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Levitation of a magnet by superconductor has been an active area of research to explore the quantum mechanical phenomenon. One of the techniques used is to measure the levitation of a magnet placed inside the superconducting microwave cavity. The levitation height can be probed by measuring the change in microwave frequency. Here, we report measurements of the change in resonance frequency of the microwave cavity with the Meissner-levitated permanent magnet. The change in resonant frequency and quality factor was measured as a function of input power and temperature. The change in resonate frequency is likely due to the interaction of the magnet with the radio-frequency field inside the microwave cavity.

Researchers point to four potential issues related to the popularisation of quantum science and technology. These include a lack of explaining underlying quantum concepts of quantum 2.0 technology, framing quantum science and technology as spooky and enigmatic, framing quantum technology narrowly in terms of public good and having a strong focus on quantum computing. To date, no research has yet assessed whether these potential issues are actually present in popular communication about quantum science. In this content analysis, we have examined the presence of these potential issues in 501 TEDx talks with quantum science and technology content. Results show that while most experts (70%) explained at least one underlying quantum concept (superposition, entanglement or contextuality) of quantum 2.0 technology, only 28% of the non-experts did so. Secondly, the spooky/enigmatic frame was present in about a quarter of the talks. Thirdly, a narrow public good frame was found, predominantly by highlighting the benefits of quantum science and technology (found in over 6 times more talks than risks). Finally, the main focus was on quantum computing at the expense of other quantum technologies. In conclusion, the proposed frames are indeed found in TEDx talks, there is indeed a focus on quantum computing, but at least experts explain underlying quantum concepts often., 30 pages, 7 figures

Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the classification. However, as the output states of a previous test cannot be reused for a new test in the Swap Test, the quantum algorithm LS-QSVM has to be repeated in preparing qubits, manipulating operations, and carrying out the measurement. This paper proposes a QSVM based on the generalized quantum amplitude estimation (AE-QSVM) which gets rid of the constraint of repetitive processes and saves the quantum resources. At first, AE-QSVM is trained by using the quantum singular value decomposition. Then, a query sample is classified by using the generalized quantum amplitude estimation in which high accuracy can be achieved by adding auxiliary qubits instead of repeating the algorithm. The complexity of AE-QSVM is reduced to $O(\kappa^{3}\varepsilon^{-3}(log(mn)+1))$ with an accuracy $\varepsilon$, where $m$ is the number of training vectors, $n$ is the dimension of the feature space, and $\kappa$ is the condition number. Experiments demonstrate that AE-QSVM is advantageous in terms of training matrix, the number of iterations, space complexity, and time complexity., Comment: 10 pages,4 figures

The mathematical equivalence between finite state stochastic machine and non-dissipative and dissipative quantum tight-binding and Schroedinger model is derived. Stochastic Finite state machine is also expressed by classical epidemic model and can reproduce the quantum entanglement emerging in the case of electrostatically coupled qubits described by von-Neumann entropy both in non-dissipative and dissipative case. The obtained results shows that quantum mechanical phenomena might be simulated by classical statistical model as represented by finite state stochastic machine. It includes the quantum like entanglement and superposition of states. Therefore coupled epidemic models expressed by classical systems in terms of classical physics can be the base for possible incorporation of quantum technologies and in particular for quantum like computation and quantum like communication. The classical density matrix is derived and described by the equation of motion in terms of anticommutator. Existence of Rabi like oscillations is pointed in classical epidemic model. Furthermore the existence of Aharonov-Bohm effect in quantum systems can also be reproduced by the classical epidemic model or in broader sense by finite state stochastic machine. Every quantum system made from quantum dots and described by simplistic tight-binding model by use of position-based qubits can be effectively described by classical statistical model encoded in finite stochastic state machine with very specific structure of S matrix that has twice bigger size as it is the case of quantum matrix Hamiltonian. Furthermore the description of linear and non-linear stochastic finite state machine is mapped to tight-binding and Schroedinger model. The concept of N dimensional complex time is incorporated into tight-binding model, so the description of dissipation in most general case is possible., 47 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2012.09923

Quantum Approximate Optimization Algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the execution time of QAOA scales exponentially with the problem size. We propose a Divide-and-Conquer QAOA (DC-QAOA) to address the above challenges for graph maximum cut (MaxCut) problem. The algorithm works by recursively partitioning a larger graph into smaller ones whose MaxCut solutions are obtained with small-size NISQ computers. The overall solution is retrieved from the sub-solutions by applying the combination policy of quantum state reconstruction. Multiple partitioning and reconstruction methods are proposed/ compared. DC-QAOA achieves 97.14% approximation ratio (20.32% higher than classical counterpart), and 94.79% expectation value (15.80% higher than quantum annealing). DC-QAOA also reduces the time complexity of conventional QAOA from exponential to quadratic.

Quantum(-inspired) annealers show promise in solving combinatorial optimisation problems in practice. There has been extensive researches demonstrating the utility of D-Wave quantum annealer and quantum-inspired annealer, i.e., Fujitsu Digital Annealer on various applications, but few works are comparing these platforms. In this paper, we benchmark quantum(-inspired) annealers with three combinatorial optimisation problems ranging from generic scientific problems to complex problems in practical use. In the case where the problem size goes beyond the capacity of a quantum(-inspired) computer, we evaluate them in the context of decomposition. Experiments suggest that both annealers are effective on problems with small size and simple settings, but lose their utility when facing problems in practical size and settings. Decomposition methods extend the scalability of annealers, but they are still far away from practical use. Based on the experiments and comparison, we discuss the advantages and limitations of quantum(-inspired) annealers, as well as the research directions that may improve the utility and scalability of the these emerging computing technologies.

We show how the numerical range of a matrix can be used to bound the optimal value of certain optimization problems over real tensor product vectors. Our bound is stronger than the trivial bounds based on eigenvalues, and can be computed significantly faster than bounds provided by semidefinite programming relaxations. We discuss numerous applications to other hard linear algebra problems, such as showing that a real subspace of matrices contains no rank-one matrix, and showing that a linear map acting on matrices is positive., Comment: 22 pages

We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell's S or Eberhard's J. Further improvement is obtained by using Wilks' likelihood ratio test based on the four tetranomially distributed vectors of counts of the four different outcome combinations, one 4-vector for each of the four setting combinations. The methodology is illustrated by application to the loophole-free Bell experiments of 2015 and 2016 performed in Delft and Munich, at NIST, and in Vienna respectively; and also to the earlier Innsbruck experiment of Weihs et al. (1998) and the recent Munich experiment of Zhang et al. (2022), which investigates use of a loophole-free Bell experiment as part of a protocol for Device Independent Quantum Key Distribution, DIQKD., 16 pages. Version 4: added a section with a potted history of Bell experiments in order to give a useful bibliography and a starting point for those wanting to learn more about the physics context

One of the commonly used chemical-inspired approaches in variational quantum computing is the unitary coupled-cluster (UCC) ansatze. Despite being a systematic way of approaching the exact limit, the number of parameters in the standard UCC ansatze exhibits unfavorable scaling with respect to the system size, hindering its practical use on near-term quantum devices. Efforts have been taken to propose some variants of UCC ansatze with better scaling. In this paper we explore the parameter redundancy in the preparation of unitary coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted formulation, small amplitude filtration, and entropy-based orbital selection approaches. Numerical results of using our approach on some small molecules have exhibited a significant cost reduction in the number of parameters to be optimized and in the time to convergence compared with conventional UCCSD-VQE simulations. We also discuss the potential application of some machine learning techniques in further exploring the parameter redundancy, providing a possible direction for future studies.

Particle-hole symmetry plays an important role for the characterization of topological phases in solid-state systems. It is found, for example, in free-fermion systems at half filling, and it is closely related to the notion of antiparticles in relativistic field theories. In the low energy limit, graphene is a prime example of a gapless particle-hole symmetric system described by an effective Dirac equation, where topological phases can be understood by studying ways to open a gap by preserving (or breaking) symmetries. An important example is the intrinsic Kane-Mele spin-orbit gap of graphene, which leads to a lifting of the spin-valley degeneracy and renders graphene a topological insulator in a quantum spin Hall phase, while preserving particle-hole symmetry. Here, we show that bilayer graphene allows realizing electron-hole double quantum-dots that exhibit nearly perfect particle-hole symmetry, where transport occurs via the creation and annihilation of single electron-hole pairs with opposite quantum numbers. Moreover, we show that this particle-hole symmetry results in a protected single-particle spin-valley blockade. The latter will allow robust spin-to-charge conversion and valley-to-charge conversion, which is essential for the operation of spin and valley qubits.

We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group products. The existence and structure of this Hilbert space algebra has a number of consequences. The algebra product, which can be expressed in terms of integer ribbon graph reconnection coefficients, is used to define solvable Hamiltonians with eigenvalues expressed in terms of normalized characters of symmetric group elements and degeneracies given in terms of Kronecker coefficients, which are tensor product multiplicities of symmetric group representations. The square of the Kronecker coefficient for a triple of Young diagrams is shown to be equal to the dimension of a sub-lattice in the lattice of ribbon graphs. This leads to an answer to the long-standing question of a combinatoric interpretation of the Kronecker coefficients. As an avenue to explore quantum supremacy and its implications for computational complexity theory, we outline experiments to detect non-vanishing Kronecker coefficients for hypothetical quantum realizations/simulations of these quantum systems. The correspondence between ribbon graphs and Belyi maps leads to an interpretation of these quantum mechanical systems in terms of quantum membrane world-volumes interpolating between string geometries., Version 1 - 49 pages; 12 pages of Appendices; 1 figure; revision V2 - added Lemma 1 which simplifies the proof of the main theorems; revision V3 - published version

Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required hardware, but also in identifying the most promising application areas and developing the corresponding quantum algorithms. The availability of intermediate-scale noisy quantum computers is now propelling the developments of novel algorithms, with applications across a variety of domains, including in aeroscience. Variational quantum algorithms are particularly promising since they are comparatively noise tolerant and aim to achieve a quantum advantage with only a few hundred qubits. Furthermore, they are applicable to a wide range of optimization problems arising throughout the natural sciences and industry. To demonstrate the possibilities for the aeroscience community, we give a perspective on how variational quantum algorithms can be utilized in computational fluid dynamics. We discuss how classical problems are translated into quantum algorithms and their logarithmic scaling with problem size. As an explicit example we apply this method to Burgers' Equation in one spatial dimension. We argue that a quantum advantage over classical computing methods could be achieved by the end of this decade if quantum hardware progresses as currently envisaged and emphasize the importance of joining up development of quantum algorithms with application-specific expertise to achieve real-world impact., Comment: 22 pages, 5 figures, submitted to AIAA Virtual collection "Short Surveys of Quantum Information Science and Technology for Aerospace Research"

Hole spin qubits based on germanium (Ge) have strong tunable spin orbit interaction (SOI) and ultrafast qubit operation speed. Here we report that the Rabi frequency (f_Rabi) of a hole spin qubit in a Ge hut wire (HW) double quantum dot (DQD) is electrically tuned through the detuning energy and middle gate voltage (V_M). f_Rabi gradually decreases with increasing detuning energy; on the contrary, f_Rabi is positively correlated with V_M. We attribute our results to the change of electric field on SOI and the contribution of the excited state in quantum dots to f_Rabi. We further demonstrate an ultrafast f_Rabi exceeding 1.2 GHz, which evidences the strong SOI in our device. The discovery of an ultrafast and electrically tunable f_Rabi in a hole spin qubit has potential applications in semiconductor quantum computing., 19 pages, 4 figures

Finding high-quality parameters is a central obstacle to using the quantum approximate optimization algorithm (QAOA). Previous work partially addresses this issue for QAOA on unweighted MaxCut problems by leveraging similarities in the objective landscape among different problem instances. However, we show that the more general weighted MaxCut problem has significantly modified objective landscapes, with a proliferation of poor local optima. Our main contribution is a simple rescaling scheme that overcomes these deleterious effects of weights. We show that for a given QAOA depth, a single “typical” vector of QAOA parameters can be successfully transferred to weighted MaxCut instances. This transfer leads to a median decrease in the approximation ratio of only 2.0 percentage points relative to a considerably more expensive direct optimization on a dataset of 34,701 instances with up to 20 nodes and multiple weight distributions. This decrease can be reduced to 1.2 percentage points at the cost of only 10 additional QAOA circuit evaluations with parameters sampled from a pretrained metadistribution, or the transferred parameters can be used as a starting point for a single local optimization run to obtain approximation ratios equivalent to those achieved by exhaustive optimization in 96.35% of our cases.

The superposition principle is one of the most fundamental principles of quantum mechanics. According to the Schr\"odinger equation, a physical system can be in any linear combination of its possible states. While the validity of this principle is routinely validated for microscopic systems, it is still unclear why we do not observe macroscopic objects to be in superpositions of states that can be distinguished by some classical property. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr\"odinger cat states of motion, where the constituent atoms are in a superposition of oscillating with two opposite phases. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states. Apart from shedding light at the boundary between the quantum and the classical world, our results are of interest for quantum technologies, as they pave the way towards continuous-variable quantum information processing and quantum metrology with mechanical resonators.

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Due to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization. Here we achieve this goal by realizing quantum critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and time-evolution of the Schr\"odinger equation in small spin glasses. We then measure dynamics in 3D spin glasses on thousands of qubits, where simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for a scaling advantage in reducing energy as a function of annealing time.

International audience; The Trotterized Unitary Coupled Cluster Single and Double (UCCSD) ansatz has recently attracted interest due to its use in Variation Quantum Eigensolver (VQE) molecular simulations on quantum computers. However, when the size of molecules increases, UCCSD becomes less interesting as it cannot achieve sufficient accuracy. Including higher-order excitations is therefore mandatory to recover the UCC's missing correlation effects. In this Letter, we extend the Trotterized UCC approach via the addition of (true) Triple T excitations introducing UCCSDT. We also include both spin and orbital symmetries. Indeed, in practice, these later help to reduce unnecessarily circuit excitations and thus accelerate the optimization process enabling to tackle larger molecules. Our initial numerical tests (12-14 qubits) show that UCCSDT improves the overall accuracy by at least two-orders of magnitudes with respect to standard UCCSD. Overall, the UCCSDT ansatz is shown to reach chemical accuracy and to be competitive with the CCSD(T) gold-standard classical method of quantum chemistry.

Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to additional applications of larger scale. We present a straightforward and effective method for solving larger-than-QPU lattice-structured Ising optimization problems. Performance is compared against simulated annealing with promising results, and improvement is shown as a function of the generation of D-Wave QPU used., 21 pages, 15 figures, supplementary code attachment

We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive direct and converse bounds for the one-shot capacity region, represented by the smooth conditional entropies and the error tolerance. The proof is based on the randomized partial decoupling theorem, which is a generalization of the decoupling theorem. The two bounds match in the asymptotic limit of infinitely many uses of a memoryless channel and coincide with the previous result obtained by Hsieh and Wilde. Direct and converse bounds for various communication tasks are obtained as corollaries, both for the one-shot and asymptotic scenarios.

Using techniques from semidefinite programming, we study the problem of finding a closest quantum channel to the projection onto a matricial subsystem. We derive two invariants of matricial subsystems which are related to the quantum Lov\'asz theta function of Duan, Severini, and Winter., Comment: Final version; minor changes

Current quantum systems based on spin qubits are controlled by classical electronics located outside the cryostat at room temperature. This approach creates a major wiring bottleneck, which is one of the main roadblocks toward truly scalable quantum computers. Thus, we propose a scalable memristor-based programmable DC source that could be used to perform biasing of quantum dots inside of the cryostat (i.e. in-situ). This novel cryogenic approach would enable to control the applied voltage on the electrostatic gates by programming the resistance of the memristors, thus storing in the latter the appropriate conditions to form the quantum dots. In this study, we first demonstrate multilevel resistance programming of a TiO2-based memristors at 4.2 K, an essential feature to achieve voltage tunability of the memristor-based DC source. We then report hardwarebased simulations of the electrical performance of the proposed DC source. A cryogenic TiO2-based memristor model fitted on our experimental data at 4.2 K was used to show a 1 V voltage range and 100 uV in-situ memristor-based DC source. Finally, we simulate the biasing of double quantum dots enabling sub-2 minutes in-situ charge stability diagrams. This demonstration is a first step towards more advanced cryogenic applications for resistive memories such as cryogenic control electronics for quantum computers.

A lossless beam-splitter has certain (complex-valued) probability amplitudes for sending an incoming photon into one of two possible directions. We use elementary laws of classical and quantum optics to obtain general relations among the magnitudes and phases of these probability amplitudes. Proceeding to examine a pair of (nearly) single-mode wavepackets in the number-states |n1> and |n2> that simultaneously arrive at the splitter's input ports, we find the distribution of photon-number states at the output ports using an argument inspired by Feynman's scattering analysis of indistinguishable Bose particles. The result thus obtained coincides with that of the standard quantum-optical treatment of beam-splitters via annihilation and creation operators a and a†. A simple application of the Feynman method provides a form of justification for the Bose enhancement implicit in the well-known formulas a|n>=sqrt(n)|n-1> and a†|n>=sqrt(n+1)|n+1>., 13 pages, 2 figures, 22 equations, 18 references and endnotes

The purpose of this paper is to present a comprehensive study of the Tavis-Cummings model from a system-theoretic perspective. A typical form of the Tavis-Cummings model is composed of an ensemble of non-interacting two-level systems (TLSs) that are collectively coupled to a common cavity resonator. The associated quantum linear passive system is proposed, whose canonical form reveals typical features of the Tavis-Cummings model, including $\sqrt{N}$- scaling, dark states, bright states, single-excitation superradiant and subradiant states. The passivity of this linear system is related to the vacuum Rabi mode splitting phenomenon in Tavis-Cummings systems. On the basis of the linear model, an analytic form is presented for the steady-state output state of the Tavis-Cummings model driven by a single-photon state. Master equations are used to study the excitation properties of the Tavis-Cummings model in the multi-excitation scenario. Finally, in terms of the transition matrix for a linear time-varying system, a computational framework is proposed for calculating the state of the Tavis-Cummings model, which is applicable to the multi-excitation case., 16 pages, 8 figures, IEEE Transactions on Automatic Control, to appear

Closed cycle $He^{3}-He^{4}$ dilution cryostats became the platform of choice in quantum sciences in the era of helium shortage. However, in many experiments, the mechanical vibrations induced by the pulsed cryocoolers present a significant drawback reflected both in electronic and mechanical noises. Here, we present a hybrid dilution cryostat platform; we have automated a commercial closed-cycle system to operate on a cryocooler or on a liquid helium battery. We implemented a scanning SQUID microscope in the hybrid dilution refrigerator. In this work we show the design of the hybrid setup and how its operation eliminates vibration artefacts in magnetic imaging.

The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process faced an excessive generation of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. We answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is significantly longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of $G = 2.27 \pm 0.07$. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.

Noise-induced control imperfection is an important problem in applications of diamond-based nano-scale sensing, where measurement-based strategies are generally utilized to correct low-frequency noises in realtime. However, the spin-state readout requires a long time due to the low photon-detection efficiency. This inevitably introduces a delay in noise-reduction process and limits its performance. Here we introduce the deep learning approach to relax this restriction by predicting the trend of noise and compensating the delay. We experimentally implement feedforward quantum control of nitrogen-vacancy center in diamond to protect its spin coherence and improve the sensing performance against noise. The new approach effectively enhances the decoherence time of the electron spin, which enables exploring more physics from its resonant spectroscopy. A theoretical model is provided to explain the improvement. This scheme could be applied in general sensing schemes and extended to other quantum systems., Comment: 6 pages,5 figures, comments are welcome

The trapped-ion system has been a leading platform for practical quantum computation and quantum simulation since the first scheme of a quantum gate was proposed by Cirac and Zoller in 1995. Quantum gates with trapped ions have shown the highest fidelity among all physical platforms. Recently, sophisticated schemes of quantum gates such as amplitude, phase, frequency modulation, or multi-frequency application, have been developed to make the gates fast, robust to many types of imperfections, and applicable to multiple qubits. Here, we review the basic principle and recent development of quantum gates with trapped ions., 19 pages, 10 figures. Review paper invited to the Journal of Korean Physical Society (JKPS) special issue commemorating the 30th anniversary of the division of atomic molecular and optical (AMO) physics

Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as new dynamical phases in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics., Comment: Review article for Annual Review of Condensed Matter Physics; comments welcome

The Posner molecule (calcium phosphate trimer), has been hypothesized to function as a biological quantum information processor due to its supposedly long-lived entangled $^{31}$P nuclear spin states. This hypothesis was challenged by our recent finding that the molecule lacks a well-defined rotational axis of symmetry -- an essential assumption in the proposal for Posner-mediated neural processing -- and exists as an asymmetric dynamical ensemble. Following up, we investigate here the spin dynamics of the molecule's entangled $^{31}$P nuclear spins within the asymmetric ensemble. Our simulations show that entanglement between two nuclear spins prepared in a Bell state in separate Posner molecules decays on a sub-second timescale -- much faster than previously hypothesized, and not long enough for super-cellular neuronal processing. Calcium phosphate dimers however, are found to be surprisingly resilient to decoherence and are able to preserve entangled nuclear spins for hundreds of seconds, suggesting that neural processing might occur through them instead.

In this paper, we study the recursion of measurement outcomes for open quantum networks under sequential measurements. Open quantum networks are networked quantum subsystems (e.g., qubits) with the state evolutions described by a continuous Lindblad master equation. When measurements are performed sequentially along such continuous dynamics, the quantum network states undergo random jumps and the corresponding measurement outcomes can be described by a vector of probabilistic Boolean variables. The induced recursion of the Boolean vectors forms a probabilistic Boolean network. First of all, we show that the state transition of the induced Boolean networks can be explicitly represented through realification of the master equation. Next, when the open quantum dynamics is relaxing in the sense that it possesses a unique equilibrium as a global attractor, structural properties including absorbing states, reducibility, and periodicity for the induced Boolean network are direct consequences of the relaxing property. Particularly, we show that generically, relaxing quantum dynamics leads to irreducible and aperiodic chains for the measurement outcomes. Finally, we show that for quantum consensus networks as a type of non-relaxing open quantum network dynamics, the communication classes of the measurement-induced Boolean networks are encoded in the quantum Laplacian of the underlying interaction graph., 21 pages, 3 figures

In any medium there are fluctuations due to temperature or due to the quantum nature of its constituents. If a material body is immersed into such a medium, its shape and the properties of its constituents modify the properties of the surrounding medium and its fluctuations. If in the same medium there is a second body then -- in addition to all direct interactions between them -- the modifications due to the first body influence the modifications due to the second body. This mutual influence results in a force between these bodies. If the excitations of the medium, which mediate the effective interaction between the bodies, are massless, this force is long-ranged and nowadays known as a Casimir force. If the fluctuating medium consists of the confined electromagnetic field in vacuum, one speaks of the quantum mechanical Casimir effect. In the case that the order parameter of material fields fluctuates - such as differences of number densities or concentrations - and that the corresponding fluctuations of the order parameter are long-ranged, one speaks of the critical Casimir effect. This holds, e.g., in the case of systems which undergo a second-order phase transition and which are thermodynamically located near the corresponding critical point, or for systems with a continuous symmetry exhibiting Goldstone mode excitations. Here we review the currently available exact results concerning the critical Casimir effect in systems encompassing the one-dimensional Ising, XY, and Heisenberg models, the two-dimensional Ising model, the Gaussian and the spherical models, as well as the mean field results for the Ising and the XY model. Special attention is paid to the influence of the boundary conditions on the behavior of the Casimir force., Comment: 218 pages, 68 figures

The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. In this paper, we derive the exact exponent for the asymptotic decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance. We then apply this result to the problem of privacy amplification against quantum side information, and we obtain an upper bound for the exponent of the asymptotic decreasing of the insecurity, measured using either purified distance or relative entropy. Our upper bound complements the earlier lower bound established by Hayashi, and the two bounds match when the rate of randomness extraction is above a critical value. Thus, for the case of high rate, we have determined the exact security exponent. Following this, we give examples and show that in the low-rate case, neither the upper bound nor the lower bound is tight in general. This exhibits a picture similar to that of the error exponent in channel coding. Lastly, we investigate the asymptotics of equivocation and its exponent under the security measure using the sandwiched R\'enyi divergence of order $s\in (1,2]$, which has not been addressed previously in the quantum setting., Comment: V3: close to published version

Noise spectroscopy elucidates the fundamental noise sources in spin systems, which is essential for developing spin qubits with long coherence times for quantum information processing, communication, and sensing. But noise spectroscopy typically relies on microwave coherent spin control to extract the noise spectrum, which becomes infeasible when there are high-frequency noise components stronger than the available microwave power. Here, we demonstrate an alternative all-optical approach to performing noise spectroscopy. Our approach utilises coherent Raman rotations of the spin state with controlled timing and phase to implement Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences. Analysing the spin dynamics under these sequences enables us to extract the noise spectrum of a dense ensemble of nuclear spins interacting with a single spin in a quantum dot, which has thus far only been modelled theoretically. By providing large spectral bandwidths of over 100 MHz, our Raman-based approach could serve as an important tool to study spin dynamics and decoherence mechanisms for a broad range of solid-state spin qubits.

The quantum circuit layout (QCL) problem is to map a quantum circuit such that the constraints of the device are satisfied. We introduce a quantum circuit mapping heuristic, QXX, and its machine learning version, QXX-MLP. The latter infers automatically the optimal QXX parameter values such that the layed out circuit has a reduced depth. In order to speed up circuit compilation, before laying the circuits out, we are using a Gaussian function to estimate the depth of the compiled circuits. This Gaussian also informs the compiler about the circuit region that influences most the resulting circuit's depth. We present empiric evidence for the feasibility of learning the layout method using approximation. QXX and QXX-MLP open the path to feasible large scale QCL methods., Comment: accepted in ACM Transactions on Quantum Computing

We present an efficient method for construction of a fully anti-commutative set of Pauli generators (elements of the Pauli group) from a commutative set of operators that are composed exclusively from Pauli $\hat x_i$ operators (purely X generators) and sorted by an associated numerical measure, such as absolute energy gradients. Our approach uses the Gauss-Jordan elimination applied to a binary matrix that encodes the set of X generators to bring it to the reduced row echelon form, followed by the construction of an anti-commutative system in a standard basis by means of a modified Jordan-Wigner transformation and returning to the original basis. The algorithm complexity is linear in the size of the X set and quadratic in the number of qubits. The resulting anti-commutative sets are used to construct the qubit coupled cluster Ansatz with involutory linear combinations of anti-commuting Paulis (QCC-ILCAP) proposed in [J. Chem. Theory Comput. 2021, 17, 1, 66-78]. We applied the iterative qubit coupled cluster method with the QCC-ILCAP Ansatz to calculations of ground-state potential energy curves for symmetric stretching of the water molecule (36 qubits) and dissociation of N$_2$ (56 qubits).

We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum eigensolvers (VQE). We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubit-coupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamond and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time., 36 pages, 8 figures

It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schr\"odinger) equation or for Klein-Gordon and Dirac wavefunctions defined in the Foldy-Wouthuysen representation. In this work we investigate quantitatively the degree of non-causality for free propagation for different types of wavepackets all having initially a compact spatial support. In the studied examples we find that non-causality appears as a small transient effect that can in most cases be neglected. We display several numerical results and discuss the fundamental and practical consequences of our findings concerning this peculiar dynamical feature., Comment: Slightly expanded; typos corrected

Noise in existing quantum processors only enables an approximation to ideal quantum computation. However, these approximations can be vastly improved by error mitigation, for the computation of expectation values, as shown by small-scale experimental demonstrations. However, the practical scaling of these methods to larger system sizes remains unknown. Here, we demonstrate the utility of zero-noise extrapolation for relevant quantum circuits using up to 26 qubits, circuit depths of 60, and 1080 CNOT gates. We study the scaling of the method for canonical examples of product states and entangling Clifford circuits of increasing size, and extend it to the quench dynamics of 2-D Ising spin lattices with varying couplings. We show that the efficacy of the error mitigation is greatly enhanced by additional error suppression techniques and native gate decomposition that reduce the circuit time. By combining these methods, we demonstrate an accuracy in the approximate quantum simulation of the quench dynamics that surpasses the classical approximations obtained from a state-of-the-art 2-D tensor network method. These results reveal a path to a relevant quantum advantage with noisy, digital, quantum processors., 7 pages, 3 figures

We report recent progress towards the realization of a sub-mK, low-vibration environment at the bottom stage of a dry dilution refrigerator for use in mechanical tests of quantum mechanics. Using adiabatic nuclear demagnetization, we have cooled a silicon cantilever force sensor to $T\approx 1$ mK. The temperature of the tip-holder of the cantilever chip was determined via a primary magnetic flux noise thermometer. The quality factor of the cantilever continues to increase with decreasing temperature, reaching $Q\approx 4\cdot 10^4$ at $2$ mK. To demonstrate that the vibration isolation is not compromised, we report the detection of the thermal motion of the cantilever down to $T \approx 20$ mK, only limited by the coupling to the SQUID readout circuit. We discuss feasible improvements that will allow us to probe unexplored regions of the parameter space of continuous spontaneous localization models., Comment: Submission to the special issue "Mechanical Resonators at Low Temperatures" in Journal of Low Temperature Physics

Strongly driven systems of emitters offer an attractive source of light over broad spectral ranges up to the X-ray region. A key limitation of these systems is that the light they emit is for the most part classical. We challenge this paradigm by building a quantum-optical theory of strongly driven many-body systems, showing that the presence of correlations among the emitters creates emission of nonclassical many-photon states of light. We consider the example of high-harmonic generation (HHG), by which a strongly driven system emits photons at integer multiples of the drive frequency. In the conventional case of uncorrelated emitters, the harmonics are in an almost perfectly multi-mode coherent state lacking any correlation between harmonics. By contrast, a correlation of the emitters prior to the strong drive is converted onto nonclassical features of the output light, including doubly-peaked photon statistics, ring-shaped Wigner functions, and quantum correlations between harmonics. We propose schemes for implementing these concepts, creating the correlations between emitters via an interaction between them or their joint interaction with the background electromagnetic field (as in superradiance). By tuning the time at which these processes are interrupted by the strong drive, one can control the amount of correlations between the emitters, and correspondingly the deviation of the emitted light from a classical state. Our work paves the way towards the engineering of novel many-photon states of light over a broadband spectrum of frequencies, and suggests HHG as a diagnostic tool for characterizing correlations in many-body systems with attosecond temporal resolution., Comment: 26 pages main (5 figures), 23 pages Supplementary Information

The nonequilibrium steady state (NESS) of a quantum network is central to a host of physical and biological scenarios. Examples include natural processes such as vision and photosynthesis, as well as technical devices such as photocells, both activated by incoherent light (e.g. sunlight) and leading to quantum transport. Here, a completely general approach to defining components of a quantum network in the NESS, and obtaining rates of processes between these components is provided. Quantum effects are explicitly included throughout, both in (a) defining network components via projection operators, and (b) in determining the role of coherences in rate processes. As examples, the methodology is applied to model cases, two versions of the V-level system, and to the spin-boson model, wherein the role of the environment and of internal system properties in determining the rates is examined. In addition, the role of Markovian vs. non-Markovian contributions is quantified, exposing conditions under which NESS rates can be obtained by perturbing the nonequilibrium steady state.

We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees differentiability of the universal functional by occupying all states and additionally not fully occupying the states in a fermionic system. We use convexity of the universal functional and invertibility of the potential-to-1RDM map to show that the subgradient contains only one element which is equivalent to differentiability. This allows us to show that all 1RDMs with a purely fractional occupation number spectrum ($0 < n_i < 1 \; \forall_i$) are uniquely $v$-representable up to a constant., 7 pages, 1 figure

Over the past few years, quantum computers and quantum algorithms have attracted considerable interest and attention from numerous scientific disciplines. In this article, we aim to provide a nontechnical yet informative introduction to key aspects of quantum computing. We discuss whether quantum computers one day might become useful tools for numerical weather and climate prediction. Using a recently developed quantum algorithm for solving nonlinear differential equations, we integrate a simple nonlinear model. In addition to considering the advantages that quantum computers have to offer, we shall also discuss the challenges one faces when trying to use quantum computers for real-world problems involving “big data,” such as weather prediction.

Collisional resonances are an important tool which has been used to modify interactions in ultracold gases, for realizing novel Hamiltonians in quantum simulations, for creating molecules from atomic gases and for controlling chemical reactions. So far, such resonances have been observed for atom-atom collisions, atom-molecule collisions and collisions between Feshbach molecules which are very weakly bound. Whether such resonances exist for ultracold ground state molecules has been debated due to the possibly high density of states and/or rapid decay of the resonant complex. Here we report a very pronounced and narrow (25 mG) Feshbach resonance in collisions between two ground state NaLi molecules. This molecular Feshbach resonance has two special characteristics. First, the collisional loss rate is enhanced by more than two orders of magnitude above the background loss rate which is saturated at the $p$-wave universal value, due to strong chemical reactivity. Second, the resonance is located at a magnetic field where two open channels become nearly degenerate. This implies the intermediate complex predominantly decays to the second open channel. We describe the resonant loss feature using a model with coupled modes which is analogous to a Fabry-P\'erot cavity. Our observations prove the existence of long-lived coherent intermediate complexes even in systems without reaction barriers and open up the possibility of coherent control of chemical reactions.

Resonant transmission occurs when constructive interference results in the complete passage of an incoming wave through an array of barriers. In this paper we explore such a scenario with one dimensional models. We adopt wave packets with finite width to illustrate the deterioration of resonance with decreasing wave packet width, and suggest an approximate wave function for the transmitted and reflected components, derived from aspects of both the wave packet and plane wave approaches. A comparison with exact numerical calculations shows excellent agreement, and provides insight into the scattering process., Comment: 15 pages, 6 figures

In this paper, we present a quantum algorithm for the dynamic programming approach for problems on directed acyclic graphs (DAGs). The running time of the algorithm is $O(\sqrt{\hat{n}m}\log \hat{n})$, and the running time of the best known deterministic algorithm is $O(n+m)$, where $n$ is the number of vertices, $\hat{n}$ is the number of vertices with at least one outgoing edge; $m$ is the number of edges. We show that we can solve problems that use OR, AND, NAND, MAX, and MIN functions as the main transition steps. The approach is useful for a couple of problems. One of them is computing a Boolean formula that is represented by Zhegalkin polynomial, a Boolean circuit with shared input and non-constant depth evaluation. Another two are the single source longest paths search for weighted DAGs and the diameter search problem for unweighted DAGs.

One possibility of defining a quantum R\'enyi $\alpha$-divergence of two quantum states is to optimize the classical R\'enyi $\alpha$-divergence of their post-measurement probability distributions over all possible measurements (measured R\'enyi divergence), and maybe regularize these quantities over multiple copies of the two states (regularized measured R\'enyi $\alpha$-divergence). A key observation behind the theorem for the strong converse exponent of asymptotic binary quantum state discrimination is that the regularized measured R\'enyi $\alpha$-divergence coincides with the sandwiched R\'enyi $\alpha$-divergence when $\alpha>1$. Moreover, it also follows from the same theorem that to achieve this, it is sufficient to consider $2$-outcome measurements (tests) for any number of copies (this is somewhat surprising, as achieving the measured R\'enyi $\alpha$-divergence for $n$ copies might require a number of measurement outcomes that diverges in $n$, in general). In view of this, it seems natural to expect the same when $\alpha1$ case., Comment: v3: 30 pages, minor improvements. Thanks to a comment by an anonymous reviewer, we can now show that the two different ways to regularize the test-measured R\'enyi $\alpha$-divergence lead to different quantities