Resolving correlated states of benzyne with an error-mitigated contracted quantum eigensolver

Smart, Scott E.; Boyn, Jan-Niklas; Mazziotti, David A.

doi:10.1103/physreva.105.022405

Cited by 34 publications

(36 citation statements)

References 97 publications

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“…Finally, we compare the CQE approach utilizing a BFGS optimization with other known quantum algorithms. While in previous work [14] similarities between iterative nature of the ACSE and ADAPT-VQE were discussed, here, we provide example calculations of VQE, ADAPT-VQE, and the ACSE that demonstrate fundamental differences in these algorithms. These are included in Figure 3, as well as in Table V.…”

Section: Comparison With Vqementioning

confidence: 80%

“…[9][10][11][12] Recently, the ACSE has been solved on quantum devices with applications to hydrogen chains as well as the benzyne isomers. [13][14][15] On a quantum computer the ACSE algorithm, known as a contracted quantum eigensolver (CQE), iteratively minimizes the residual of the ACSE in contrast to the variational quantum eigensolvers (VQE) that minimize the energy with respect to parameters according to the Rayleigh-Ritz variational principle. Instead of propagating only the 2-RDM as in the classical algorithm, we propagate a wave function through state preparation on a quantum computer.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized Optimization

Smart¹,

Mazziotti²

2022

Preprint

Self Cite

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A contracted quantum eigensolver (CQE) finds a solution to the many-electron Schr ödinger equation by solving its integration (or contraction) to the 2-electron space-a contracted Schr ödinger equation (CSE)-on a quantum computer. When applied to the anti-Hermitian part of the CSE (ACSE), the CQE iterations optimize the wave function with respect to a general product ansatz of two-body exponential unitary transformations that can exactly solve the Schr ödinger equation. In this work, we accelerate the convergence of the CQE and its wavefunction ansatz via tools from classical optimization theory. By treating the CQE algorithm as an optimization in a local parameter space, we can apply quasi-secondorder optimization techniques, such as quasi-Newton approaches or non-linear conjugate gradient approaches. Practically these algorithms result in superlinear convergence of the wavefunction to a solution of the ACSE. Convergence acceleration is important because it can both minimize the accumulation of noise on near-term intermediate-scale quantum (NISQ) computers and achieve highly accurate solutions on future fault-tolerant quantum devices. We demonstrate the algorithm, as well as some heuristic implementations relevant for cost-reduction considerations, comparisons with other common methods such as variational quantum eigensolvers, and a fermionic-encoding-free form of the CQE.

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Section: Comparison With Vqementioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized Optimization

Smart¹,

Mazziotti²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…[7][8][9][10][11] In the present noisy intermediate-scale quantum (NISQ) era, 12 variational quantum eigensolver (VQE), as one of the most popular quantum-classical algorithms, 4,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] has been exploited to experimentally study molecules from H 2 (2 qubits), 14 BeH 2 (6 qubits), 15 H 2 O (8 qubits), 26 to H 12 (12 qubits) 16 and isomers of benzyne C 6 H 4 (4 qubits). 28,29 Meanwhile, the largest scale numerical molecular VQE simulation is C 2 H 4 (28 qubits). 27 The simulation of even large molecular systems might be realized in the future with the recently developed fermionic quantum emulator, 30 which utilizes the particle number and spin symmetry along with custom evolution routines for Hamiltonians to reduce the memory requirement.…”

Section: Introductionmentioning

confidence: 99%

Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers

Huang²,

Cao³

et al. 2022

Chem. Sci.

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“…Boyn el al. [9] obtained active-space 2-RDMs from quantum computations and post-processed them with two classical correlation methods, the anti-Hermitian contracted Schrödinger equation (ACSE) theory [10][11][12] and multiconfigurational pair-density functional theory (MC-PDFT) [13]. Fujii el al.…”

Section: Introductionmentioning

confidence: 99%

Leveraging small scale quantum computers with unitarily downfolded Hamiltonians

Huang¹,

Li²,

Evangelista³

2022

Preprint

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In this work, we propose a quantum unitary downfolding formalism based on the driven similarity renormalization group (QDSRG) that may be combined with quantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a classical polynomially-scaling downfolding method that avoids the evaluation of costly three-and higher-body reduced density matrices while retaining the accuracy of classical multireference many-body theories. We calibrate and test the QDSRG on several challenging chemical problems and propose a strategy for avoiding classical exponentialscaling steps in the QDSRG scheme. We report QDSRG computations of two chemical systems using the variational quantum eigensolver on IBM quantum devices: i) the dissociation curve of H2 using a quintuple-ζ basis and ii) the bicyclobutane isomerization reaction to trans-butadiene, demonstrating the reduction of problems that require several hundred qubits to a single qubit. Our work shows that the QDSRG is a viable approach to leverage near-term quantum devices for the accurate estimation of molecular properties.

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Resolving correlated states of benzyne with an error-mitigated contracted quantum eigensolver

Cited by 34 publications

References 97 publications

Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized Optimization

Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized Optimization

Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers

Leveraging small scale quantum computers with unitarily downfolded Hamiltonians

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