Publisher Correction: Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

Motta, Mário; Sun, Chong; Tan, Adrian T. K.; O’Rourke, Matthew J.; Ye, Erika; Minnich, Austin J.; Brandão, Fernando G. S. L.; Chan, Garnet Kin‐Lic

doi:10.1038/s41567-019-0756-5

Cited by 5 publications

(6 citation statements)

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“…This issue introduces numerical instabilities in the generalized eigenvalue problem and is potentially amplified by poor gate fidelity and measurement errors. Bases generated by variational optimization 44 and real 45 or imaginary 43 time propagation are all plagued (to various degrees) by linear dependencies.…”

Section: ̂̂|ψ⟩ †mentioning

confidence: 99%

“…These references are selected via a scheme that exploits quantum measurement to identify the most important determinants in a simple trial wave function. The resulting multireference selected quantum Krylov (MRSQK) method (see Figure 1) is combined with basis generation via real-time propagation 43,45 and benchmarked on a series of problems involving strongly correlated electronic states.…”

Section: ̂̂|ψ⟩ †mentioning

confidence: 99%

“…A third and emerging family of methods, which we refer to as Quantum Subspace Diagonalization (QSD) schemes, diagonalize the Hamiltonian in a general non-orthogonal basis of many-body states. ,,− There is a long tradition of using such a strategy in quantum chemistry. − A natural way to extend it to quantum computing is to construct a basis of states and measure the corresponding matrix elements with a quantum device, and later solve the associated generalized eigenvalue problem via a classical computer . Compared to a fully classical approach, QSD schemes can take advantage of the ability of quantum computers to store arbitrarily complex states.…”

Section: Introductionmentioning

confidence: 99%

“…The quantum subspace expansion (QSE) method of McClean and co-workers, diagonalizes the Hamiltonian in the basis of states , where Ψ is a reference state prepared via VQE. ,, Matrix element of the Hamiltonian in this basis are obtained by measuring the three- and four-body density matrices. QSD approaches are particularly advantageous if the many-body basis is constructed as a Krylov space and does not require extensive parameter optimization. This is the case for the Quantum Lanczos (QLanczos) algorithm, where the Hamiltonian is diagonalized in a basis of correlated states generated by imaginary-time propagation .…”

Section: Introductionmentioning

confidence: 99%

“…QSD approaches are particularly advantageous if the many-body basis is constructed as a Krylov space and does not require extensive parameter optimization. This is the case for the Quantum Lanczos (QLanczos) algorithm, where the Hamiltonian is diagonalized in a basis of correlated states generated by imaginary-time propagation . This basis is obtained from a single reference state by sampling at regular intervals in imaginary time.…”

Section: Introductionmentioning

confidence: 99%

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A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

Stair

Huang

Evangelista

2020

J. Chem. Theory Comput.

142

123

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We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H 6 , H 8 , and BeH 2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

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Section: ̂̂|ψ⟩ †mentioning

confidence: 99%

Section: ̂̂|ψ⟩ †mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

Stair

Huang

Evangelista

2020

J. Chem. Theory Comput.

142

123

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Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation

Stair

Evangelista

2020

The Journal of Chemical Physics

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This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

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