Implementation of measurement reduction for the variational quantum eigensolver

Ralli, Alexis; Love, Peter J.; Tranter, Andrew; Coveney, Peter V.

doi:10.1103/physrevresearch.3.033195

Cited by 17 publications

(25 citation statements)

References 40 publications

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“…This grouping premise has been shown to allow a linear reduction in the number of terms in the Hamiltonian, similar to what can be achieved with GC grouping [327,353,354]. The next step is to implement the joint measurement of all the elements of each unitary group identified.…”

Section: Unitary Partitioning Of the Hamiltonianmentioning

confidence: 82%

See 1 more Smart Citation

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

Tilly¹,

Chen²,

Cao³

et al. 2021

Preprint

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Section: Unitary Partitioning Of the Hamiltonianmentioning

confidence: 82%

“…Zhang et al [353] also show that the circuit depth can be reduced further using ancilla qubits. These methods of partitioning the Hamiltonian into unitary groups have been tested in an implementation on a quantum computer by Ralli et al [354].…”

Section: Unitary Partitioning Of the Hamiltonianmentioning

confidence: 99%

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

Tilly¹,

Chen²,

Cao³

et al. 2021

Preprint

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show abstract

“…The VQE has been extensively applied to quantum chemistry problems [16,[48][49][50] and experimentally realized on superconducting [16,49,55,56] and ion trap [1,10,57] quantum simulators. Several attempts have been made to enhance the VQE performance, including: minimizing the number of required measurements [58][59][60][61][62][63], improving the initialization [52,64,65], speeding up the classical optimization [66][67][68] and designing better circuits [69][70][71][72][73][74]. Several important phenomena in physics, such as topological phases [75], are described by the knowledge of a few low-energy eigenstates and not just the ground state.…”

Section: Introductionmentioning

confidence: 99%

Symmetry enhanced variational quantum spin eigensolver

Lyu¹,

Xu²,

Yung³

et al. 2022

Preprint

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The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

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“…A natural question that arises from this is if this can be further reduced by measurement reduction schemes [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The goal of this work was to investigate the possible reductions given by the unitary partitioning strategy [15,29,30] and whether chemical accuracy on larger molecules can be reached on currently available NISQ hardware.…”

Section: Introductionmentioning

confidence: 99%

Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver

Ralli¹,

Weaving²,

Tranter³

et al. 2022

Preprint

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The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontexual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared to solving the full Hamiltonian via traditional VQE. We simulate CS-VQE on different tapered molecular Hamiltonians and apply the unitary partitioning measurement reduction strategy to further reduce the number of measurements required to obtain the contextual correction. Our results indicate that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices. We also provide a modification to the CS-VQE algorithm, that previously could cause an exponential increase in Hamiltonian terms, that now at worst will scale quadratically.

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Implementation of measurement reduction for the variational quantum eigensolver

Cited by 17 publications

References 40 publications

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

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

Symmetry enhanced variational quantum spin eigensolver

Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver

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