Quantum chemistry is a near-term application for quantum computers. This application may be facilitated by variational quantum-classical algorithms (VQCAs), although a concern for VQCAs is the large number of measurements needed for convergence, especially for chemical accuracy. Here we introduce a strategy for reducing the number of measurements (i.e., shots) by randomly sampling operators $h_i$ from the overall Hamiltonian $H = \sum_i c_i h_i$. In particular, we employ weighted sampling, which is important when the $c_i$'s are highly non-uniform, as is typical in chemistry. We integrate this strategy with an adaptive optimizer developed recently by our group to construct an improved optimizer called Rosalin (Random Operator Sampling for Adaptive Learning with Individual Number of shots). Rosalin implements stochastic gradient descent while adapting the shot noise for each partial derivative and randomly assigning the shots amongst the $h_i$ according to a weighted distribution. We implement this and other optimizers to find the ground states of molecules H$_2$, LiH, and BeH$_2$, without and with quantum hardware noise, and Rosalin outperforms other optimizers in most cases.
Variational hybrid quantum-classical algorithms (VHQCAs) have the potential to be useful in the era of near-term quantum computing. However, recently there has been concern regarding the number of measurements needed for convergence of VHQCAs. Here, we address this concern by investigating the classical optimizer in VHQCAs. We introduce a novel optimizer called individual Coupled Adaptive Number of Shots (iCANS). This adaptive optimizer frugally selects the number of measurements (i.e., number of shots) both for a given iteration and for a given partial derivative in a stochastic gradient desc…
Resource frugal optimizer for quantum machine learning
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Leiden University（莱顿大学）；Universidad Autónoma de Madrid（马德里自治大学）；University of Warsaw（华沙大学）；Normal Computing Corporation（诺默尔计算公司）
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…
Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this paper, we propose an iterative Layer VQE (L-VQE) approach, inspired by the Variational Quantum Eigensolver (VQE). We present a large-scale numerical study, simulating circuits with up to 40 qubits and 352 parameters, that demonstrates the potential of the proposed approach. We evaluate quantum optimization heuristics on the problem of detecting multiple communities in networks, for which …
Variational quantum algorithms, which have risen to prominence in the noisy intermediate-scale quantum setting, require the implementation of a stochastic optimizer on classical hardware. To date, most research has employed algorithms based on the stochastic gradient iteration as the stochastic classical optimizer. In this work we propose instead using stochastic optimization algorithms that yield stochastic processes emulating the dynamics of classical deterministic algorithms. This approach results in methods with theoretically superior worst-case iteration complexities, at the expense of gr…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of California, Berkeley（加州大学伯克利分校）；University of Waterloo（滑铁卢大学）
Variational Quantum Algorithms (VQAs) are a promising approach for practical applications like chemistry and materials science on near-term quantum computers as they typically reduce quantum resource requirements. However, in order to implement VQAs, an efficient classical optimization strategy is required. Here we present a new stochastic gradient descent method using an adaptive number of shots at each step, called the global Coupled Adaptive Number of Shots (gCANS) method, which improves on prior art in both the number of iterations as well as the number of shots required. These improvement…
A rigorous hybridization of variational quantum eigensolver with classical neural network
Seoul National University（首尔大学）；NextQuantum, Seoul National University（NextQuantum，首尔大学）；Automation and Systems Research Institute, Seoul National University（自动化与系统研究所，首尔大学）；Institute for Convergence Research and Education in Advanced Technology, Yonsei University（先进技术研究融合教育与研究所，延世大学）；Department of Quantum Information, Yonsei University（量子信息系，延世大学）
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is optimized to obtain the ground state energy. In our work, we investigate the variational Hamiltonian Ansatz (VHA), where the trial state is given by a non-interacting reference state modified by unitary rotations using generators that are part of the Hamiltonian describing the system. The lowest energy is obtained by optimizing the angles of those unitary ro…
Classical optimisation of reduced density matrix estimations with classical shadows using N-representability conditions under shot noise considerations
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 th…
We present the variational separability verifier (VSV), which is a novel variational quantum algorithm (VQA) that determines the closest separable state (CSS) of an arbitrary quantum state with respect to the Hilbert-Schmidt distance (HSD). We first assess the performance of the VSV by investigating the convergence of the optimization procedure for Greenberger-Horne-Zeilinger (GHZ) states of up to seven qubits, using both statevector and shot-based simulations. We also numerically determine the (CSS) of maximally entangled multipartite $X$-states ($X$-MEMS), and subsequently use the results of…
Hybrid quantum-classical embedding methods for correlated materials simulations provide a path towards potential quantum advantage. However, the required quantum resources arising from the multi-band nature of $d$ and $f$ electron materials remain largely unexplored. Here we compare the performance of different variational quantum eigensolvers in ground state preparation for interacting multi-orbital embedding impurity models, which is the computationally most demanding step in quantum embedding theories. Focusing on adaptive algorithms and models with 8 spin-orbitals, we show that state prepa…
Zero- Versus Infinite-Temperature Damping in Variational Quantum Circuits: Feature Scale, Sampling Cost, and Frame Gauge
Faculty of Electronics and Telecommunications, University of Science, Vietnam National University Ho Chi Minh City (VNU-HCM)（越南国家大学胡志明市科学大学电子与电信学院）；Identity Quantum Computing JSC（Identity量子计算股份公司）
From Barren Plateaus to SPSA Optimization in Variational Quantum Eigensolvers
Michigan Institute for Computational Discovery and Engineering, Department of Electrical Engineering and Computer Science and Department of Statistics, University of Michigan（密歇根大学计算发现与工程研究所、电气工程和计算机科学系以及统计学系）
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）
Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology（埃因霍温理工大学电子工程系信号处理系统组）；KCLIP lab, Center for Intelligent Information Processing Systems, Department of Engineering, King's College London（伦敦大学金史密斯学院工程系智能信息处理系统中心）
