Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits need to be executed for sufficiently reducing shot-noise. We consider metric-aware quantum algorithms: variational algorithms that use a quantum computer to efficiently estimate both a matrix and a vector object. For example, the recently introduced quantum natural gradient approach uses the quantum Fisher information matrix as a metric tensor to correct the gradient vector for the co-dependence of the circuit parameters. We rigorously characterise and upper bound the number of measurements required to determine an iteration step to a fixed precision, and propose a general approach for optimally distributing samples between matrix and vector entries. Finally, we establish that the number of circuit repetitions needed for estimating the quantum Fisher information matrix is asymptotically negligible for an increasing number of iterations and qubits.
Late Breaking Results: Hardware-Aware Compilation Reshapes Trainability in Variational Quantum Circuits
eBRAIN Lab, Division of Engineering, New York University (NYU) Abu Dhabi（纽约大学阿布扎比分校工程学院）；Center for Quantum and Topological Systems, NYUAD Research Institute, NYU Abu Dhabi（纽约大学阿布扎比分校研究学院量子与拓扑系统中心）
Beyond Logical Circuits: Hardware-Aware Analysis of Expressibility and Trainability in Variational Quantum Algorithms
Division of Engineering, New York University Abu Dhabi (NYUAD)（纽约大学阿布扎比分校工程学院）；Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD（纽约大学阿布扎比分校研究院量子与拓扑系统中心）
Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide the quantum system to a target state that minimizes a cost function, by varying certain parameters in a quantum circuit. This paper proposes a new approach for engineering cost functions to improve the performance of a certain class of these variational algorithms on today's small qubit systems. We apply this approach to a variational algorithm that generates thermofield double states of the transv…
Exact gradient for general cost functions in variational quantum algorithms
Graduate School of Information Science, Tohoku University（东北大学情报科学研究生院）；Frontier Research Institute for Interdisciplinary Sciences, Tohoku University（东北大学跨学科前沿科学研究机构）；Department of Applied Physics, Graduate School of Engineering, Tohoku University（东北大学工程学院应用物理系）
Efficient classical optimizers are crucial in practical implementations of Variational Quantum Algorithms (VQAs). In particular, to make Stochastic Gradient Descent (SGD) resource efficient, adaptive strategies have been proposed to determine the number of measurement shots used to estimate the gradient. However, existing strategies overlook the overhead that occurs in each iteration. In terms of wall-clock runtime, significant circuit-switching and communication latency can slow the optimization process when using a large number of iterations. In terms of economic cost when using cloud servic…
In the context of variational compiling of a continuous-variable (CV) unitary operation, the architecture and parameter space of the Xanadu X8 processor constrain both the set of feasible compiling problems and the allowed cost functions. In this paper, we motivate a faithful cost function for variational compiling of a two-mode, continuous-variable beamsplitter gate with real matrix elements (i.e., a "zero-phase" beamsplitter) that complies with the constraints of the X8 processor. This cost function is then computed on the X8. Despite the noise in the processor, we find that the cost functio…
Variational Quantum Eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule by performing separate measurements of $O(N^4)$ terms. Several recent papers observed that this scaling may be reducible to $O(N^3)$ by partitioning the terms into linear-sized commuting families that can be measured simultaneously. We confirm these empirical observations by studying the MIN-COMMUTING-PARTITION problem at the level of the fermionic Hamiltonian and its encoding into qubits. Moreover, we provide a fast, pre-computable pro…
Hamiltonian-Aware ADAPT Variational Quantum Eigensolver for Molecular Ground-State Simulation
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；East China Normal University（华东师范大学）；MindSpore Quantum Special Interest Group（MindSpore量子特别兴趣组）；Arclight Quantum Co., LTD. Chinese Academy of Sciences（中科院光量子科技有限公司）
We propose a variational quantum attack algorithm (VQAA) for classical AES-like symmetric cryptography, as exemplified the simplified-data encryption standard (S-DES). In the VQAA, the known ciphertext is encoded as the ground state of a Hamiltonian that is constructed through a regular graph, and the ground state can be found using a variational approach. We designed the ansatz and cost function for the S-DES's variational quantum attack. It is surprising that sometimes the VQAA is even faster than Grove's algorithm as demonstrated by our simulation results. The relationships of the entanglem…
Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost evaluation), and a classical computer uses this information to adjust the parameters of the gate sequence. Here we present such an algorithm for quantum state diagonalization. State diagonalization has applications in condensed matter physics (e.g., entanglement spectroscopy) as well as in machine learning (e.g., principal component analysis). For a quantum stat…
Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a problem-dependent cost function. Although such algorithms are powerful in principle, the non-convexity of the associated cost landscapes and the prevalence of local minima means that local optimization methods such as gradient descent typically fail to reach good solutions. In this work we suggest a method to improve gradient-based approaches to variational quantum circ…
Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition, variations of these VQAs are also adapted to perform other useful functions such as quantum state learning and approximate fractional inverses. The common theme shared by the proposed algorithms is that their cost functions are all based on minimizing the quantum purity of a quantum state. Strategies to mitigate or avoid the problem of exponentially vanishing c…
Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE) -- an algorithm to calculate the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE, and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact …
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in sufficiently expressive parametrized quantum circuits. It has been established that the onset of a barren plateau regime depends on the cost function, although the particular behavior has been demonstrated only for certain classes of cost functions. Here we derive a lower bound on the variance of the gradient, which depends mainly on the width of the circuit …
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the algorithm increases. Previous work cannot handle the gradient vanishing induced by the inevitable noise effects on realistic quantum hardware. In this paper, we propose a novel training scheme to mitigate such noise-induced gradient vanishing. We first introduce a new cost function of which the gradients are significantly augmented by employing traceless observ…
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the algorithm increases. Previous work cannot handle the gradient vanishing induced by the inevitable noise effects on realistic quantum hardware. In this paper, we propose a novel training scheme to mitigate such noise-induced gradient vanishing. We first introduce a new cost function of which the gradients are significantly augmented by employing traceless observ…
Variational Quantum Algorithms (VQA) are promising to demonstrate quantum advantages on near-term devices. Designing ansatz, a variational circuit with parameterized gates, is of paramount importance for VQA as it lays the foundation for parameter optimizations. Due to the large noise on Noisy-Intermediate Scale Quantum (NISQ) machines, considering circuit size and real device noise in the ansatz design process is necessary. Unfortunately, recent works on ansatz design either consider no noise impact or only treat the real device as a black box with no specific noise information. In this work,…
Adaptive Observation Cost Control for Variational Quantum Eigensolvers
Berlin Institute for the Foundations of Learning and Data (BIFOLD)（柏林学习与数据基础研究所（BIFOLD））；University of Bonn（波恩大学）；Helmholtz Institute for Radiation and Nuclear Physics (HISKP)（亥姆霍兹辐射与核物理研究所（HISKP））；RIKEN Center for AIP（日本理化学研究所先进智能项目中心）
We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed tensor network $\mathcal{T}$, we prove that if the environment of a single tensor from the network can be evaluated with computational cost $κ$, then the environment of any other tensor from $\mathcal{T}$ can be evaluated with identical cost $κ$. Moreover, we describe how the set of all single tensor environments from $\mathcal{T}$ can be simultaneously evaluat…
RobustState: Boosting Fidelity of Quantum State Preparation via Noise-Aware Variational Training
MIT（麻省理工学院）；CMU（卡内基梅隆大学）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；University of Notre Dame（圣母大学）；Purdue University（普渡大学）；Yale University（耶鲁大学）；University of Chicago（芝加哥大学）
Optimizing resource allocation for accuracy in noisy variational quantum algorithms
MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Laboratory（MajuLab，CNRS-UCA-SU-NUS-NTU国际联合研究实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；CPHT, CNRS, École Polytechnique, IP Paris（法国国家科学研究中心高等物理与化学中心，巴黎综合理工学院，巴黎理工学院）；Eviden Quantum Laboratory（Eviden量子实验室）；Université Grenoble Alpes, CNRS, LPMMC（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，LPMMC）
