Trotterized adiabatic quantum simulation and its application to a simple all-optical system

Sun, Yifan; Zhang, Jun‐Yi; Byrd, Mark; Wu, Lian-Ao

doi:10.1088/1367-2630/ab7a31

Cited by 12 publications

(7 citation statements)

References 47 publications

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“…Instead of using Trotterization methods [51], [53], QAOA prepares a pair of unitary operators in terms of H f and H B . For ease of computation, we introduce the following remark to simplify H f .…”

Section: B Implementation Of Qaoamentioning

confidence: 99%

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Cui

Xiong

et al. 2022

IEEE Trans. Commun.

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Section: B Implementation Of Qaoamentioning

confidence: 99%

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Cui

Xiong

et al. 2022

IEEE Trans. Commun.

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“…Instead of using Trotterization methods [50], [52], QAOA prepares a pair of unitary operators in terms of H f and H B . For ease of computation, we introduce the following remark to simplify…”

Section: B Implementation Of Qaoamentioning

confidence: 99%

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Cui¹,

Xiong²,

Ng³

et al. 2021

Preprint

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Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where quantum approximation optimization algorithms (QAOAs) constitute promising candidates for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multipleinput and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-p QAOA circuit having 2p variational parameters, which can be optimized by classical optimizers. This level-p QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in p consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian.Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical minimum mean squared error (MMSE) detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector. This paves the way for a host of large-scale classical optimization problems to be solved by NISQ computers.

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“…According to the adiabatic theorem [16,28,29], we are guaranteed to obtain the deuteron ground state at the end of the evolution. This adiabatic evolution can be solved as [46][47][48][49]:…”

Section: The Deuteron Ground State Energymentioning

confidence: 99%

“…We can approximate the complete adiabatic evolution by a sequence of discrete adiabatic steps (time discretization). That is, we approximate the time-evolution operator U (t f ; t i ) as a product of n unitaries [46][47][48][49]:…”

Section: The Deuteron Ground State Energymentioning

confidence: 99%

Ab initio nuclear structure via quantum adiabatic algorithm

Du,

Vary,

Zhao

et al. 2021

Preprint

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Background: Solving nuclear many-body problems with an ab initio approach is widely recognized as a computationally challenging problem. Quantum computers offer a promising path to address this challenge.There are urgent needs to develop quantum algorithms for this purpose.Objective: In this work, we explore the application of the quantum algorithm of adiabatic state preparation with quantum phase estimation in ab initio nuclear structure theory. We focus on solving the low-lying spectra (including both the ground and excited states) of simple nuclear systems.Ideas: The efficiency of this algorithm is hindered by the emergence of small energy gaps (level crossings) during the adiabatic evolution. In order to improve the efficiency, we introduce techniques to avoid level crossings: 1) by suitable design of the reference Hamiltonian; 2) by insertions of perturbation terms to modify the adiabatic path.Results: We illustrate this algorithm by solving the deuteron ground state energy and the spectrum of the deuteron bounded in a harmonic oscillator trap implementing the IBM Qiskit quantum simulator. The quantum results agree well the classical results obtained by matrix diagonalization.Outlook: With our improvements to the efficiency, this algorithm provides a promising tool for investigating the low-lying spectra of complex nuclei on future quantum computers.

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Trotterized adiabatic quantum simulation and its application to a simple all-optical system

Cited by 12 publications

References 47 publications

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Ab initio nuclear structure via quantum adiabatic algorithm

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