Rafael Chaves, Fernando de Melo
A scheme to evaluate computation fidelities within the one-way model is developed and explored to understand the role of correlations in the quality of noisy quantum computations. The formalism is promptly applied to many computation instances, and unveils that a higher amount of entanglement in the noisy resource state does not necessarily imply a better computation.
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A discussion on the robustness of continuous-variable entangled states under noisy environment is briefly given in direct relation to Phys. Rev. Lett. 105, 100503 (2010).
In this paper, we show how to use low-fidelity operations to control the dynamics of quantum systems. Noisy operations usually drive a system to evolve into a mixed state and damage the coherence. Sometimes frequent noisy operations result in the coherent evolution of a subsystem, and the dynamics of the subsystem is controlled by tuning noisy operations. Based on this, we find that universal quantum computation can be carried out by low-fidelity (fidelity $<90\%$) operations.
Quantum work extraction efficiency for noisy quantum batteries: the role of coherence
本文建立了量子功容量与最大渐近功/能量比的直接联系，分析了自放电、热化和退相干等噪声模型，发现输入量子相干性可显著提升含噪量子电池的存储性能。
We address the degradation of continuous variable (CV) entanglement in a noisy channel focusing on the set of photon-number entangled states. We exploit several separability criteria and compare the resulting separation times with the value of non-Gaussianity at any time, thus showing that in the low-temperature regime: i) non-Gaussianity is a bound for the relative entropy of entanglement and ii) Simon' criterion provides a reliable estimate of the separation time also for nonGaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust …
Work extraction processes from noisy quantum batteries: the role of non local resources
本研究揭示了在量子电池功提取中，非局域恢复操作比非局域纠缠态更能有效减轻噪声影响，从而提升功的提取量。
Noisy computation and reversible computation have been studied separately, and it is known that they are as powerful as unrestricted computation. We study the case where both noise and reversibility are combined and show that the combined model is weaker than unrestricted computation. In our noisy reversible circuits, each wire is flipped with probability p each time step, and all the inputs to the circuit are present in time 0. We prove that any noisy reversible circuit must have size exponential in its depth in order to compute a function with high probability. This is tight as we show that …
We examine the adiabatic dynamics of a quantum system coupled to a noisy classical control field. A stochastic phase shift is shown to arise in the off-diagonal elements of the system's density matrix which can cause decoherence. We derive the condition for onset of decoherence, and identify the noise properties that drive decoherence. We show how this decoherence mechansim causes: (1) a dephasing of the observable consequences of the adiabatic geometric phase; and (2) the loss of computational efficiency of the Shor algorithm when run on a sufficiently noisy geometric quantum computer.
With the development of delegated quantum computation, clients will want to ensure confidentiality of their data and algorithms, and the integrity of their computations. While protocols for blind and verifiable quantum computation exist, they suffer from high overheads and from over-sensitivity: When running on noisy devices, imperfections trigger the same detection mechanisms as malicious attacks, resulting in perpetually aborted computations. We introduce the first blind and verifiable protocol for delegating BQP computations to a powerful server with repetition as the only overhead. It is c…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly. Here, we develop a tensor network formalism to simulate the time-dynamics and the Fourier spectrum of noisy quantum circuits. We prove that under general conditions most of the quantum circuits at any constant level of noise per gate can be efficiently simulated classically with the cost increasing only polynomially with the size of the circuits. The result…
In a recent work (Allegra et al, Phys. Rev. Lett. 105, 100503, 2010) we addressed the evolution of photon-number entangled states in noisy Gaussian channels. Upon exploiting several non equivalent separability criteria we found evidence that entanglement of Gaussian PNES survives longer, and thus we drew a conjecture about the generality of this result. In their Comment to our work, Lee et al. use an additional entanglement criterion (NDPT) which allows them to show some counterexamples to our conjecture, i.e., nonGaussian states whose entanglement survives longer. In this reply, we argue that…
Limitations of Noisy Quantum Devices in Computational and Entangling Power
研究噪声量子设备在无纠错情况下的计算和纠缠能力限制，发现深度超过Ω(log(n))时，n量子比特设备与随机硬币无法区分，且多项式时间算法无计算优势。
Quantum computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum computation face technical challenges due to the noise and errors that arise from imperfect implementation of the technology. Here, we frame the concepts of computational accuracy, result reproducibility, device reliability and program stability in the context of quantum computation. We provide intuitive definitions for these concepts in the context of quantu…
Quantum correlations as the resource for quantum communication can be distributed over long distances by quantum repeaters. In this Letter, we introduce the notion of a noisy quantum repeater, and examine its role in quantum communication. Quantum correlations shared through noisy quantum repeaters are then characterized and their secrecy properties are studied. Remarkably, noisy quantum repeaters naturally introduce private states in the key distillation scenario, and consequently key distillation protocols are demonstrated to be more tolerant.
Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langleψ_t|\hatρ_{\rm out}|ψ_t\rangle$ between an actual $n$-qubit output state $\hatρ_{\rm …
The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground truth obtained by conventional means. We implement several different types of ansatz circuits derived from unitary coupled cluster theory for the purposes of estimating the ground-state energy of So…
Quantum computational advantage of noisy boson sampling with partially distinguishable photons
本文研究部分可区分光子噪声对 boson sampling 经典不可解性的影响，证明平均 O(log N) 个可区分光子仍保持理想复杂度，为含噪实验实现量子计算优越性提供理论依据。
Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the inherent fragile nature of the physical computing elements, qubits, achieving quantum advantages over classical computation requires extremely low error rates for qubit operations as well as a significant overhead of physical qubits, in order to realize fault-tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of…
NRQNN: The Role of Observable Selection in Noise-Resilient Quantum Neural Networks
本文研究噪声环境下量子神经网络训练难题，提出通过精心选择测量可观测量（如自定义厄米算子）增强抗噪性，避免贫瘠高原，提升至10量子比特的可训练性。
The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time complexities has recently been proposed. However, the algorithm requires a large number of samples to be loaded in a highly entangled state and it is unclear whether such a precondition on the quantum speedup can be obtained efficiently. Here, we present a complete analysis of the quantum solvability of the NBLP by considering the entire algorithm process, name…
We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a quantum network. The complexity associated with the generation of multiparticle entangled states is quantified in terms of the concept of global cost. This parameter allows us to compare the use of physical resources in different schemes. We show that for ideal channels and for a sufficiently large number of nodes, the use of maximally entangled states is advantageous over uncorrelated ones. For noisy channels, one has to use entanglement purification procedures in order to create entang…
Tremendous efforts have been paid for realization of fault-tolerant quantum computation so far. However, preexisting fault-tolerant schemes assume that a lot of qubits live together in a single quantum system, which is incompatible with actual situations of experiment. Here we propose a novel architecture for practically scalable quantum computation, where quantum computation is distributed over small-size (four-qubit) local systems, which are connected by quantum channels. We show that the proposed architecture works even with the error probability 0.1% of local operations, which breaks throu…
Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy quantum computers can provide computational advantage over classical computers. Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device. In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via m…
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state $ρ$, which should be regarded as a parameter of the model. Our goal is to determine for which $ρ$ universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of $ρ$ and produce a single output qubit with higher polarization. The protocols allow one to …
In theory, quantum computers can efficiently simulate quantum physics, factor large numbers and estimate integrals, thus solving otherwise intractable computational problems. In practice, quantum computers must operate with noisy devices called ``gates'' that tend to destroy the fragile quantum states needed for computation. The goal of fault-tolerant quantum computing is to compute accurately even when gates have a high probability of error each time they are used. Here we give evidence that accurate quantum computing is possible with error probabilities above 3% per gate, which is significan…
We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender's share of the noisy entanglement plays the role of mutual information in the completely classical case. A consequence of our results is that bound entangled states cannot increase the capacity of a noiseless quantum channel.
It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation above the boundary, we…
Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments
本文提出基于有效线路体积的统一框架，解释含噪量子实验中可观测量信噪比与经典计算成本的权衡，并在随机线路采样、量子信息置乱和Floquet实验上验证，实现单GPU每点不到一秒复现结果。
Enhancing classical simulation with noisy quantum devices
利用噪声量子设备提升经典模拟效率，通过学习噪声下的电路表示来减少采样成本。
Characterizing noisy quantum computation with imperfectly addressed errors
本文提出基于随机超算符系综和矩阵Chernoff集中的理论框架，表征不完全寻址噪声对量子误差校正与缓解的影响，并用于诊断噪声量子计算机输出的可信度。
We reformulate the information causality in a more general framework by adopting the results of signal propagation and computation in a noisy circuit. In our framework, the information causality leads to a broad class of Tsirelson inequalities. This fact allows us to subject information causality to experimental scrutiny. A no-go theorem for reliable nonlocal computation is also derived. Information causality prevents any physical circuit from performing reliable computations.
We consider the realization of universal quantum computation through braiding of Majorana fermions supplemented by unprotected preparation of noisy ancillae. It has been shown by Bravyi [Phys. Rev. A 73, 042313 (2006)] that under the assumption of perfect braiding operations, universal quantum computation is possible if the noise rate on a particular 4-fermion ancilla is below 40%. We show that beyond a noise rate of 89% on this ancilla the quantum computation can be efficiently simulated classically: we explicitly show that the noisy ancilla is a convex mixture of Gaussian fermionic states in…
We report the results of an in-depth study of the role of graph topology on quantum transport efficiency in random removal and Watts-Strogatz networks. By using four different environmental models -- noiseless, driving by classical random telegraph noise (RTN), thermal quantum bath, and bath+RTN -- we compare the role of the environment and of the change in network topology in determining the quantum transport efficiency. We find that small and specific changes in network topology is more effective in causing large change in efficiency compared to that achievable by environmental manipulations…
Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the unavoidable influence of noise. Here we obtain a quantum limit for the uncertainty in the estimation of a resonant classical force acting on a noisy quantum-mechanical oscillator. We determine the best initial state of the oscillator and the best measurement procedure, thus getting a rigorous and useful benchmark for experiments aiming to detect extremely small…
Error-tolerant oblivious transfer in the noisy-storage model
本文利用熵不确定性关系，推导了在可信与不可信噪声并存下oblivious transfer安全性的紧致界限，解决了实验设备噪声可能被作弊者利用的安全隐患。
The reliability of logical operations is indispensable for the reliable operation of computational systems. Since the down-sizing of micro-fabrication generates non-negligible noise in these systems, a new approach for designing noise-immune gates is required. In this paper, we demonstrate that noise-immune gates can be designed by combining Bayesian inference theory with the idea of computation over a noisy signal. To reveal their practical advantages, the performance of these gates is evaluated in comparison with a stochastic resonance-based gate proposed previously. This approach for comput…
Gyroscope for rotation sensing plays a key role in inertial navigation systems. Developing more precise gyroscopes than the conventional ones bounded by classical shot-noise limit by using quantum resources has attracted much attention. However, existing quantum gyroscope schemes suffer severe deterioration under the influence of decoherence, which is called the no-go theorem of noisy metrology. Here, by using two quantized optical fields as quantum probe, we propose a quantum gyroscope scheme breaking through the constraint of the no-go theorem. Our exact analysis of the non-Markovian noise r…
Routing plays an important role in programming noisy, intermediate-scale quantum (NISQ) devices, where limited connectivity in the register is overcome by swapping quantum information between locations. However, routing a quantum state using noisy gates introduces non-trivial noise dynamics, and deciding on an optimal route to minimize accumulated error requires estimates of the expected state fidelity. Here we validate a model for state-dependent routing dynamics in a NISQ processor based on correlated binary noise. We develop a composable, state-dependent noise model for CNOT and SWAP operat…
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 class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in the presence of physically motivated constraints. First, we show that there is a family of sparse IQP circuits that can be implemented on a square lattice of n qubits in depth O(sqrt(n) log n), and which is likely hard to simulate classically. Next, we show that, if an arbitrarily small constant amount of noise is applied to each qubit at the end of any IQP ci…
Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set of samples, a hidden vector or structure involved in $\mathbf{b}$ is obtained by solving a noise-corrupted linear equation $\hat{A}\mathbf{x} \approx \mathbf{b} + \boldsymbolη$, where $\boldsymbolη$ is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, whe…
Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two non-classical features of the coherent information are demonstrated: the failure of subadditivity, and the fail…
Procrustes Tomography -- reconstructing noisy quantum channels made easy
研究针对量子设备表征中昂贵的量子过程层析成像问题，提出普罗克汝斯忒斯层析成像方法，该方法在多方面优于现有方法，并通过有噪声量子信道典型示例展示了其效用。
Dynamical decoupling (DD) refers to a well-established family of methods for error mitigation, comprising pulse sequences aimed at averaging away slowly evolving noise in quantum systems. Here, we revisit the question of its efficacy in the presence of noisy pulses in scenarios important for quantum devices today: pulses with gate control errors, and the computational setting where DD is used to reduce noise in every computational gate. We focus on the well-known schemes of periodic (or universal) DD, and its extension, concatenated DD, for scaling up its power. The qualitative conclusions fro…
As a promising candidate for exhibiting quantum computational supremacy, Gaussian Boson Sampling (GBS) is designed to exploit the ease of experimental preparation of Gaussian states. However, sufficiently large and inevitable experimental noise might render GBS classically simulable. In this work, we formalize this intuition by establishing a sufficient condition for approximate polynomial-time classical simulation of noisy GBS --- in the form of an inequality between the input squeezing parameter, the overall transmission rate and the quality of photon detectors. Our result serves as a non-cl…
Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two- and single-qubit gates. In practical applications, however, a quantum gate prepared as a unitary transformation may appear as a noisy channel and consequently may inhibit quantum advantages. In this work, we apply the scheme of channel discrimination to detect if a quantum gate that is actually realized is unitary or noisy. We show that a two-qubit unitary transformation and its noisy counterpart can be optimally discriminated…
Quantum metrology overcomes standard precision limits and plays a central role in science and technology. Practically it is vulnerable to imperfections such as decoherence. Here, we demonstrate quantum metrology for noisy channels such that entanglement with ancillary qubits enhances the quantum Fisher information for phase estimation but not otherwise. Our photonic experiment covers a range of noise for various types of channels, including for two randomly alternating channels such that assisted entanglement fails for each noisy channel individually. We have simulated noisy channels by implem…
Quantum information processing exploits all the features quantum mechanics offers. Among them there is the possibility to induce nonlinear maps on a quantum system by involving two or more identical copies of the given system in the same state. Such maps play a central role in distillation protocols used for quantum key distribution. We determine that such protocols may exhibit sensitive, quasi-chaotic evolution not only for pure initial states but also for mixed states, i.e. the complex dynamical behavior is not destroyed by small initial uncertainty. We show that the appearance of sensitive,…
Verification of entangled states under noisy measurements
本研究提出了一种在噪声测量下验证纠缠态的算法，通过分析噪声对验证效率的影响，提供了一种有效的方法来唯一确定目标态。
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…
This is an introduction to software methods of quantum fault tolerance. Broadly speaking, these methods describe strategies for using the noisy hardware components of a quantum computer to perform computations while continually monitoring and actively correcting the hardware faults. We discuss parallels and differences with similar methods for ordinary digital computation, we discuss some of the noise models used in designing and analyzing noisy quantum circuits, and we sketch the logic of some of the central results in this area of research.
In this work, a novel protocol is proposed for bidirectional controlled quantum teleportation (BCQT) in which a quantum channel is used with the eight-qubit entangled state. Using the protocol, two users can teleport an arbitrary entangled state and a pure two-qubit state (QBS) to each other simultaneously under the permission of a third party in the role of controller. This protocol is based on the controlled-not operation, appropriate single-qubit (SIQ) UOs and SIQ measurements in the Z and X-basis. Reduction of the predictability of the controller's qubit (QB) by the eavesdropper and also, …
Synergy between noisy quantum computers and scalable classical deep learning
本文提出将噪声量子计算机与经典卷积神经网络相结合，利用含噪期望值和电路结构信息预测量子伊辛模型Trotter电路的精确期望值，在经典方法失败时仍有效并优于零噪声外推，展示了量子-经典协同提升计算精度的优势。
Useful entanglement can be extracted from noisy graph states
通过设计线性图结构，以最小的物理量子比特开销从噪声图状态中提取稳健的纠缠，为基于测量的量子计算中的噪声减少提供数学框架。
The universal quantum computation model based on quantum walk by Childs has opened the door for a new way of studying the limitations and advantages of quantum computation, as well as for its intermediate-term simulation. In recent years, the growing interest in noisy intermediate-scale quantum computers (NISQ) has lead to intense efforts being directed at understanding the computational advantages of open quantum systems. In this work, we extend the quantum walk model to open noisy systems in order to provide such a tool for the study of NISQ computers. Our method does not use explicit purifi…
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 …
Post-processing noisy quantum computations utilizing N-representability constraints
本文提出利用 1/2-RDM 的 N-可表示性约束及多扇区投影后处理含噪量子化学计算，显著降低能量误差与测量方差。
Accelerating Simulation of Quantum Circuits under Noise via Computational Reuse
针对含噪声量子电路模拟因多次迭代产生的高开销问题，提出基于树的TQSim技术，通过动态划分子电路复用中间结果，实现最高3.89倍加速，且适配多节点并保障保真度。
Currently available noisy intermediate-scale quantum (NISQ) devices are limited by the number of qubits that can be used for quantum chemistry calculations on molecules. We show herein that the number of qubits required for simulations on a quantum computer can be reduced by limiting the number of orbitals in the active space. Thus, we have utilized ansätze that approximate exact classical matrix eigenvalue decomposition methods (Full Configuration Interaction). Such methods are appropriate for computations with the Variational Quantum Eigensolver algorithm to perform computational investigati…
Non-zero noise extrapolation: accurately simulating noisy quantum circuits with tensor networks
针对高保真纠缠电路在低噪声区间难以用张量网络精确模拟的问题，本文提出非零噪声外推方法，通过添加噪声改善可模拟性并外推回目标区间。
Directly estimating the fidelity of measurement-based quantum computation
本文研究了基于测量的量子计算中噪声对保真度的影响，推导出输出态保真度与关联函数的关系，并提出直接估计平均保真度的方法。
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