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We report NMR scattering circuit experiments that reveal causal structure. The scattering circuit involves interacting a probe qubit with the system of interest and finally measuring the probe qubit. The scattering circuit thereby implements a coarse-grained projective measurement. Causal structure refers to which events influence others and in the quantum case corresponds to different quantum circuit structures. In classical scenarios, intervention is commonly used to infer causal structure. In this quantum scenario of a bipartite system at two times, we demonstrate via scattering circuit experiments that coarse-grained measurements alone suffice for determining the causal structure. The experiment is undertaken by manipulating the nuclear spins of four Carbon-13 atoms in crotonic acid. The data analysis determines the compatibility of the data with given causal structures via representing the data as a pseudo density matrix (PDM) and analysing properties of the PDM. We demonstrate the successful identification of the causal structure for partial swap channels and fully decohering channels., Comment: 10 pages,10 figures, a companion paper appeared the same day, comments are welcome!

We probe the foundations of causal structure inference experimentally. The causal structure concerns which events influence other events. We probe whether causal structure can be determined without intervention in quantum systems. Intervention is commonly used to determine causal structure in classical scenarios, but in the more fundamental quantum theory, there is evidence that measurements alone, even coarse-grained measurements, can suffice. We demonstrate the experimental discrimination between several possible causal structures for a bipartite quantum system at two times, solely via coarse-grained projective measurements. The measurements are implemented by an approach known as scattering circuits in a nuclear magnetic resonance platform. Using recent analytical methods the data thus gathered is sufficient to determine the causal structure. Coarse-grained projective measurements disturb the quantum state less than fine-grained projective measurements and much less than interventions that reset the system to a fixed state., Comment: 6 pages, 4 figures, a companion paper appeared the same day. Comments are Welcome!

The accurate determination of the electronic structure of strongly correlated materials using first principle methods is of paramount importance in condensed matter physics, computational chemistry, and material science. However, due to the exponential scaling of computational resources, incorporating such materials into classical computation frameworks becomes prohibitively expensive. In 2016, Bauer et al. proposed a hybrid quantum-classical approach to correlated materials Phys. Rev. X 6, 031045 (2016)}] that can efficiently tackle the electronic structure of complex correlated materials. Here, we experimentally demonstrate that approach to tackle the computational challenges associated with strongly correlated materials. By seamlessly integrating quantum computation into classical computers, we address the most computationally demanding aspect of the calculation, namely the computation of the Green's function, using a spin quantum processor. Furthermore, we realize a self-consistent determination of the single impurity Anderson model through a feedback loop between quantum and classical computations. A quantum phase transition in the Hubbard model from the metallic phase to the Mott insulator is observed as the strength of electron correlation increases. As the number of qubits with high control fidelity continues to grow, our experimental findings pave the way for solving even more complex models, such as strongly correlated crystalline materials or intricate molecules., Comment: 6 pages + appendices

A fundamental challenge in quantum thermodynamics is the exploration of inherent dimensional constraints in thermodynamic machines. In the context of two-level systems, the most compact refrigerator necessitates the involvement of three entities, operating under self-contained conditions that preclude the use of external work sources. Here, we build such a smallest refrigerator using a nuclear spin system, where three distinct two-level carbon-13 nuclei in the same molecule are involved to facilitate the refrigeration process. The self-contained feature enables it to operate without relying on net external work, and the unique mechanism sets this refrigerator apart from its classical counterparts. We evaluate its performance under varying conditions and systematically scrutinize the cooling constraints across a spectrum of scenarios, which sheds light on the interplay between quantum information and thermodynamics., Comment: 6 pages + appendices

Quantum control plays a crucial role in enhancing precision scaling for quantum sensing. However, most existing protocols require perfect control, even though real-world devices inevitably have control imperfections. Here, we consider a fundamental setting of quantum sensing with imperfect clocks, where the duration of control pulses and the interrogation time are all subject to uncertainty. Under this scenario, we investigate the task of frequency estimation in the presence of a non-Markovian environment. We design a control strategy and prove that it outperforms any control-free strategies, recovering the optimal Heisenberg scaling up to a small error term that is intrinsic to this model. We further demonstrate the advantage of our control strategy via experiments on a nuclear magnetic resonance (NMR) platform. Our finding confirms that the advantage of quantum control in quantum sensing persists even in the presence of imperfections., Comment: 18 pages, 7 figures

Quantum state readout plays a pivotal role in quantum technologies, spanning applications in sensing, computation, and secure communication. In this work, we introduce a new approach for efficiently reading populations of hybrid-spin states in the nitrogen-vacancy center of diamond using a single laser pulse, which utilizes the excited state level anti-crossing mechanism at around 500 Gs. Reading spin state populations through this approach achieves the same outcome as traditional quantum state diagonal tomography but significantly reduces the experimental time by an order of magnitude while maintaining fidelity. Moreover, this approach may be extended to encompass full-state tomography, thereby obviating the requirement for a sequence of spin manipulations and mitigating errors induced by decoherence throughout the procedure.

We consider the certification of temporal quantum correlations using the pseudo-density matrix (PDM), an extension of the density matrix to the time domain, where negative eigenvalues are key indicators of temporal correlations. Conventional methods for detecting these correlations rely on PDM tomography, which often involves excessive redundant information and requires exponential resources. In this work, we develop an efficient protocol for temporal correlation detection by virtually preparing the PDM within a single time slice and estimating its second-order moments using randomized measurements. Through sample complexity analysis, we demonstrate that our protocol requires only a constant number of measurement bases, making it particularly advantageous for systems utilizing ensemble average measurements, as it maintains constant runtime complexity regardless of the number of qubits. We experimentally validate our protocol on a nuclear magnetic resonance platform, a typical thermodynamic quantum system, where the experimental results closely align with theoretical predictions, confirming the effectiveness of our protocol., Comment: 19 pages, 11 figures, comments are welcome

In this report, we introduce MammothModa, yet another multi-modal large language model (MLLM) designed to achieve state-of-the-art performance starting from an elementary baseline. We focus on three key design insights: (i) Integrating Visual Capabilities while Maintaining Complex Language Understanding: In addition to the vision encoder, we incorporated the Visual Attention Experts into the LLM to enhance its visual capabilities. (ii) Extending Context Window for High-Resolution and Long-Duration Visual Feature: We explore the Visual Merger Module to effectively reduce the token number of high-resolution images and incorporated frame position ids to avoid position interpolation. (iii) High-Quality Bilingual Datasets: We meticulously curated and filtered a high-quality bilingual multimodal dataset to reduce visual hallucinations. With above recipe we build MammothModa that consistently outperforms the state-of-the-art models, e.g., LLaVA-series, across main real-world visual language benchmarks without bells and whistles., Comment: Technical report

Quantum simulation offers an analog approach for exploring exotic quantum phenomena using controllable platforms, typically necessitating ultracold temperatures to maintain the quantum coherence. Superradiance lattices (SLs) have been harnessed to simulate coherent topological physics at room temperature, but the thermal motion of atoms remains a notable challenge in accurately measuring the physical quantities. To overcome this obstacle, we invent and validate a velocity scanning tomography technique to discern the responses of atoms with different velocities, allowing cold-atom spectroscopic resolution within room-temperature SLs. By comparing absorption spectra with and without atoms moving at specific velocities, we can derive the Wannier-Stark ladders of the SL across various effective static electric fields, their strengths being proportional to the atomic velocities. We extract the Zak phase of the SL by monitoring the ladder frequency shift as a function of the atomic velocity, effectively demonstrating the topological winding of the energy bands. Our research signifies the feasibility of room-temperature quantum simulation and facilitates their applications in quantum information processing., Comment: 6 pages, 4 figures

We experimentally probe the interplay of the quantum switch with the laws of thermodynamics. The quantum switch places two channels in a superposition of orders and may be applied to thermalizing channels. Quantum-switching thermal channels has been shown to give apparent violations of the second law. Central to these apparent violations is how quantum switching channels can increase the capacity to communicate information. We experimentally show this increase and how it is consistent with the laws of thermodynamics, demonstrating how thermodynamic resources are consumed. We use a nuclear magnetic resonance approach with coherently controlled interactions of nuclear spin qubits. We verify an analytical upper bound on the increase in capacity for channels that preserve energy and thermal states, and demonstrate that the bound can be exceeded for an energy-altering channel. We show that the switch can be used to take a thermal state to a state that is not thermal, whilst consuming free energy associated with the coherence of a control system. The results show how the switch can be incorporated into quantum thermodynamics experiments as an additional resource., Comment: 6 pages, 4 figures. Comments are welcome!

High-quality control is a fundamental requirement for quantum computation, but practically it is often hampered by the presence of various types of noises, which can be static or time-dependent. In many realistic scenarios, multiple noise sources coexist, and their resulting noise effects need be corrected to a sufficient order, posing significant challenges for the design of effective robust control methods. Here, we explore the method of robust quantum optimal control to generally tackle the problem of resisting multiple noises from a complicated noise environment. Specifically, we confine our analysis to unitary noises that can be described by classical noise models. This method employs a gradient-based multiobjective optimization algorithm to maximize the control figure of merit, and meanwhile to minimize the perturbative effects of the noises that are allowed for. To verify its effectiveness, we apply this method to a number of examples, including roubust entangling gate in trapped ion system and robust controlled-Z gate in superconducting qubits, under commonly encountered static and time-dependent noises. Our simulation results reveal that robust optimal control can find smooth, robust pulses that can simultaneously resist several noises and thus achieve high-fidelity gates. Therefore, we expect that this method will find wide applications on current noisy quantum computing devices., Comment: 13 pages, 5 figures, accepted by Physical Review Applied

People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of quantum computing have inspired insights and breakthroughs in quantum technologies, both in theories and in experiments. In this review, we introduce the basic principles of quantum computing and the multilayer architecture for a quantum computer. There are different experimental platforms for implementing quantum computing. In this review, based on a mature experimental platform, the Nuclear Magnetic Resonance (NMR) platform, we introduce the basic steps to experimentally implement quantum computing, as well as common challenges and techniques., Comment: 76 pages

Quantum computers have made extraordinary progress over the past decade, and significant milestones have been achieved along the path of pursuing universal fault-tolerant quantum computers. Quantum advantage, the tipping point heralding the quantum era, has been accomplished along with several waves of breakthroughs. Quantum hardware has become more integrated and architectural compared to its toddler days. The controlling precision of various physical systems is pushed beyond the fault-tolerant threshold. Meanwhile, quantum computation research has established a new norm by embracing industrialization and commercialization. The joint power of governments, private investors, and tech companies has significantly shaped a new vibrant environment that accelerates the development of this field, now at the beginning of the noisy intermediate-scale quantum era. Here, we first discuss the progress achieved in the field of quantum computation by reviewing the most important algorithms and advances in the most promising technical routes, and then summarizing the next-stage challenges. Furthermore, we illustrate our confidence that solid foundations have been built for the fault-tolerant quantum computer and our optimism that the emergence of quantum killer applications essential for human society shall happen in the future.

The nitrogen-vacancy (NV) center in diamond has been developed as a promising platform for quantum sensing, especially for magnetic field measurements in the nano-tesla range with a nanometer resolution. Optical spin readout performance has a direct effect on the signal-to-noise ratio (SNR) of experiments. In this work, we introduce an online optimization method to customize the laser waveform for readout. Both simulations and experiments reveal that our new scheme optimizes the optically detected magnetic resonance in NV center. The SNR of optical spin readout has been witnessed a 44.1% increase in experiments. In addition, we applied the scheme to the Rabi oscillation experiment, which shows an improvement of 46.0% in contrast and a reduction of 12.1% in mean deviation compared to traditional constant laser power SNR optimization. This scheme is promising to improve sensitivities for a wide range of NV-based applications in the future., Comment: 7 pages, 4 figures

Non-Hermitian quantum systems have recently attracted considerable attention due to their exotic properties. Though many experimental realizations of non-Hermitian systems have been reported, the non-Hermiticity usually resorts to the hard-to-control environments and cannot last for too long times. An alternative approach is to use quantum simulation with the closed system, whereas how to simulate non-Hermitian Hamiltonian dynamics remains a great challenge. To tackle this problem, we propose a protocol which combines a dilation method with the variational quantum algorithm. The dilation method is used to transform a non-Hermitian Hamiltonian into a Hermitian one through an exquisite quantum circuit, while the variational quantum algorithm is for efficiently approximating the complex entangled gates in this circuit. As a demonstration, we apply our protocol to simulate the dynamics of an Ising chain with nonlocal non-Hermitian perturbations, which is an important model to study quantum phase transition at nonzero temperatures. The numerical simulation results are highly consistent with the theoretical predictions, revealing the effectiveness of our protocol. The presented protocol paves the way for practically simulating small-scale non-Hermitian dynamics., Comment: 9 pages, 5 figures

Quantum metrology is supposed to significantly improve the precision of parameter estimation by utilizing suitable quantum resources. However, the predicted precision can be severely distorted by realistic noises. Here, we propose a control-enhanced quantum metrology scheme to defend against these noises for improving the metrology performance. Our scheme can automatically alter the parameter encoding dynamics with adjustable controls, thus leading to optimal resultant states that are less sensitive to the noises under consideration. As a demonstration, we numerically apply it to the problem of frequency estimation under several typical Markovian noise channels. Through comparing our control-enhanced scheme with the standard scheme and the ancilla-assisted scheme, we show that our scheme performs better and can improve the estimation precision up to around one order of magnitude. Furthermore, we conduct a proof-of-principle experiment in nuclear magnetic resonance system to verify the effectiveness of the proposed scheme. The research here is helpful for current quantum platforms to harness the power of quantum metrology in realistic noise environments., Comment: 9 pages, 5 figures

Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local disturbances. The topological protection, however, requires rather complicated lattice models and hard-to-manipulate dynamics; even the simplest system that can realize universal TQC--the Fibonacci anyon system--lacks a physical realization, let alone braiding the non-Abelian anyons. Here, we propose a disk model that can realize the Fibonacci anyon system, and construct the topologically protected logical spaces with the Fibonacci anyons. Via braiding the Fibonacci anyons, we can implement universal quantum gates on the logical space. Our proposal is platform-independent. As a demonstration, we implement a topological Hadamard gate on a logical qubit through a sequence of $15$ braiding operations of three Fibonacci anyons with merely $2$ nuclear spin qubits. The gate fidelity reaches 97.18% by randomized benchmarking. We further prove by experiment that the logical space and Hadamard gate are topologically protected: local disturbances due to thermal fluctuations result in a global phase only. Our work is a proof of principle of TQC and paves the way towards fault-tolerant quantum computation., Comment: 8 pages, 4 figures

Entanglement is a key property in the development of quantum technologies and in the study of quantum many-body simulations. However, entanglement measurement typically requires quantum full-state tomography (FST). Here we present a neural network-assisted protocol for measuring entanglement in equilibrium and non-equilibrium states of local Hamiltonians. Instead of FST, it can learn comprehensive entanglement quantities from single-qubit or two-qubit Pauli measurements, such as R\'enyi entropy, partially-transposed (PT) moments, and coherence. It is also exciting that our neural network is able to learn the future entanglement dynamics using only single-qubit traces from the previous time. In addition, we perform experiments using a nuclear spin quantum processor and train an adoptive neural network to study entanglement in the ground and dynamical states of a one-dimensional spin chain. Quantum phase transitions (QPT) are revealed by measuring static entanglement in ground states, and the entanglement dynamics beyond measurement time is accurately estimated in dynamical states. These precise results validate our neural network. Our work will have a wide range of applications in quantum many-body systems, from quantum phase transitions to intriguing non-equilibrium phenomena such as quantum thermalization., Comment: 5 pages, 4 figures. All comments are welcome

The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around volatility, trying to improve the understanding of it and remove the gap between the theory and market data. Unlike this, we propose to replace volatility with trading volume in stock pricing models. This pricing strategy is based on two hypotheses: a price-volume relation with an idea borrowed from fluid flows and a white-noise hypothesis for the price rate of change (ROC) that is verified via statistic testing on actual market data. The new framework can be easily adopted to local volume and stochastic volume models for the option pricing problem, which will point out a new possible direction for this central problem in quantitative finance., Comment: major revision

In open quantum systems, the precision of metrology inevitably suffers from the noise. {In Markovian open quantum dynamics, the precision can not be improved by using entangled probes although the measurement time is effectively shortened.} However, it was predicted over one decade ago that in a non-Markovian one, the error can be significantly reduced by the quantum Zeno effect (QZE) [Chin, Huelga, and Plenio, Phys. Rev. Lett. \textbf{109}, 233601 (2012)]. In this work, we apply a recently-developed quantum simulation approach to experimentally verify that entangled probes can improve the precision of metrology by the QZE. Up to $n=7$ qubits, we demonstrate that the precision has been improved by a factor of $n^{1/4}$, which is consistent with the theoretical prediction. Our quantum simulation approach may provide an intriguing platform for experimental verification of various quantum metrology schemes., Comment: 6 pages, 4 figures

Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological phases requires the robust topological invariants, whereas measuring these global quantities presents an outstanding challenge for experiments, especially in interacting systems. Here we report the real-space observation of a symmetry-protected topological phase with interacting nuclear spins, and probe the interaction-induced transition between two topologically distinct phases, both of which are classified by many-body Chern numbers obtained from the dynamical response to the external magnetic fields. The resulting value of Chern number ($\bar{\mathcal{C}h} = 1.958 \pm 0.070$) demonstrates the robust ground state degeneracy, and also determines the number of nontrivial edge states. Our findings enable direct characterization of topological features of quantum many-body states through gradually decreasing the strength of the introduced external fields., Comment: 17 + 28 pages, 4 + 15 figures, 2 tables. Comments are welcome!

Noise is ubiquitous in real quantum systems, leading to non-Hermitian quantum dynamics, and may affect the fundamental states of matter. Here we report in experiment a quantum simulation of the two-dimensional non-Hermitian quantum anomalous Hall (QAH) model using the nuclear magnetic resonance processor. Unlike the usual experiments using auxiliary qubits, we develop a stochastic average approach based on the stochastic Schr\"odinger equation to realize the non-Hermitian dissipative quantum dynamics, which has advantages in saving the quantum simulation sources and simplifies implementation of quantum gates. We demonstrate the stability of dynamical topology against weak noise, and observe two types of dynamical topological transitions driven by strong noise. Moreover, a region that the emergent topology is always robust regardless of the noise strength is observed. Our work shows a feasible quantum simulation approach for dissipative quantum dynamics with stochastic Schr\"odinger equation and opens a route to investigate non-Hermitian dynamical topological physics.

Entanglement, as a key resource for modern quantum technologies, is extremely fragile due to the decoherence. Here, we show that a quantum autoencoder, which is trained to compress a particular set of quantum entangled states into a subspace that is robust to decoherence, can be employed to preserve entanglement. The training process is based on a hybrid quantum-classical approach to improve the efficiency in building the autoencoder and reduce the experimental errors during the optimization. Using nitrogen-vacancy centers in diamond, we demonstrate that the entangled states between the electron and nuclear spins can be encoded into the nucleus subspace which has much longer coherence time. As a result, lifetime of the Bell states in this solid-spin system is extended from 2.22 {\pm} 0.43 {\mu}s to 3.03 {\pm} 0.56 ms, yielding a three orders of magnitude improvement. The quantum autoencoder approach is universal, paving the way of utilizing long lifetime nuclear spins as immediate-access quantum memories in quantum information tasks.

In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As a demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient Ans\"atze for the variational quantum algorithm, leading to improved performance in solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks., Comment: 9 pages, 7 figures

Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of noises. In particular, time-dependent noises are frequently encountered in experiments but how to overcome them remains a challenging problem. In this work, we extend and apply the recently proposed robust control technique of inverse geometric optimization to time-dependent noises by working it in the filter-function formalism. The basic idea is to parameterize the control filter function geometrically and minimize its overlap with the noise spectral density. This then effectively reduces the noise susceptibility of the controlled system evolution. We show that the proposed method can produce high-quality robust pulses for realizing desired quantum evolutions under realistic noise models, and thus will find practical applications for current physical platforms., Comment: 5+7 pages, 3+4 figures

Deep learning models for automatic readability assessment generally discard linguistic features traditionally used in machine learning models for the task. We propose to incorporate linguistic features into neural network models by learning syntactic dense embeddings based on linguistic features. To cope with the relationships between the features, we form a correlation graph among features and use it to learn their embeddings so that similar features will be represented by similar embeddings. Experiments with six data sets of two proficiency levels demonstrate that our proposed methodology can complement BERT-only model to achieve significantly better performances for automatic readability assessment., Comment: Accepted to the 59th Annual Meeting of the Association for Computational Linguistics (ACL 2021)

SpinQ Gemini is a commercial desktop quantum computer designed and manufactured by SpinQ Technology. It is an integrated hardware-software system. The first generation product with two qubits was launched in January 2020. The hardware is based on NMR spectrometer, with permanent magnets providing $\sim 1$ T magnetic field. SpinQ Gemini operates under room temperature ($0$-$30^{\circ}$C), highlighting its lightweight (55 kg with a volume of $70\times 40 \times 80$ cm$^3$), cost-effective (under $50$k USD), and maintenance-free. SpinQ Gemini aims to provide real-device experience for quantum computing education for K-12 and at the college level. It also features quantum control design capabilities that benefit the researchers studying quantum control and quantum noise. Since its first launch, SpinQ Gemini has been shipped to institutions in Canada, Taiwan and Mainland China. This paper introduces the system of design of SpinQ Gemini, from hardware to software. We also demonstrate examples for performing quantum computing tasks on SpinQ Gemini, including one task for a variational quantum eigensolver of a two-qubit Heisenberg model. The next generations of SpinQ quantum computing devices will adopt models of more qubits, advanced control functions for researchers with comparable cost, as well as simplified models for much lower cost (under $5$k USD) for K-12 education. We believe that low-cost portable quantum computer products will facilitate hands-on experience for teaching quantum computing at all levels, well-prepare younger generations of students and researchers for the future of quantum technologies., Comment: 14 pages, 17 figures

It is natural to measure the observables from the Hamiltonian-based quantum dynamics, and its inverse process that Hamiltonians are estimated from the measured data also is a vital topic. In this work, we propose a recurrent neural network to learn the parameters of the target Hamiltonians from the temporal records of single-qubit measurements. The method does not require the assumption of ground states and only measures single-qubit observables. It is applicable on both time-independent and time-dependent Hamiltonians and can simultaneously capture the magnitude and sign of Hamiltonian parameters. Taking quantum Ising Hamiltonians with the nearest-neighbor interactions as examples, we trained our recurrent neural networks to learn the Hamiltonian parameters with high accuracy, including the magnetic fields and coupling values. The numerical study also shows that our method has good robustness against the measurement noise and decoherence effect. Therefore, it has widespread applications in estimating the parameters of quantum devices and characterizing the Hamiltonian-based quantum dynamics., Comment: 9 pages and 6 figures. All comments are welcome

Indefinite causal order (ICO) is playing a key role in recent quantum technologies. Here, we experimentally study quantum thermodynamics driven by ICO on nuclear spins using the nuclear magnetic resonance system. We realize the ICO of two thermalizing channels to exhibit how the mechanism works, and show that the working substance can be cooled or heated albeit it undergoes thermal contacts with reservoirs of the same temperature. Moreover, we construct a single cycle of the ICO refrigerator based on the Maxwell's demon mechanism, and evaluate its performance by measuring the work consumption and the heat energy extracted from the low-temperature reservoir. Unlike classical refrigerators in which the coefficient of performance (COP) is perversely higher the closer the temperature of the high-temperature and low-temperature reservoirs are to each other, the ICO refrigerator's COP is always bounded to small values due to the non-unit success probability in projecting the ancillary qubit to the preferable subspace. To enhance the COP, we propose and experimentally demonstrate a general framework based on the density matrix exponentiation (DME) approach, as an extension to the ICO refrigeration. The COP is observed to be enhanced by more than three times with the DME approach. Our work demonstrates a new way for non-classical heat exchange, and paves the way towards construction of quantum refrigerators on a quantum system., Comment: 5 pages, 4 figures

Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here, we report a systematic, scalable approach based on dynamical invariants to realize HQGs without using additional Hilbert spaces. While presenting the theoretical framework of our approach, we design and experimentally evaluate single-qubit and two-qubits HQGs for the nuclear magnetic resonance system. The single-qubit gates acquire average fidelity 0.9972 by randomized benchmarking, and the controlled-NOT gate acquires fidelity 0.9782 by quantum process tomography. Our approach is also platform-independent, and thus may open a way to large-scale holonomic quantum computation., Comment: 9 pages, 3 figures

To obtain a complete description of a quantum system, one usually employs standard quantum state tomography, which however requires exponential number of measurements to perform and hence is impractical when the system's size grows large. In this work, we introduce a self-learning tomographic scheme based on the variational hybrid quantum-classical method. The key part of the scheme is a learning procedure, in which we learn a control sequence capable of driving the unknown target state coherently to a simple fiducial state, so that the target state can be directly reconstructed by applying the control sequence reversely. In this manner, the state tomography problem is converted to a state-to-state transfer problem. To solve the latter problem, we use the closed-loop learning control approach. Our scheme is further experimentally tested using techniques of a 4-qubit nuclear magnetic resonance. {Experimental results indicate that the proposed tomographic scheme can handle a broad class of states including entangled states in quantum information, as well as dynamical states of quantum many-body systems common to condensed matter physics., Comment: 9 pages, 5 figures. To be published in Physical Review Applied

The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our work paves the way towards the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions., Comment: 6 pages for main text+ 5 pages for supplementary information

The out-of-time-ordered correlators (OTOC) have been established as a fundamental concept for quantifying quantum information scrambling and diagnosing quantum chaotic behavior. Recently, it was theoretically proposed that the OTOC can be used as an order parameter to dynamically detect both equilibrium quantum phase transitions (EQPTs) and dynamical quantum phase transitions (DQPTs) in one-dimensional many-body systems. Here we report the first experimental observation of EQPTs and DQPTs in a quantum spin chain via quench dynamics of OTOC on a nuclear magnetic resonance quantum simulator. We observe that the quench dynamics of both the order parameter and the two-body correlation function cannot detect the DQPTs, but the OTOC can unambiguously detect the DQPTs. Moreover, we demonstrate that the long-time average value of the OTOC in quantum quench signals the equilibrium quantum critical point and ordered quantum phases, thus one can measure the EQPTs from the non-equilibrium quantum quench dynamics. Our experiment paves a way for experimentally investigating DQPTs through OTOCs and for studying the EQPTs through the non-equilibrium quantum quench dynamics with quantum simulators., Comment: 5 pages and 3 figures. Supplementary Materials contain 4 pages and 5 figures

The nitrogen-vacancy (N-V) center in diamond is a widely-used platform for quantum information processing and metrology. The electron-spin state of N-V center could be initialized and readout optically, and manipulated by resonate microwave fields. In this work, we analyze the dependence of electron-spin initialization on widths of laser pulses. We build a numerical model to simulate this process and verify the simulation results in experiment. Both simulations and experiments reveal a fact that shorter laser pulses are helpful to the electron-spin polarization. We therefore propose to use extremely-short laser pulses for electron-spin initialization. In this new scheme, the spin-state contrast could be improved about 10% in experiment by using laser pulses as short as 4 ns in width. Furthermore, we provide a mechanism to explain this effect which is due to the occupation time in the meta-stable spin-singlet states of N-V center. Our new scheme is applicable in a broad range of NV-based applications in the future., Comment: 7 pages, 4 figures

We experimentally demonstrate a dynamical classification approach for investigation of topological quantum phases using a solid-state spin system through nitrogen-vacancy (NV) center in diamond. Similar to the bulkboundary correspondence in real space at equilibrium, we observe a dynamical bulk-surface correspondence in the momentum space from a dynamical quench process. An emergent dynamical topological invariant is precisely measured in experiment by imaging the dynamical spin-textures on the recently defined band-inversion surfaces, with high topological numbers being implemented. Importantly, the dynamical classification approach is shown to be independent of quench ways and robust to the decoherence effects, offering a novel and practical strategy for dynamical topology characterization, especially for high dimensional gapped topological phases., Comment: 6 pages, 4 figures

Out-of-time-order correlator (OTOC), been suggested as a measure of quantum information scrambling in quantum many-body systems, has received enormous attention recently. The experimental measurement of OTOC is quite challenging. The existing theoretical protocols consist in implementing time-reversal operations or using ancillary quantum systems, therefore only a few experiments have been reported. Recently, a new protocol to detect OTOC using statistical correlations between randomized measurements was put forward. In this work, we detect the OTOCs of a kicked-Ising model using this new measurement method on a 4-qubit nuclear magnetic resonance quantum simulator. In experiment, we use random Hamiltonian evolutions to generate the random operations that are required by the randomized OTOC detection protocol. Our experimental results are in good agreement with the theoretical predictions, thus confirming the feasibility of the protocols. Therefore, our work represents a step in exploring realistic quantum chaotic dynamics in complicated quantum systems., Comment: 7 pages, 5 figures

Modern applications of quantum control in quantum information science and technology require the precise characterization of quantum states and quantum channels. In particular, high-performance quantum state engineering often demands that quantum states are transferred with optimal efficiency via realizable controlled evolution, the latter often modeled by quantum channels. When an appropriate quantum control model for an interested system is constructed, the exploration of optimal bounds on state transfer for the underlying quantum channel is then an important task. In this work, we analyze the state transfer efficiency problem for different class of quantum channels, including unitary, mixed unitary and Markovian. We then apply the theory to nuclear magnetic resonance (NMR) experiments. We show that two most commonly used control techniques in NMR, namely gradient field control and phase cycling, can be described by mixed unitary channels. Then we show that employing mixed unitary channels does not extend the unitarily accessible region of states. Also, we present a strategy of optimal experiment design, which incorporates coherent radio-frequency field control, gradient field control and phase cycling, aiming at maximizing state transfer efficiency and meanwhile minimizing the number of experiments required. Finally, we perform pseudopure state preparation experiments on two- and three-spin systems, in order to test the bound theory and to demonstrate the usefulness of non-unitary control means., Comment: 11 pages, 8 figures

Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing these objects in realistic physical systems can be a challenging task. In this work, we study quantum pseudorandomness generation on a 12-spin nuclear magnetic resonance system. The experimental process is based on the recently proposed design Hamiltonian approach, which has the merit of being significantly more efficient than previous protocols. By applying random refocusing sequences to the experimental system we create a design Hamiltonian the dynamics of which quickly forms unitary designs. We then use multiple-quantum techniques to measure spreading of quantum coherences over system's degrees of freedom, and so to probe the growth of quantum pseudorandomness. The measured multiple-quantum coherence spectra indicate that substantial quantum pseudorandomness have been achieved., Comment: 13 pages, 9 figures, 2 tables

Quantum state tomography is a daunting challenge of experimental quantum computing even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the reconstruction of the full state thereafter is hard. Here, we present a machine learning method to recover the full quantum state from its local information, where a fully-connected neural network is built to fulfill the task with up to seven qubits. In particular, we test the neural network model with a practical dataset, that in a 4-qubit nuclear magnetic resonance system our method yields global states via the 2-local information with high accuracy. Our work paves the way towards scalable state tomography in large quantum systems., Comment: 10 pages, 4 figures, 3 tables

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$, obtain a target vector $\textbf{\emph{x}}(t)$ as a function of time $t$ according to the constraint $d\textbf{\emph{x}}(t)/dt=\mathcal{M}\textbf{\emph{x}}(t)+\textbf{\emph{b}}$. We show that our algorithm exhibits an exponential speedup over its classical counterpart in certain circumstances. In addition, we demonstrate our quantum algorithm for a $4\times4$ linear differential equation using a 4-qubit nuclear magnetic resonance quantum information processor. Our algorithm provides a key technique for solving many important problems which rely on the solutions to linear differential equations., Comment: 12 pages, 5 figures, and all comments are welcome!