A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We present a method to mitigate the depolarizing noise by first estimating its rate with a noise-estimation circuit and then correcting the output of the target circuit using the estimated rate. The method is experimentally validated on the simulation of the Heisenberg model. We find that our approach in combination with readout-error correction, randomized compiling, and zero-noise extrapolation produces results close to exact results even for circuits containing hundreds of CNOT gates.
We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small c…
Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. As a novel approach, quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations and may eventually outperform classical computers. However, current quantum devices still suffer from inherent quantum noise. In this work, we propose an error mitigation scheme suitable for parametric quantum circuits. This scheme is based on projecting a general quantum noise channel onto depolarization errors…
We show that quantum circuits cannot be made fault-tolerant against a depolarizing noise level of approximately 45%, thereby improving on a previous bound of 50% (due to Razborov). Our precise quantum circuit model enables perfect gates from the Clifford group (CNOT, Hadamard, S, X, Y, Z) and arbitrary additional one-qubit gates that are subject to that much depolarizing noise. We prove that this set of gates cannot be universal for arbitrary (even classical) computation, from which the upper bound on the noise threshold for fault-tolerant quantum computation follows.
Noise in quantum operations often negates the advantage of quantum computation. However, most classical simulations of quantum computers calculate the ideal probability amplitudes either storing full state vectors or using sophisticated tensor network contractions. Here, we investigate sampling-based classical simulation methods for noisy quantum circuits. Specifically, we characterize the simulation costs of two major schemes, stabilizer-state sampling of magic states and Heisenberg propagation, for quantum circuits being subject to stochastic Pauli noise, such as depolarizing and dephasing n…
A polynomial-time classical sampler for noisy quantum circuits from statistical mechanics
University of Maryland, College Park（马里兰大学帕克分校）；Electrical & Computer Engineering Department, UCLA（加州大学洛杉矶分校电气与计算机工程系）；Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气与计算机工程系）；QuEra Computing Inc.（QuEra计算公司）；Department of Physics, Stanford University（斯坦福大学物理系）
Amplitude amplification provides a quadratic speed-up for an array of quantum algorithms when run on a quantum machine perfectly isolated from its environment. However, the advantage is substantially diminished as the NISQ-era quantum machines lack the large number of qubits necessary to provide error correction. Noise in the computation grows with the number of gate counts in the circuit with each iteration of amplitude amplification. After a certain number of amplifications, the loss in accuracy from the gate noise starts to overshadow the gain in accuracy due to amplification, forming an in…
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…
Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic quantum processors subjected to noise. The first checkpoint for a fully operational QEC circuit is to create genuine multipartite entanglement across all subsystems of physical qubits. We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) that is efficient in the number of subsystems and, importantly, robust against experimental noise and imperfections. Specifically, we prove that the detection of entanglement in a linear nu…
Conventional computers have evolved to device components that demonstrate failure rates of 1e-17 or less, while current quantum computing devices typically exhibit error rates of 1e-2 or greater. This raises concerns about the reliability and reproducibility of the results obtained from quantum computers. The problem is highlighted by experimental observation that today's NISQ devices are inherently unstable. Remote quantum cloud servers typically do not provide users with the ability to calibrate the device themselves. Using inaccurate characterization data for error mitigation can have devas…
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general …
Limitations of Noisy Geometrically Local Quantum Circuits
University of Maryland（马里兰大学）；Joint Center for Quantum Information & Computer Science, University of Maryland and NIST（马里兰大学与美国国家标准与技术研究院联合量子信息与计算中心）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Complexity of tensor network simulation for noisy quantum circuits
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）；Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）；Department of Mathematics, Tsinghua University（清华大学数学系）
In this paper, we analyze the quantum counting under the decoherence, which can find the number of solutions satisfying a given oracle. We investigate probability distributions related to the first order term of the error rate on the quantum counting with the depolarizing channel. We also implement two circuits for the quantum counting -- the ascending-order circuit and the descending-order circuit -- by reversing ordering of application of controlled-Grover operations. By theoretical and numerical calculations for probability distributions, we reveal the difference of probability distribution…
Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm model to demonstrate quantum advantage, are simulated with depolarizing noise on experiment relevant two-dimensional architecture. With comprehensive numerical simulation and theoretical analysis, we find that the maximum achievable operator entanglement entropy, which indicates maximal simulation cost, has area law scaling with the system size for constant nois…
The Gottesman-Knill theorem allows for the efficient simulation of stabilizer-based quantum error-correction circuits. Errors in these circuits are commonly modeled as depolarizing channels by using Monte Carlo methods to insert Pauli gates randomly throughout the circuit. Although convenient, these channels are poor approximations of common, realistic channels like amplitude damping. Here we analyze a larger set of efficiently simulable error channels by allowing the random insertion of any one-qubit gate or measurement that can be efficiently simulated within the stabilizer formalism. Our ne…
Mitigating errors in state preparation and measurement with noncomputational states
IBM Quantum, IBM Research Europe – Zurich（IBM量子，IBM欧洲苏黎世研究部）；Laboratory of Theoretical Physics of Nanosystems, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院纳米系统理论物理实验室）；Theory and Simulation of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料理论与模拟）
Hardness and Complexity Transition of Noisy Random Circuit Sampling
NextQuantum Center, Department of Physics and Astronomy, Seoul National University（首尔大学物理与天文学系 NextQuantum 中心）；Department of Physics, Korea Advanced Institute of Science and Technology（韩国科学技术院物理系）
Quantum computers offer the possibility to implement lattice gauge theory in Minkowski rather than Euclidean spacetime, thus allowing calculations of processes that evolve in real time. In this work, calculations within SU(2) pure gauge theory are able to show the motion of an excitation traveling across a spatial lattice in real time. This is accomplished by using a simple yet powerful method for error mitigation, where the original circuit is used both forward and backward in time. For a two-plaquette lattice, meaningful results are obtained from a circuit containing hundreds of CNOT gates. …
Distributions of Noisy Expectation Values over Sets of Measurement Operators
Department of Physics & Astronomy, University of Waterloo（滑铁卢大学物理与天文系）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily studies of quantum memory[1, 2], an important first step towards quantum computation, where the objective is to increase the lifetime of the encoded quantum information. Additionally, several works have explored the implementation of logical gates[3-5]. In this work we study a next step - fault-tolerantly implementing quantum circuits. We choose the $[[4, 1, 2]]$…
Pilot-Wave Simulator: Exact Classical Sampling from Ideal and Noisy Quantum Circuits up to Hundreds of Qubits
Lomonosov Moscow State University（莫斯科国立大学）；University of Science and Technology of China（中国科学技术大学）；Peking University（北京大学）；Southern University of Science and Technology（南方科技大学）
Nonstabilizerness and Error Resilience in Noisy Quantum Circuits
University of Augsburg（奥格斯堡大学）；Joint Center for Quantum Information and Computer Science, NIST and University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院和马里兰大学）
Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called classical-quantum hybrid variational algorithms. Here we develop a low-depth quantum algorithm to generative neural networks using variational quantum circuits. We introduce a method which employs the quantum approximate optimization algorithm as a subroutine in order produce then sample low-energy distributions of Ising Hamiltonians. We sample these states to train neur…
We prove new upper bounds on the tolerable level of noise in a quantum circuit. We consider circuits consisting of unitary k-qubit gates each of whose input wires is subject to depolarizing noise of strength p, as well as arbitrary one-qubit gates that are essentially noise-free. We assume that the output of the circuit is the result of measuring some designated qubit in the final state. Our main result is that for p>1-Θ(1/\sqrt{k}), the output of any such circuit of large enough depth is essentially independent of its input, thereby making the circuit useless. For the important special case o…
Mitigating errors by quantum verification and post-selection
School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；Quandela SAS（Quandela公司）；Laboratoire d’Informatique de Paris 6, Centre National de la Recherche Scientifique, Sorbonne Université（巴黎第六大学计算机实验室，法国国家科学研究中心，索邦大学）
To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data. We highlight the effectiveness of our mitigation via two examples of recent interest in quantum many-body physics: entanglement measurements and real time dynamics of confinement in quantum spi…
A major problem in exploiting microscopic systems for developing a new technology based on the principles of Quantum Information is the influence of noise which tends to work against the quantum features of such systems. It becomes then crucial to understand how noise affects the evolution of quantum circuits: several techniques have been proposed among which stochastic differential equations (SDEs) can represent a very convenient tool. We show how SDEs naturally map any Markovian noise into a linear operator, which we will call a noise gate, acting on the wave function describing the state of…
