Preparation of many-body ground states by time evolution with variational microscopic magnetic fields and incomplete interactions

Lu, Ying; Li, Yuemin; Zhou, Pengfei; Ran, Shi-Ju

doi:10.1103/physreva.104.052413

Cited by 5 publications

(4 citation statements)

References 59 publications

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“…[1] Quantum simulation in general requires to prepare an evolved state at any time and make measurement with respect to a physical observable. [2][3][4][5][6] In particular, the ground state preparation for a given Hamiltonian system is of great significance. By using the Jordan-Wigner or Bravyi-Kitaev [7] transformations, the molecule Hamiltonian can be transformed into qubit Hamiltonian in many quantum chemistry problems.…”

Section: Introductionmentioning

confidence: 99%

Improved Iterative Quantum Algorithm for Ground‐State Preparation

Liang

Shen

et al. 2022

Adv Quantum Tech

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Finding the ground state of a Hamiltonian system is of great significance in many‐body quantum physics and quantum chemistry. An improved iterative quantum algorithm to prepare the ground state of a Hamiltonian is proposed. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. Practical guideline on the selection of the learning rate in QGD are provided by finding a fundamental upper bound and establishing a relationship between the algorithm and the first‐order approximation of the imaginary time evolution. Furthermore, a variational quantum state preparation method is adapted as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of the algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, the approach has advantages including the higher success probability at each iteration, the measurement precision‐independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.

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Section: Introductionmentioning

confidence: 99%

Improved Iterative Quantum Algorithm for Ground‐State Preparation

Liang

Shen

et al. 2022

Adv Quantum Tech

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“…For the two-qubit gates, such as the controlled-not (CNOT) gate, the time costs with optimal control have theoretically given bounds [20][21][22]. For the N -qubit gates with N > 2, such bounds are not rigorously given in most cases, and variational methods including the machine learning (ML) techniques are used in the optimal-control problems [23][24][25][26][27][28][29][30][31][32][33]. Besides, the quantum many-body systems have also been used to im-plement the measurement-based quantum computation [34][35][36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

“…We employ two algorithms to implement the optimizations, namely the global time optimization (GTO) and fine-grained time optimization (FGTO) [32]. GTO is a simple gradientdescent method, where the strengths of the magnetic fields for all time slices are updated simultaneously by Eq.…”

Section: Introductionmentioning

confidence: 99%

Circuit encapsulation for efficient quantum computing based on controlled many-body dynamics

Lü¹,

Peng-Fei²,

Fei³

et al. 2022

Preprint

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Controlling the time evolution of interacting spin systems is an important approach of implementing quantum computing. Different from the approaches by compiling the circuits into the product of multiple elementary gates, we here propose the quantum circuit encapsulation (QCE), where we encapsulate the circuits into different parts, and optimize the magnetic fields to realize the unitary transformation of each part by the time evolution. The QCE is demonstrated to possess well-controlled error and time cost, which avoids the error accumulations by aiming at finding the shortest path directly to the target unitary. We test four different encapsulation ways to realize the multi-qubit quantum Fourier transformations by controlling the time evolution of the quantum Ising chain. The scaling behaviors of the time costs and errors against the number of two-qubit controlled gates are demonstrated. The QCE provides an alternative compiling scheme that translates the circuits into a physicallyexecutable form based on the quantum many-body dynamics, where the key issue becomes the encapsulation way to balance between the efficiency and flexibility.

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“…One of the most promising applications of quantum computers is to simulate the dynamics of chemical and physical systems [1]. Quantum simulation in general requires to prepare an evolved state at any time and make measurement with respect to a physical observable [2][3][4][5][6]. In particular, the ground state preparation for a given Hamiltonian system is of great significance.…”

mentioning

confidence: 99%

Improved iterative quantum algorithm for ground-state preparation

Liang,

Lv,

Shen

et al. 2022

Preprint

View full text Add to dashboard Cite

Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. We provide practical guideline on the selection of the learning rate in QGD by finding a fundamental upper bound and establishing a relationship between our algorithm and the first-order approximation of the imaginary time evolution. Furthermore, we adapt a variational quantum state preparation method as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of our algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, our approach has advantages including the higher success probability at each iteration, the measurement precision-independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.

show abstract

Preparation of many-body ground states by time evolution with variational microscopic magnetic fields and incomplete interactions

Cited by 5 publications

References 59 publications

Improved Iterative Quantum Algorithm for Ground‐State Preparation

Improved Iterative Quantum Algorithm for Ground‐State Preparation

Circuit encapsulation for efficient quantum computing based on controlled many-body dynamics

Improved iterative quantum algorithm for ground-state preparation

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