A generalized circuit for the Hamiltonian dynamics through the truncated series

Daskin, Ammar; Kais, Sabre

doi:10.1007/s11128-018-2099-z

Cited by 3 publications

(3 citation statements)

References 37 publications

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“…Here we only discuss first order case for simplicity. For simulation, a forward iterative PEA [18]-which estimates the phase starting from the most significant bit-can be used to save more time. The circuit for the forward iterative PEA is shown in FIG.…”

Section: A Trotter Phase Estimate Algorithm (Trotter-pea)mentioning

confidence: 99%

“…Babbush et al [15] further shows that it is possible to reduce the gate depth of the circuit to O(n) by using plane wave orbitals. Recently, a direct circuit implementation of the Hamiltonian within the phase estimation (Direct-PEA) is presented by authors of paper [16][17][18]: the circuit designs are provided to the time evolution operator by using the truncated series such as U = I − iH κ and U = tH + i(I − t 2 H 2 2 ), in which κ and t are parameters to restrict truncation error. These unitary operators are much simpler to implement than those of a Trotter decomposition, and can be also used to calculate ground state energies of molecular Hamiltonians.…”

Section: Introductionmentioning

confidence: 99%

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Quantum computing methods for electronic states of the water molecule

et al. 2019

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We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm based on the direct implementation of the Hamiltonian, direct measurement based on the implementation of the Hamiltonian and a specific variational quantum eigensolver, Pairwise VQE. After deriving the Hamiltonian using STO-3G basis, we first explain how each method works and then compare the simulation results in terms of gate complexity and the number of measurements for the ground state of the water molecule with different O-H bond lengths. Moreover, we present the analytical analyses of the error and the gate-complexity for each method. While the required number of qubits for each method is almost the same, the number of gates and the error vary a lot. In conclusion, among methods based on the phase estimation algorithm, the second order direct method provides the most efficient circuit implementations in terms of the gate complexity. With large scale quantum computation, the second order direct method seems to be better for large molecule systems. Moreover, Pairewise VQE serves the most practical method for near-term applications on the current available quantum computers. Finally the possibility of extending the calculation to excited states and resonances is discussed.

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Section: A Trotter Phase Estimate Algorithm (Trotter-pea)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum computing methods for electronic states of the water molecule

et al. 2019

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“…In [16], a method is presented to write a general matrix as a sum of unitary matrices. In this method, first without changing the location of any element, two indices i and k are assigned to all 2 × 2 subma-trices inside the matrix.…”

Section: General H With 0-1 Elementsmentioning

confidence: 99%

Context-aware quantum simulation of a matrix stored in quantum memory

Daskin

Bian

Xia

et al. 2019

Quantum Inf Process

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In this paper a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series, we generalize the idea to (0-1) matrices and discuss the generalization for the real matrices. The presented circuit requires O(n) number of quantum gates and yields the correct output with the success probability depending on the number of elements: for matrices with poly(n), the success probability is 1/poly(n). Since the operations on the circuit are controlled by the data itself, the circuit can be considered as a context aware computing gadget. In addition, it can be used in variational quantum eigensolver and in the simulation of molecular Hamiltonians.

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Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?

Sugisaki

2024

AIP Advances

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Electronic structure calculations of atoms and molecules are considered to be a promising application for quantum computers. Two key algorithms, the quantum phase estimation (QPE) and the variational quantum eigensolver (VQE), have been extensively studied. The condition that the energy of a dimer consisting of two monomers separated by a large distance should be equal to twice the energy of a monomer, known as size consistency, is essential in quantum chemical calculations. Recently, we reported that the size consistency condition can be violated by Trotterization in the unitary coupled cluster singles and doubles ansatz in the VQE when employing molecular orbitals delocalized to the dimer [Sugisaki et al., J. Comput. Chem. 45, 2204 (2024)]. It is well known that the full configuration interaction (full-CI) energy is invariant to arbitrary rotations of molecular orbitals, and therefore, the QPE-based full-CI should theoretically satisfy the size consistency. However, Trotterization of the time evolution operator can break the size consistency conditions. In this work, we investigated whether size consistency can be maintained with Trotterization of the time evolution operator in QPE-based full-CI calculations. Our numerical simulations revealed that size consistency in the QPE-based full-CI is not automatically violated by using molecular orbitals delocalized to the dimer, but employing an appropriate Trotter decomposition condition is crucial to maintain size consistency. We also report on the acceleration of QPE simulations through the sequential addition of ancillary qubits.

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A generalized circuit for the Hamiltonian dynamics through the truncated series

Cited by 3 publications

References 37 publications

Quantum computing methods for electronic states of the water molecule

Quantum computing methods for electronic states of the water molecule

Context-aware quantum simulation of a matrix stored in quantum memory

Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?

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