Variational Quantum Eigensolver with Reduced Circuit Complexity

Cincio, Łukasz; Negre, Christian F. A.; Czarnik, Piotr; Coles, Patrick J.; Anisimov, Petr M.; Mniszewski, Susan M.; Tretiak, Sergei; Dub, Pavel A.

doi:10.48550/arxiv.2106.07619

Cited by 14 publications

(23 citation statements)

References 71 publications

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“…Repressive examples contain grouping compatible operators [72,74] and classical-shadows based methods [75,76]. Last, a promising direction is combining QUDIO with a recent work [77], which splits the input quantum circuits into several individual quantum circuits with distributed optimization.…”

Section: Discussionmentioning

confidence: 99%

Accelerating variational quantum algorithms with multiple quantum processors

Du¹,

Yang²,

Tao³

2021

Preprint

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Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead, hampered by the tradition of employing a solitary quantum processor to handle large-volume data. As such, to better exert the superiority of VQAs, it is of great significance to improve their runtime efficiency. Here we devise an efficient distributed optimization scheme, called QUDIO, to address this issue. Specifically, in QUDIO, a classical central server partitions the learning problem into multiple subproblems and allocate them to multiple local nodes where each of them consists of a quantum processor and a classical optimizer. During the training procedure, all local nodes proceed parallel optimization and the classical server synchronizes optimization information among local nodes timely. In doing so, we prove a sublinear convergence rate of QUDIO in terms of the number of global iteration under the ideal scenario, while the system imperfection may incur divergent optimization. Numerical results on standard benchmarks demonstrate that QUDIO can surprisingly achieve a superlinear runtime speedup with respect to the number of local nodes. Our proposal can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with quantum advantage.

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Section: Discussionmentioning

confidence: 99%

Accelerating variational quantum algorithms with multiple quantum processors

Du¹,

Yang²,

Tao³

2021

Preprint

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“…ClusterVQE: In Ref. [471], Zhang et al present a method that borrows ideas from ADAPT-VQE, iQCC and Mutual Information (MI) assisted Adaptive VQE to optimize the use of quantum resources. The first step in this method is to create a cluster of qubits (across the qubit register of the QPU used) that have strong MI within, and low MI across, each cluster.…”

Section: Iqccmentioning

confidence: 99%

The Variational Quantum Eigensolver: a review of methods and best practices

Tilly¹,

Chen²,

Cao³

et al. 2021

Preprint

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“…A majority of these efforts utilize the variational quantum eigensolver (VQE) algorithm in conjunction with unitary coupled-cluster based ansatzes [7,8,20,21] and are able to produce highly compact quantum circuits through a variational minimization of the expectation value of the Hamiltonian with respect to the circuit parameters, and hence by construction, are more suited for contemporary quantum hardware. Some specific examples include development of adaptive ansatzes for simulation of ground [9][10][11] and excitedstates [12,13], correlation informed permutation of qubits (PermVQE) [14] or qubits clustering (ClusterVQE) [19] approaches, construction of highly compact molecular Hamiltonians through a basis-set free formalism [15] utilizing pair-natural orbital (PNO) based compression [22,23] in conjunction with multi-resolution [24] strategies, low rank factorization techniques for approximating operators [16]. In a similar work, Bauman et al employed the QPE algorithm and double unitary coupled-cluster (DUCC) formalism to downfold or embed manybody correlation effects into active-spaces of effective Hamiltonians for both ground [17] and excited states [18].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the mostly oneto-one correspondence between spin-orbitals and qubits ensures that the quantum simulations can only utilize a minimal number of qubits which can, at most, only give a qualitative description of the desired solution. Thus, a lot of efforts lately have focused on reducing the quantum resource requirements for electronic structure simulations on noisy intermediate-scale quantum (NISQ) devices [9][10][11][12][13][14][15][16][17][18][19]. A majority of these efforts utilize the variational quantum eigensolver (VQE) algorithm in conjunction with unitary coupled-cluster based ansatzes [7,8,20,21] and are able to produce highly compact quantum circuits through a variational minimization of the expectation value of the Hamiltonian with respect to the circuit parameters, and hence by construction, are more suited for contemporary quantum hardware.…”

Section: Introductionmentioning

confidence: 99%

Accurate quantum simulation of molecular ground and excited states with a transcorrelated Hamiltonian

Kumar¹,

Asthana²,

Masteran³

et al. 2022

Preprint

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NISQ era devices suffer from a number of challenges like limited qubit connectivity, short coherence times and sizable gate error rates. Thus, quantum algorithms are desired that require shallow circuit depths and low qubit counts to take advantage of these devices. We attempt to reduce quantum resource requirements for molecular simulations on a quantum computer, a promising application on NISQ devices, while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically through an approximate similarity transformation of the Hamiltonian with a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorelated Hamiltonians are able to describe both ground and excited states of molecular systems in a balanced manner. Using the fermionic-ADAPT-VQE method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the much larger cc-pVTZ basis. This leads to a potential reduction in the number of required CNOT gates by more than three orders of magnitude for the chemical species studied in this work. Furthermore, using the qEOM formalism in conjunction with the transcorrelated Hamiltonian, we reduce the errors in excitation energies by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only oneand two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

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Variational Quantum Eigensolver with Reduced Circuit Complexity

Cited by 14 publications

References 71 publications

Accelerating variational quantum algorithms with multiple quantum processors

Accelerating variational quantum algorithms with multiple quantum processors

The Variational Quantum Eigensolver: a review of methods and best practices

Accurate quantum simulation of molecular ground and excited states with a transcorrelated Hamiltonian

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