A variational quantum algorithm for Hamiltonian diagonalization

Zeng, Jinfeng; Cao, Chenfeng; Zhang, Chao; Xu, Pengxiang; Zeng, Bei

doi:10.1088/2058-9565/ac11a7

Cited by 13 publications

(8 citation statements)

References 39 publications

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“…Here the key criterion for comparison is practicality because this flexible approach leaves open the possibility that a compressed circuit will be found. Variational circuits can be readily applied in near-term [50,51] but it has been shown that the task of finding the right circuit is computationally demanding [52,53] if system sizes increase.…”

Section: Relation To Prior Work and Open Questionsmentioning

confidence: 99%

Double-bracket flow quantum algorithm for diagonalization

Gluza¹

2022

Preprint

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A quantum algorithm for preparing eigenstates of quantum systems is presented which makes use of only forward and backward evolutions under a prescribed Hamiltonian and phase flips. It is based on the Głazek-Wilson-Wegner flow method from condensed-matter physics or more generally double-bracket flows considered in dynamical systems. The phase flips are used to implement a dephasing of offdiagonal interaction terms and evolution reversal is employed for the quantum computer to approximate the group commutator needed for unitary propagation under the double-bracket generator of the diagonalizing flow. The presented algorithm is recursive and involves no qubit overheads. Its efficacy for near-term quantum devices is discussed using numerical examples. In particular, variational doublebracket flow generators, optimized flow step durations and heuristics for pinching via efficient unitary mixing approximations are considered. More broadly, this work opens a pathway for constructing purposeful quantum algorithms based on double-bracket flows also for tasks different from diagonalization and thus enlarges the quantum computing toolkit geared towards practical physics problems.Studying quantum many-body systems is an area where quantum computing may lead to practical advances outside the scope of what we can compute numerically. We often gain physics understanding by analyzing eigenstates and eigenvalues of quantum models so quantum algorithms for diagonalization could be key for achieving new insights. While looking into the past does not always inform accurately how to proceed into the future, it seems that three characteristics of numerical algorithms may continue being relevant. Firstly, the best-performing diagonalization algorithms use iterative schemes [1]. Secondly, they involve operations which come naturally to a classical architecture [2]. Finally, the diagonalization is the fixed-point of the iteration [3].Typical numerical diagonalization iterations involve powers of the input matrix [1]. This is an issue for quantum computers which support composing unitary evolutions governed by prescribed Hermitian matrices more naturally than multiplying or adding

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Section: Relation To Prior Work and Open Questionsmentioning

confidence: 99%

Double-bracket flow quantum algorithm for diagonalization

Gluza¹

2022

Preprint

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“…it diagonalizes a quantum state. It has several applications, including quantum state fidelity estimation [2], device certification [3], Hamiltonian diagonalization [4], and as a method to extract entanglement properties of a system [1,5]. VQSD generalizes the well-studied problem of quantum state preparation, which can be understood as quantum state tomography for pure states 7 .…”

Section: Introductionmentioning

confidence: 99%

Enhancing variational quantum state diagonalization using reinforcement learning techniques

Kundu,

Bedełek,

Ostaszewski

et al. 2024

New J. Phys.

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The variational quantum algorithms are crucial for the application of NISQ computers. Such algorithms require short quantum circuits, which are more amenable to implementation on near-term hardware, and many such methods have been developed. One of particular interest is the so-called variational quantum state diagonalization method, which constitutes an important algorithmic subroutine and can be used directly to work with data encoded in quantum states. In particular, it can be applied to discern the features of quantum states, such as entanglement properties of a system, or in quantum machine learning algorithms. In this work, we tackle the problem of designing a very shallow quantum circuit, required in the quantum state diagonalization task, by utilizing reinforcement learning (RL). We use a novel encoding method for the RL-state, a dense reward function, and an $\epsilon$-greedy policy to achieve this. We demonstrate that the circuits proposed by the reinforcement learning methods are shallower than the standard variational quantum state diagonalization algorithm and thus can be used in situations where hardware capabilities limit the depth of quantum circuits. The methods we propose in the paper can be readily adapted to address a wide range of variational quantum algorithms.

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“…To be specific, VQAs adopt the classical computers to find the optimal parameters of the objective function, and quantum devices mainly compute the values of function by training the neural networks and performing measurements. In recent years, a variety VQAs have been proposed such as variational eigenvalue solver [10][11][12][13][14], variational quantum singular value decomposition [15,16], variational quantum diagonalization [17,18], quantum approximate optimization algorithms [19], variational ansatzbased quantum simulation [20], and quantum linear equations solver [21,22]; see, e.g. [8,9] for comprehensive surveys.…”

Section: Introductionmentioning

confidence: 99%

Variational quantum algorithms for trace norms and their applications

Li¹,

Liang²,

Shen³

et al. 2021

Commun. Theor. Phys.

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The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today's noisy intermediate scale quantum (NISQ) devices is a crucial task for information processing. In this paper, we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different situations. Compared with the previous methods, our means greatly reduce the requirement for quantum resources. Numerical experiments are provided to illustrate the effectiveness of our algorithms.

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A variational quantum algorithm for Hamiltonian diagonalization

Cited by 13 publications

References 39 publications

Double-bracket flow quantum algorithm for diagonalization

Double-bracket flow quantum algorithm for diagonalization

Enhancing variational quantum state diagonalization using reinforcement learning techniques

Variational quantum algorithms for trace norms and their applications

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