Quantum networks are of high interest nowadays. In short, they describe the distribution of quantum sources represented by edges to different parties represented by nodes in the networks. Bundles of tools have been developed recently to characterize quantum states from the network in the ideal case. However, features of quantum networks in the noisy intermediate-scale quantum (NISQ) era invalidate most of them and call for feasible tools. By utilizing purity, covariance, and topology of quantum networks, we provide a systematic approach to tackle with arbitrary quantum networks in the NISQ era, which can be noisy, intermediate-scale, random, and sparse. One application of our method is to witness the progress of essential elements in quantum networks, like the quality of multipartite entangled sources and quantum memory.
We provide $poly\log$ sparse quantum codes for correcting the erasure channel arbitrarily close to the capacity. Specifically, we provide $[[n, k, d]]$ quantum stabilizer codes that correct for the erasure channel arbitrarily close to the capacity if the erasure probability is at least $0.33$, and with a generating set $\langle S_1, S_2, ... S_{n-k} \rangle$ such that $|S_i|\leq \log^{2+ζ}(n)$ for all $i$ and for any $ζ> 0$ with high probability. In this work we show that the result of Delfosse et al. is tight: one can construct capacity approaching codes with weight almost $O(1)$.
The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the …
Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already been performed. In this perspective, we discuss in a very broad sense what it means for an algorithm to be hybrid quantum-classical. We first explore this concept very directly, by building a definition based on previous work in abstraction/representation theory, arguing that what makes an algorithm hybrid is not directly how it is run (or how many classica…
In order to understand the bounds of utilization of the Grover's search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled by the IBM QISKit. We apply three forms of Grover's algorithms: (1) the standard one, with 4-10 qubits, (2) recently published modified Grover's algorithm, set to reduce the circuit depth, and (3) the algorithms in (1) and (2) with multi-control Toffoli's modified by addition of an ancilla qubit. Based on these simulations, we find the upper bound of noise …
Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness of quantum cryptographic protocols. In this work, we benchmark the performance of different QKD protocols on noisy quantum devices, with and without error correction. We obtain the secure key rates of BB84, B92 and BBM92 QKD protocols over a quantum channel that is subject to amplitude-damping noise. We demonstrate, theoretically and via implementations on t…
The progress in developing quantum hardware with functional quantum processors integrating tens of noisy qubits, together with the availability of near-term quantum algorithms has led to the release of the first quantum computers. These quantum computing systems already integrate different software and hardware components of the so-called "full-stack", bridging quantum applications to quantum devices. In this paper, we will provide an overview on current full-stack quantum computing systems. We will emphasize the need for tight co-design among adjacent layers as well as vertical cross-layer de…
We characterize the boundary of the convex compact set of absolutely separable states, referred as {\bf AS}, that cannot be transformed to entangled states by global unitary operators, in $2\otimes d$ Hilbert space. However, we show that the absolutely separable states of rank-$(2d-1)$ are extreme points of such sets. We then discuss conditions to examine if a given full-rank absolutely separable state is an interior point or a boundary point of {\bf AS}. Moreover, we construct two-qubit absolutely separable states which are boundary points but not extreme points of {\bf AS} and prove the exis…
Noisy intermediate-scale quantum (NISQ) devices offer unique platforms to test and evaluate the behavior of non-fault-tolerant quantum computing. However, validating programs on NISQ devices is difficult due to fluctuations in the underlying noise sources and other non-reproducible behaviors that generate computational errors. Efficient and effective methods for modeling NISQ behaviors are necessary to debug these devices and develop programming techniques that mitigate against errors. We present a test-driven approach to characterizing NISQ programs that manages the complexity of noisy circui…
Near-term quantum computation holds potential across multiple application domains. However, imperfect preparation and evolution of states due to algorithmic and experimental shortcomings, characteristic in the near-term implementation, would typically result in measurement outcomes deviating from the ideal setting. It is thus crucial for any near-term application to quantify and bound these output errors. We address this need by deriving robustness intervals which are guaranteed to contain the output in the ideal setting. The first type of interval is based on formulating robustness bounds as …
Random dynamics in isolated quantum systems is of practical use in quantum information and is of theoretical interest in fundamental physics. Despite a large number of theoretical studies, it has not been addressed how random dynamics can be verified from experimental data. In this paper, based on an information-theoretic formulation of random dynamics, i.e., unitary $t$-designs, we propose a method for verifying random dynamics from the data that is experimentally easy-to-access. More specifically, we use measurement probabilities estimated by a finite number of measurements of quantum states…
Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum reservoir computing is a relevant machine learning algorithm. Its simplicity of training and implementation allows to perform challenging computations on today available machines. In this Letter, we provide a criterion to select optimal quantum reservoirs, requiring few and simple gates. Our findings demonstrate that they render better results than other comm…
We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted Boltzmann machine. We demonstrate its practical use for state reconstruction, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. Intended for use on experimental noisy intermediate-scale quantum (NISQ) devices, we review recent efforts in reconstruct…
Characterizing quantum correlations and quantum teleportation in $gg \to t\bar{t}$ and $q\bar{q} \to t\bar{t}$ processes under noisy channels
Ibnou Zohr University（伊本·佐赫尔大学）；Mohammed V University in Rabat（拉巴特穆罕默德五世大学）；Princess Nourah bint Abdulrahman University（公主努拉·宾特·阿卜杜勒拉赫曼大学）；Umm Al-Qura University（乌姆古拉大学）；University of Bisha（比沙大学）
We study the problem of determining the photon number statistics of an unknown quantum state by simultaneously measuring conjugate quadratures with double homodyne detectors. Classically, the sum of the squared outputs of the two homodyne detectors is proportional to the intensity (thus the photon number) of the input light. Quantum mechanically, due to vacuum noise, the above photon number measurement is intrinsically noisy. We quantify the information gain in a single-shot measurement and discuss potential applications of this technology in quantum key distribution. We also show that the pho…
Noisy Intermediate-Scale Quantum (NISQ) hardware has unavoidable noises, and crosstalk error is a significant error source. When multiple quantum operations are executed simultaneously, the quantum state can be corrupted due to the crosstalk between gates during simultaneous operations, decreasing the circuit fidelity. In this work, we first report on several protocols for characterizing crosstalk. Then, we discuss different crosstalk mitigation methods from the hardware and software perspectives. Finally, we perform crosstalk injection experiments on the IBM quantum device and demonstrate the…
In the era of noisy-intermediate-scale quantum computers, we expect to see quantum devices with increasing numbers of qubits emerge in the foreseeable future. To practically run quantum programs, logical qubits have to be mapped to the physical qubits by a qubit allocation algorithm. However, on present day devices, qubits differ by their error rate and connectivity. Here, we establish and demonstrate on current experimental devices a new allocation algorithm that combines the simulated annealing method with local search of the solution space using Dijkstra's algorithm. Our algorithm takes int…
Prior entanglement between sender and receiver, which exactly doubles the classical capacity of a noiseless quantum channel, can increase the classical capacity of some noisy quantum channels by an arbitrarily large constant factor depending on the channel, relative to the best known classical capacity achievable without entanglement. The enhancement factor is greatest for very noisy channels, with positive classical capacity but zero quantum capacity. Although such quantum channels can be simulated classically, no violation of causality is implied, because the simulation requires at least as …
Effective methods for characterizing the noise in quantum computing devices are essential for programming and debugging circuit performance. Existing approaches vary in the information obtained as well as the amount of quantum and classical resources required, with more information generally requiring more resources. Here we benchmark the characterization methods of gate set tomography, Pauli channel noise reconstruction, and empirical direct characterization for developing models that describe noisy quantum circuit performance on a 27-qubit superconducting transmon device. We evaluate these m…
We investigate quantum coherences in the presence of noise by entangling the spin and path degrees of freedom of the output neutron beam from a noisy three-blade perfect crystal neutron interferometer. We find that in the presence of dephasing noise on the path degree of freedom the entanglement of the output state reduces to zero, however the quantum discord remains non-zero for all noise values. Hence even in the presence of strong phase noise non-classical correlations persist between the spin and path of the neutron beam. This indicates that measurements performed on the spin of the neutro…
Implementing a quantum algorithm on a NISQ device has several challenges that arise from the fact that such devices are noisy and have limited quantum resources. Thus, various factors contributing to the depth and width as well as to the noise of an implementation of an algorithm must be understood in order to assess whether an implementation will execute successfully on a given NISQ device. In this contribution, we discuss these factors and their impact on algorithm implementations. Especially, we will cover state preparation, oracle expansion, connectivity, circuit rewriting, and readout: th…
We present a method for characterizing the performance of noisy quantum processors using discrete time crystals. Deviations from ideal persistent oscillatory behavior give rise to numerical scores by which relative quantum processor capabilities can be measured. We construct small sets of qubit layouts that cover the full topology of a target system, and execute our metric over these sets on a wide range of IBM Quantum processors. We show that there is a large variability in scores, not only across multiple processors, but between different circuit layouts over individual devices. The stabilit…
Due to several physical limitations in the realisation of quantum hardware, today's quantum computers are qualified as Noisy Intermediate-Scale Quantum (NISQ) hardware. NISQ hardware is characterized by a small number of qubits (50 to a few hundred) and noisy operations. Moreover, current realisations of superconducting quantum chips do not have the ideal all-to-all connectivity between qubits but rather at most a nearest-neighbour connectivity. All these hardware restrictions add supplementary low-level requirements. They need to be addressed before submitting the quantum circuit to an actual…
First quantum computers very recently have demonstrated "quantum supremacy" or "quantum advantage": Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several "NISQ-era algorithms" are assumed to match the specifics of such computers; for instance, variation…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of probes or the probing energy). Typically, it scales as 1/N^(1/2). Quantum strategies may improve the precision, for noiseless processes, by an extra factor 1/N^(1/2). For noisy processes, it is not known in general if and when this improvement can be achieved. Here we propose a general framework for obtaining attainable and useful lower bounds for the ultima…
Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Shanghai Research Center for Quantum Sciences and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学上海量子科学研究中心及中科院量子信息与量子物理卓越创新中心）；Institut für Theoretische Physik and IQST, Universität Ulm（乌尔姆大学理论物理研究所和IQST）；Department of Physics, Indian Institute of Technology (BHU), Varanasi（瓦拉纳西印度理工学院（贝拿勒斯）物理系）
Lower bounds on bipartite entanglement in noisy graph states
James C. Wyant College of Optical Sciences, University of Arizona（亚利桑那大学詹姆斯·C·怀安特光学科学学院）；Cisco Quantum Lab（思科量子实验室）；College of Information and Computer Sciences, University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校信息与计算机科学学院）
We derive fundamental bounds on the maximal achievable precision in multiparameter noisy quantum metrology, valid under the most general entanglement-assisted adaptive strategy, which are tighter than the bounds obtained by a direct use of single-parameter results. This allows us to study the issue of the optimal probe incompatibility in the simultaneous estimation of multiple parameters in generic noisy channels, while so far the issue has been studied mostly in effectively noiseless scenarios (where the Heisenberg scaling is possible). We apply our results to the estimation of both unitary a…
Exploring Noisy Quantum Thermodynamical Processes via the Depolarizing-Channel Approximation
Technische Universität Wien（维也纳工业大学）；Vienna Center for Quantum Science and Technology (VCQ)（维也纳量子科学与技术中心）；University of Vienna（维也纳大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所跨学科理论与数学科学中心）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）
Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the protocol can efficiently simulate a large set of multi-qubit mixed states that are not mixtures of stabilizer states. The existence of these 'bound states' was previously only known for odd-dimensional systems like qutrits. The algorithm also has the favorable property that circuits with depolarizing noise are simulated much faster than unitary circuits. Th…
We are in the Noisy Intermediate-Scale Quantum (NISQ) devices' era, in which quantum hardware has become available for application in real-world problems. However, demonstrating the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the issue of train dispatching consequences caused by the arrival of an already delayed train to the network segment being considered. This problem is computationally hard and needs to be solved almost in real-time. We introduce a …
Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources, and thus nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise.…
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away --- we should regard it as a significant step toward the more powerful quantum technologi…
