughout the time crystal phase. As the spin exchange coupling varies, the system goes through a sharp phase transition and enters a non-time crystal phase in which the performance of the probe considerably decreases. We characterize this phase transition as a second-order type and determine its critical properties through a comprehensive finite-size scaling analysis. The performance is independent of the initial states and may even benefit from imperfections in the driving pulse. A simple set of projective measurements can capture the quantum-enhanced sensitivity., Comment: Comments are welcome!

Stark systems in which a linear gradient field is applied across a many-body system have recently been harnessed for quantum sensing. Here, we explore sensing capacity of Stark models, in both single-particle and many-body interacting systems, for estimating the strength of both linear and nonlinear Stark fields. The problem naturally lies in the context of multi-parameter estimation. We determine the phase diagram of the system in terms of both linear and nonlinear gradient fields showing how the extended phase turns into a localized one as the Stark fields increase. We also characterize the properties of the phase transition, including critical exponents, through a comprehesive finite-size scaling analysis. Interestingly, our results show that the estimation of both the linear and the nonlinear fields can achieve super-Heisenberg scaling. In fact, the scaling exponent of the sensing precision is directly proportional to the nonlinearity exponent which shows that nonlinearity enhances the estimation precision. Finally, we show that even after considering the cost of the preparation time the sensing precision still reveals super-Heisenberg scaling., Comment: 10 pages, 6 figures. Comments are welcome!

Measuring the temperature of a quantum system is an essential task in almost all aspects of quantum technologies. Theoretically, an optimal strategy for thermometry requires measuring energy which demands full accessibility over the entire system as well as complex entangled measurement basis. In this paper, we take a different approach and show that single qubit sequential measurements in the computational basis not only allows precise thermometry of a many-body system but may also achieve precision beyond the theoretical bound, avoiding demanding energy measurements at equilibrium. To obtain such precision, the time between the two subsequent measurements should be smaller than the thermalization time so that the probe never thermalizes. Therefore, the non-equilibrium dynamics of the system continuously imprint information about temperature in the state of the probe. This allows the sequential measurement scheme to reach precision beyond the accuracy achievable by complex energy measurements on equilibrium probes., Comment: 9 pages main text, 8 figures. Feedback is welcome!

Quantum many-body systems undergoing phase transitions have been proposed as probes enabling beyond-classical enhancement of sensing precision. However, this enhancement is usually limited to a very narrow region around the critical point. Here, we systematically develop a modular approach for introducing multiple phase transitions in a many-body system. This naturally allows us to enlarge the region of quantum-enhanced precision by encompassing the newly created phase boundaries. Our approach is general and can be applied to both symmetry-breaking and topological quantum sensors. In symmetry-breaking sensors, we show that the newly created critical points inherit the original universality class and a simple total magnetization measurement already suffices to locate them. In topological sensors, our modular construction creates multiple bands which leads to a rich phase diagram. In both cases, Heisenberg scaling for Hamiltonian parameter estimation is achieved at all the phase boundaries. This can be exploited to create a global sensor which significantly outperforms a uniform probe., Comment: 4+6 pages, 6+4 figures, accepted for publication in Physical Review Letters

Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin-1/2 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo (2IK) model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular -- even though the parameters to be estimated are independent -- resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters., Comment: 19 pages, 9 figures

Non-Hermitian physics predicts open quantum system dynamics with unique topological features such as exceptional points and the non-Hermitian skin effect. We show that this new paradigm of topological systems can serve as probes for bulk Hamiltonian parameters with quantum-enhanced sensitivity reaching Heisenberg scaling. Such enhancement occurs close to a spectral topological phase transition, where the entire spectrum undergoes a delocalization transition. We provide an explanation for this enhanced sensitivity based on the closing of point gap, which is a genuinely non-Hermitian energy gap with no Hermitian counterpart. This establishes a direct connection between energy-gap closing and quantum enhancement in the non-Hermitian realm. Our findings are demonstrated through several paradigmatic non-Hermitian topological models in various dimensions and potential experimental implementations., Comment: Close to published version, title edited

The conventional formulation of quantum sensing is based on the assumption that the probe is reset to its initial state after each measurement. In a very distinct approach, one can also pursue a sequential measurement scheme in which time-consuming resetting is avoided. In this situation, every measurement outcome effectively comes from a different probe, yet correlated with other data samples. Finding a proper description for the precision of sequential measurement sensing is very challenging as it requires the analysis of long sequences with exponentially large outcomes. Here, we develop a recursive formula and an efficient Monte-Carlo approach to calculate the Fisher information, as a figure of merit for sensing precision, for arbitrary lengths of sequential measurements. Our results show that Fisher information initially scales non-linearly with the number of measurements and then asymptotically saturates to linear scaling. Such transition, which fundamentally constrains the extractable information about the parameter of interest, is directly linked to the finite memory of the probe when undergoes multiple sequential measurements. Based on these, we establish a figure of merit to determine the optimal measurement sequence length and exemplify our results in three different physical systems., Comment: 4 pages main text, 5 pages Supplemental Material. Feedback is welcome!

In contrast to interferometry-based quantum sensing, where interparticle interaction is detrimental, quantum many-body probes exploit such interactions to achieve quantum-enhanced sensitivity. In most of the studied quantum many-body probes, the interaction is considered to be short-ranged. Here, we investigate the impact of long-range interaction at various filling factors on the performance of Stark quantum probes for measuring a small gradient field. These probes harness the ground state Stark localization phase transition which happens at an infinitesimal gradient field as the system size increases. Our results show that while super-Heisenberg precision is always achievable in all ranges of interaction, the long-range interacting Stark probe reveals two distinct behaviors. First, by algebraically increasing the range of interaction, the localization power enhances and thus the sensitivity of the probe decreases. Second, as the interaction range becomes close to a fully connected graph its effective localization power disappears and thus the sensitivity of the probe starts to enhance again. The super-Heisenberg precision is achievable throughout the extended phase until the transition point and remains valid even when the state preparation time is incorporated in the resource analysis. As the probe enters the localized phase, the sensitivity decreases and its performance becomes size-independent, following a universal behavior. In addition, our analysis shows that lower filling factors lead to better precision for measuring weak gradient fields., Comment: 8 Pages, 6 Figures. Comments are welcome

Near-term quantum simulators are mostly based on qubit-based architectures. However, their imperfect nature significantly limits their practical application. The situation is even worse for simulating fermionic systems, which underlie most of material science and chemistry, as one has to adopt fermion-to-qubit encodings which create significant additional resource overhead and trainability issues. Thanks to recent advances in trapping and manipulation of neutral atoms in optical tweezers, digital fermionic quantum simulators are becoming viable. A key question is whether these emerging fermionic simulators can outperform qubit-based simulators for characterizing strongly correlated electronic systems. Here, we perform a comprehensive comparison of resource efficiency between qubit and fermionic simulators for variational ground-state emulation of fermionic systems in both condensed matter systems and quantum chemistry problems. We show that the fermionic simulators indeed outperform their qubit counterparts with respect to resources for quantum evolution (circuit depth), as well as classical optimization (number of required parameters and iterations). In addition, they show less sensitivity to the random initialization of the circuit. The relative advantage of fermionic simulators becomes even more pronounced as interaction becomes stronger, or tunneling is allowed in more than one dimension, as well as for spinful fermions. Importantly, this improvement is scalable, i.e., the performance gap between fermionic and qubit simulators only grows for bigger system sizes., Comment: Accepted in Physical Review Research, 13 pages, 8 Figures, Close to published version

Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device. Variational quantum-classical algorithms have emerged as a promising approach for achieving such tasks on near-term quantum simulators, despite facing significant quantum and classical resource overheads. Here, we experimentally demonstrate multi-level variational spectroscopy for fundamental many-body Hamiltonians using a superconducting programmable digital quantum simulator. By exploiting symmetries, we effectively reduce circuit depth and optimization parameters allowing us to go beyond the ground state. Combined with the subspace search method, we achieve full spectroscopy for a 4-qubit Heisenberg spin chain, yielding an average deviation of 0.13 between experimental and theoretical energies, assuming unity coupling strength. Our method, when extended to 8-qubit Heisenberg and transverse-field Ising Hamiltonians, successfully determines the three lowest energy levels. In achieving the above, we introduce a circuit-agnostic waveform compilation method that enhances the robustness of our simulator against signal crosstalk. Our study highlights symmetry-assisted resource efficiency in variational quantum algorithms and lays the foundation for practical spectroscopy on near-term quantum simulators, with potential applications in quantum chemistry and condensed matter physics.

Classification is one of the main applications of supervised learning. Recent advancement in developing quantum computers has opened a new possibility for machine learning on such machines. Due to the noisy performance of near-term quantum computers, error mitigation techniques are essential for extracting meaningful data from noisy raw experimental measurements. Here, we propose two ensemble-learning error mitigation methods, namely bootstrap aggregating and adaptive boosting, which can significantly enhance the performance of variational quantum classifiers for both classical and quantum datasets. The idea is to combine several weak classifiers, each implemented on a shallow noisy quantum circuit, to make a strong one with high accuracy. While both of our protocols substantially outperform error-mitigated primitive classifiers, the adaptive boosting shows better performance than the bootstrap aggregating. The protocols have been exemplified for classical handwriting digits as well as quantum phase discrimination of a symmetry-protected topological Hamiltonian, in which we observe a significant improvement in accuracy. Our ensemble-learning methods provide a systematic way of utilising shallow circuits to solve complex classification problems., Comment: 14 pages, 6 figures

Gradient fields can effectively suppress particle tunneling in a lattice and localize the wave function at all energy scales, a phenomenon known as Stark localization. Here, we show that Stark systems can be used as a probe for the precise measurement of gradient fields, particularly in the weak-field regime where most sensors do not operate optimally. In the extended phase, Stark probes achieve super-Heisenberg precision, which is well beyond most of the known quantum sensing schemes. In the localized phase, the precision drops in a universal way showing fast convergence to the thermodynamic limit. For single-particle probes, we show that quantum-enhanced sensitivity, with super-Heisenberg precision, can be achieved through a simple position measurement for all the eigenstates across the entire spectrum. For such probes, we have identified several critical exponents of the Stark localization transition and established their relationship. Thermal fluctuations, whose universal behavior is identified, reduce the precision from super-Heisenberg to Heisenberg, still outperforming classical sensors. Multiparticle interacting probes also achieve super-Heisenberg scaling in their extended phase, which shows even further enhancement near the transition point. Quantum-enhanced sensitivity is still achievable even when state preparation time is included in resource analysis., Comment: 10 pages, 9 figures, (Comments are welcome!)

Quantum sensing is one of the arenas that exemplifies the superiority of quantum technologies over their classical counterparts. Such superiority, however, can be diminished due to unavoidable noise and decoherence of the probe. Thus, metrological strategies to fight against or profit from decoherence are highly desirable. This is the case of certain types of decoherence-driven many-body systems supporting dissipative phase transitions, which might be helpful for sensing. Boundary time crystals are exotic dissipative phases of matter in which the time-translational symmetry is broken, and long-lasting oscillations emerge in open quantum systems at the thermodynamic limit. We show that the transition from a symmetry unbroken into a boundary time crystal phase, described by a second-order transition, reveals quantum-enhanced sensitivity quantified through quantum Fisher information. We also determine the critical exponents of the system and establish their relationship. Our scheme is indeed a demonstration of harnessing decoherence for achieving quantum-enhanced sensitivity. From a practical perspective, it has the advantage of being independent of initialization and can be captured by a simple measurement., Comment: 7 pages main text, 5 figures

As disorder strength increases in quantum many-body systems a new phase of matter, the so-called anybody localization, emerges across the whole spectrum. This transition is energy dependent, a phenomenon known as mobility edge, such that the mid-spectrum eigenstates tend to localize at larger values of disorder in comparison to eigenstates near the edges of the spectrum. Many-body localization becomes more sophisticated in long-range interacting systems. Here, by focusing on several quantities, we draw the phase diagram as a function of disorder strength and energy spectrum, for a various range of interactions. Regardless of the underlying transition type, either second-order or Kosterlitz-Thouless, our analysis consistently determines the mobility edge, i.e. the phase boundary across the spectrum. We show that long-range interaction enhances the localization effect and shifts the phase boundary towards smaller values of disorder. In addition, we establish a hierarchy among the studied quantities concerning their corresponding transition boundary and critical exponents. Interestingly, we show that deliberately discarding some information of the system can mitigate finite-size effects and provide results in line with the analytical predictions at the thermodynamic limit., Comment: 10 pages, 6 Figures

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms become less efficient, achieving lower fidelity and demanding more optimization iterations. In particular, when the system is near its criticality the efficiency is even lower. Increasing the connectivity between distant qubits improves the results, even with less quantum and classical resources. Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the performance. Interestingly, the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations. The same design of circuits can also be used to variationally produce spin squeezed states, as a resource for quantum metrology., Comment: 12 pages, 7 figures

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design., Comment: 15 pages, 7 figures

Variational quantum algorithms (VQAs) are promising methods to demonstrate quantum advantage on near-term devices as the required resources are divided between a quantum simulator and a classical optimizer. As such, designing a VQA which is resource-efficient and robust against noise is a key factor to achieve potential advantage with the existing noisy quantum simulators. It turns out that a fixed VQA circuit design, such as the widely-used hardware efficient ansatz, is not necessarily robust against imperfections. In this work, we propose a genome-length-adjustable evolutionary algorithm to design a robust VQA circuit that is optimized over variations of both circuit ansatz and gate parameters, without any prior assumptions on circuit structure or depth. Remarkably, our method not only generates a noise-effect-minimized circuit with shallow depth, but also accelerates the classical optimization by substantially reducing the number of parameters. In this regard, the optimized circuit is far more resource-efficient with respect to both quantum and classical resources. As applications, based on two typical error models in VQA, we apply our method to calculate the ground energy of the hydrogen and the water molecules as well as the Heisenberg model. Simulations suggest that compared with conventional hardware efficient ansatz, our circuit-structure-tunable method can generate circuits apparently more robust against both coherent and incoherent noise, and hence is more likely to be implemented on near-term devices., Comment: 12 pages, 10 figures

Quantum sensors outperform their classical counterparts in their estimation precision, given the same amount of resources. So far, quantum-enhanced sensitivity has been achieved by exploiting the superposition principle. This enhancement has been obtained for particular forms of entangled states, adaptive measurement basis change, critical many-body systems, and steady-state of periodically driven systems. Here, we introduce a different approach to obtain quantum-enhanced sensitivity in a many-body probe through utilizing the nature of quantum measurement and its subsequent wave-function collapse without demanding prior entanglement. Our protocol consists of a sequence of local measurements, without re-initialization, performed regularly during the evolution of a many-body probe. As the number of sequences increases, the sensing precision is enhanced beyond the standard limit, reaching the Heisenberg bound asymptotically. The benefits of the protocol are multi-fold as it uses a product initial state and avoids complex initialization (e.g. prior entangled states or critical ground states) and allows for remote quantum sensing., Comment: 4 pages main text + 7 Supplemental Material. Comments and suggestions are welcome!

Second order quantum phase transitions, with well-known features such as long-range entanglement, symmetry breaking, and gap closing, exhibit quantum enhancement for sensing at criticality. However, it is unclear which of these features are responsible for this enhancement. To address this issue, we investigate phase transitions in free-fermionic topological systems that exhibit neither symmetry-breaking nor long-range entanglement. We analytically demonstrate that quantum enhanced sensing is possible using topological edge states near the phase boundary. Remarkably, such enhancement also endures for ground states of such models that are accessible in solid state experiments. We illustrate the results with 1D Su-Schrieffer-Heeger chain and a 2D Chern insulator which are both experimentally accessible. While neither symmetry-breaking nor long-range entanglement are essential, gap closing remains as the major candidate for the ultimate source of quantum enhanced sensing. In addition, we also provide a fixed and simple measurement strategy that achieves near-optimal precision for sensing using generic edge states irrespective of the parameter value. This paves the way for development of topological quantum sensors which are expected to also be robust against local perturbations., Comment: 6+6 pages, 2 figures (close to published version)

The fate of many-body localization in long-range interacting systems is not fully settled. For instance, the phase boundary between ergodic and many-body localized regimes is still under debate. Here, we use Floquet dynamics which can induce many-body localization in a clean long-range interacting system through spatiotemporal disorder, which are realized by regular operation of random local rotations. The phase diagram has been determined for two types of uniform and nonuniform long-range couplings. Our Floquet mechanism shows more localizing power than conventional static disorder methods as it pushes the phase boundary in favor of the localized phase. Moreover, our comprehensive long-time simulations provide strong support for obtained results based on static analysis., Comment: 7 Pages, 3 Figures. Comments are welcomed

Hybrid optomechanical systems are emerging as a fruitful architecture for quantum technologies. Hence, determining the relevant atom-light and light-mechanics couplings is an essential task in such systems. The fingerprint of these couplings is left in the global state of the system during non-equilibrium dynamics. However, in practice, performing measurements on the entire system is not feasible, and thus, one has to rely on partial access to one of the subsystems, namely the atom, the light, or the mechanics. Here, we perform a comprehensive analysis to determine the optimal subsystem for probing the couplings. We find that if the light-mechanics coupling is known or irrelevant, depending on the range of the qubit-light coupling, then the optimal subsystem can be either light or the qubit. In other scenarios, e.g., simultaneous estimation of the couplings, the light is usually the optimal subsystem. This can be explained as light is the mediator between the other two subsystems. Finally, we show that the widely used homodyne detection can extract a fair fraction of the information about the couplings from the light degrees of freedom., Comment: 10 pages, 2 appendices, 9 figures. Feedback is welcome

Local memory - the ability to extract information from a subsystem about its initial state - is a central feature of many-body localization. We introduce, investigate, and compare several information-theoretic quantifications of memory and discover a hierarchical relationship among them. We also find that while the Holevo quantity is the most complete quantifier of memory, vastly outperforming the imbalance, its decohered counterpart is significantly better at capturing the critical properties of the many-body localization transition at small system sizes. This motivates our suggestion that one can emulate the thermodynamic limit by artifically decohering otherwise quantum quantities. Applying this method to the von Neumann entropy results in critical exponents consistent with analytic predictions, a feature missing from similar small finite-size system treatments. In addition, the decohering process makes experiments significantly simpler by avoiding quantum state tomography., Comment: 11 pages, 7 figures, 1 table, updated to provide additional information and clarification (originally 9 pages, 7 figures)

Transistors are key elements for enabling computational hardware in both classical and quantum domains. Here, we propose a voltage-gated spin transistor using itinerant electrons in the Hubbard model which acts at the level of single electron spins. Going beyond classical spintronics, it enables the controlling of the flow of quantum information between distant spin qubits. The transistor has two modes of operation, open and closed, which are realized by two different charge configurations in the gate of the transistor. In the closed mode, the spin information between source and drain is blocked while in the open mode we have free spin information exchange. The switching between the modes takes place within a fraction of the operation time which allows for several subsequent operations within the coherence time of the transistor. The system shows good resilience against several imperfections and opens up a practical application for quantum dot arrays., Comment: 10 pages, 5 figures

Quantum sensing is inevitably an elegant example of the supremacy of quantum technologies over their classical counterparts. One of the desired endeavors of quantum metrology is AC field sensing. Here, by means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the ground states in critical many-body probes for parameter estimation, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system saturates to a steady state which allows achieving sensing precision well beyond the classical limit, almost reaching the Heisenberg bound. We associate the enhanced quantum precision to closing of the Floquet gap, resembling the features of quantum sensing in the ground state of critical systems. We show that the proposed protocol can also be realized in near-term quantum simulators, e.g. ion-traps, with a limited number of qubits. We show that in such systems a simple block magnetization measurement and a Bayesian inference estimator can achieve very high precision AC field sensing., Comment: 20 pages, 8+2 figures, comments welcome

Quantum sensing is one of the key areas which exemplifies the superiority of quantum technologies. Nonetheless, most quantum sensing protocols operate efficiently only when the unknown parameters vary within a very narrow region, i.e., local sensing. Here, we provide a systematic formulation for quantifying the precision of a probe for multi-parameter global sensing when there is no prior information about the parameters. In many-body probes, in which extra tunable parameters exist, our protocol can tune the performance for harnessing the quantum criticality over arbitrarily large sensing intervals. For the single-parameter sensing, our protocol optimizes a control field such that an Ising probe is tuned to always operate around its criticality. This significantly enhances the performance of the probe even when the interval of interest is so large that the precision is bounded by the standard limit. For the multi-parameter case, our protocol optimizes the control fields such that the probe operates at the most efficient point along its critical line. Interestingly, for an Ising probe, it is predominantly determined by the longitudinal field. Finally, we show that even a simple magnetization measurement significantly benefits from our optimization and moderately delivers the theoretical precision., Comment: 4 pages + supplemental material, 5 figures

As strength of disorder enhances beyond a threshold value in many-body systems, a fundamental transformation happens through which the entire spectrum localizes, a phenomenon known as many-body localization. This has profound implications as it breaks down fundamental principles of statistical mechanics, such as thermalization and ergodicity. Due to the complexity of the problem, the investigation of the many-body localization transition has remained a big challenge. The experimental exploration of the transition point is even more challenging as most of the proposed quantities for studying such effect are practically infeasible. Here, we experimentally implement a scalable protocol for detecting the many-body localization transition point, using the dynamics of a $N=12$ superconducting qubit array. We show that the sensitivity of the dynamics to random samples becomes maximum at the transition point which leaves its fingerprints in all spatial scales. By exploiting three quantities, each with different spatial resolution, we identify the transition point with excellent match between simulation and experiment. In addition, one can detect the evidence of mobility edge through slight variation of the transition point as the initial state varies. The protocol is easily scalable and can be performed across various physical platforms., Comment: 7 pages and 4 figures together with supplementary materials

Quantum thermodynamics has emerged as a separate sub-discipline, revising the concepts and laws of thermodynamics, at the quantum scale. In particular, there has been a disruptive shift in the way thermometry, and thermometers are perceived and designed. Currently, we face two major challenges in quantum thermometry. First, all of the existing optimally precise temperature probes are local, meaning their operation is optimal only for a narrow range of temperatures. Second, aforesaid optimal local probes mandate complex energy spectrum with immense degeneracy, rendering them impractical. Here, we address these challenges by formalizing the notion of global thermometry leading to the development of optimal temperature sensors over a wide range of temperatures. We observe the emergence of different phases for such optimal probes as the temperature interval is increased. In addition, we show how the best approximation of optimal global probes can be realized in spin chains, implementable in ion traps and quantum dots., Comment: 11 pages, 5 figures

The Ground-state criticality of many-body systems is a resource for quantum-enhanced sensing, namely the Heisenberg precision limit, provided that one has access to the whole system. We show that for partial accessibility, the sensing capabilities of a block of spins in the ground state reduces to the sub-Heisenberg limit. To compensate for this, we drive the hamiltonian periodically and use a local steady-state for quantum sensing. Remarkably, the steady-state sensing shows a significant enhancement in precision compared to the ground state and even achieves super-Heisenberg scaling for low frequencies. The origin of this precision enhancement is related to the closing of the Floquet quasienergy gap. It is in close correspondence with the vanishing of the energy gap at criticality for ground state sensing with global accessibility. The proposal is general to all the integrable models and can be implemented on existing quantum devices., Comment: 7+7 pages, 5+4 figures, typos corrected, close to published version

A key feature of the many-body localized phase is the breaking of ergodicity and consequently the emergence of local memory; revealed as the local preservation of information over time. As memory is necessarily a time dependent concept, it has been partially captured by a few extant studies of dynamical quantities. However, these quantities are neither optimal, nor democratic with respect to input state; and as such a fundamental and complete information theoretic understanding of local memory in the context of many-body localization remains elusive. We introduce the dynamical Holevo quantity as the true quantifier of local memory, outlining its advantages over other quantities such as the imbalance or entanglement entropy. We find clear scaling behavior in its steady-state across the many-body localization transition, and determine a family of two-parameter scaling ans\"atze which captures this behavior. We perform a comprehensive finite size scaling analysis of this dynamical quantity extracting the transition point and scaling exponents., Comment: 8 pages, 4 figures, 1 table; added new section 2, other sections heavily revised, references added

The power of a quantum circuit is determined through the number of two-qubit entangling gates that can be performed within the coherence time of the system. In the absence of parallel quantum gate operations, this would make the quantum simulators limited to shallow circuits. Here, we propose a protocol to parallelize the implementation of two-qubit entangling gates between multiple users which are spatially separated, and use a commonly shared spin chain data-bus. Our protocol works through inducing effective interaction between each pair of qubits without disturbing the others, therefore, it increases the rate of gate operations without creating crosstalk. This is achieved by tuning the Hamiltonian parameters appropriately, described in the form of two different strategies. The tuning of the parameters makes different bilocalized eigenstates responsible for the realization of the entangling gates between different pairs of distant qubits. Remarkably, the performance of our protocol is robust against increasing the length of the data-bus and the number of users. Moreover, we show that this protocol can tolerate various types of disorders and is applicable in the context of superconductor-based systems. The proposed protocol can serve for realizing two-way quantum communication., Comment: 10 pages, 7 figures. Comments are welcome

One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we first provide a quantitative comparison between the adiabatic and variational methods with respect to required quantum resources on digital quantum simulators, namely the depth of the circuit and the number of two-qubit quantum gates. Our results show that the variational methods are less demanding with respect to these resources. However, they need to be hybridized with a classical optimization which can converge slowly. Therefore, as the second result of the paper, we provide two different approaches for speeding the convergence of the classical optimizer by taking a good initial guess for the parameters of the variational circuit. We show that these approaches are applicable to a wide range of Hamiltonian and provide significant improvement in the optimization procedure., Comment: 15 pages, 10 figures

Optomechanical systems are promising platforms for controlled light-matter interactions. They are capable of providing several fundamental and practical novel features when the mechanical oscillator is cooled down to nearly reach its ground state. In this framework, measuring the effective temperature of the oscillator is perhaps the most relevant step in the characterization of those systems. In conventional schemes, the cavity is driven strongly, and the overall system is well-described by a linear (Gaussian preserving) Hamiltonian. Here, we depart from this regime by considering an undriven optomechanical system via non-Gaussian radiation-pressure interaction. To measure the temperature of the mechanical oscillator, initially in a thermal state, we use light as a probe to coherently interact with it and create an entangled state. We show that the optical probe gets a nonlinear phase, resulting from the non-Gaussian interaction, and undergoes an incoherent phase diffusion process. To efficiently infer the temperature from the entangled light-matter state, we propose using a nonlinear Kerr medium before a homodyne detector. Remarkably, placing the Kerr medium enhances the precision to nearly saturate the ultimate quantum bound given by the quantum Fisher information. Furthermore, it also simplifies the thermometry procedure as it makes the choice of the homodyne local phase independent of the temperature, which avoids the need for adaptive sensing protocols., Comment: 11 pages, 5 figures

Quantum sensors have been shown to be superior to their classical counterparts in terms of resource efficiency. Such sensors have traditionally used the time evolution of special forms of initially entangled states, adaptive measurement basis change, or the ground state of many-body systems tuned to criticality. Here, we propose a different way of doing quantum sensing which exploits the dynamics of a many-body system, initialized in a product state, along with a sequence of projective measurements in a specific basis. The procedure has multiple practical advantages as it: (i) enables remote quantum sensing, protecting a sample from the potentially invasive readout apparatus; and (ii) simplifies initialization by avoiding complex entangled or critical ground states. From a fundamental perspective, it harnesses a resource so far unexploited for sensing, namely, the residual information from the unobserved part of the many-body system after the wave-function collapses accompanying the measurements. By increasing the number of measurement sequences, through the means of a Bayesian estimator, precision beyond the standard limit, approaching the Heisenberg bound, is shown to be achievable., Comment: 4 figures, 4 pages (+2 pages of references)

The time evolution of spin chains has been extensively studied for transferring quantum states between different registers of a quantum computer. Nonetheless, in most of these protocols only one pair of sender-receivers can share the channel at each time. This significantly limits the rate of communication in a network of many users as they can only communicate through their common data-bus sequentially and not all at the same time. Here, we propose a protocol in which multiple users can share a spin chain channel simultaneously without having crosstalk between different parties. This is achieved by properly tuning the local parameters of the Hamiltonian to mediate an effective interaction between each pair of users via a distinct set of energy eigenstates of the system. We introduce three strategies with different levels of Hamiltonian tuning, each might be suitable for a different physical platform. All the three strategies provide very high transmission fidelities with vanishingly small crosstalks. We specifically show that our protocol can be experimentally realized on currently available superconducting quantum simulators., Comment: 8 pages, 7 figures, 1 table

Quantum many-body systems have been extensively studied from the perspective of quantum technology, and conversely, critical phenomena in such systems have been characterized by operationally relevant resources like entanglement. In this paper, we investigate robustness of magic (RoM), the resource in magic state injection based quantum computation schemes in the context of the transverse field anisotropic XY model. We show that the the factorizable ground state in the symmetry broken configuration is composed of an enormous number of highly magical $H$ states. We find the existence of a point very near the quantum critical point where magic contained explicitly in the correlation between two distant qubits attains a sharp maxima. Unlike bipartite entanglement, this persists over very long distances, capturing the presence of long range correlation near the phase transition. We derive scaling laws and extract corresponding exponents around criticality. Finally, we study the effect of temperature on two-qubit RoM and show that it reveals a crossover between dominance of quantum and thermal fluctuations., Comment: 22 pages, 7+1 figures

The exact nature of the many-body localization transition remains an open question. An aspect which has been posited in various studies is the emergence of scale invariance around this point, however the direct observation of this phenomenon is still absent. Here we achieve this by studying the logarithmic negativity and mutual information between disjoint blocks of varying size across the many-body localization transition. The two length scales, block sizes and the distance between them, provide a clear quantitative probe of scale invariance across different length scales. We find that at the transition point, the logarithmic negativity obeys a scale invariant exponential decay with respect to the ratio of block separation to size, whereas the mutual information obeys a polynomial decay. The observed scale invariance of the quantum correlations in a microscopic model opens the direction to probe the fractal structure in critical eigenstates using tensor network techniques and provide constraints on the theory of the many-body localization transition., Comment: 8 pages, 5 figures

Quantum simulators are engineered devices controllably designed to emulate complex and classically intractable quantum systems. A key challenge is to certify whether the simulator truly mimics the Hamiltonian of interest. This certification step requires the comparison of a simulator's output to a known answer, which is usually limited to small systems due to the exponential scaling of the Hilbert space. Here, in the context of Fermi-Hubbard spin-based analogue simulators, we propose a modular many-body spin to charge conversion scheme that scales linearly with both the system size and the number of low-energy eigenstates to discriminate. Our protocol is based on the global charge state measurement of a 1D spin chain performed at different detuning potentials along the chain. In the context of semiconductor-based systems, we identify realistic conditions for detuning the chain adiabatically in order to avoid state mixing while preserving charge coherence. Large simulators with vanishing energy gaps, including 2D arrays, can be certified block-by-block with a number of measurements scaling only linearly with the system size., Comment: 9 pages, 9 figures

Measurement is one of the key concepts which discriminates classical and quantum physics. Unlike classical systems, a measurement on a quantum system typically alters it drastically as a result of wave function collapse. Here we suggest that this feature can be exploited for inducing quench dynamics in a many-body system while leaving its Hamiltonian unchanged. Importantly, by doing away with dedicated macroscopic devices for inducing a quench -- using instead the indispensable measurement apparatus only -- the protocol is expected to be easier to implement and more resilient against decoherence. By way of various case studies, we show that our scheme also has decisive advantages beyond reducing decoherence -- for spectroscopy purposes and probing nonequilibrium scaling of critical and quantum impurity many-body systems., Comment: 6 pages, 5 figures

Entanglement not only plays a crucial role in quantum technologies, but is key to our understanding of quantum correlations in many-body systems. However, in an experiment, the only way of measuring entanglement in a generic mixed state is through reconstructive quantum tomography, requiring an exponential number of measurements in the system size. Here, we propose a machine learning assisted scheme to measure the entanglement between arbitrary subsystems of size $N_A$ and $N_B$, with $\mathcal{O}(N_A + N_B)$ measurements, and without any prior knowledge of the state. The method exploits a neural network to learn the unknown, non-linear function relating certain measurable moments and the logarithmic negativity. Our procedure will allow entanglement measurements in a wide variety of systems, including strongly interacting many body systems in both equilibrium and non-equilibrium regimes., Comment: 16 pages, 10 figures, including appendix