Qubit-efficient encoding scheme for quantum simulations of electronic structure

Shee, Yu; Tsai, Pei-Kai; Hong, Cheng-Lin; Cheng, Hao-Chung; Goan, Hsi-Sheng

doi:10.48550/arxiv.2110.04112

Cited by 4 publications

(9 citation statements)

References 42 publications

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“…Recently, Ref. [17] independently introduced an encoding scheme that is logarithmic in the number of qubits by mapping to basis states using an arbitrary map. This map lacked a functional form which we introduce using combinadics.…”

Section: Mapping Electronic Structure Hamiltonians To Quantum Computersmentioning

confidence: 99%

“…These approaches use spin operators to reduce the number of qubits to the relevant symmetry sector. Directly encoding fermion basis states to qubit basis states leads to the most compact representation of fermions on quantum computers, yet functional mapping forms are lacking in these works [16,17]. Alternatively, one can encode only the occupied orbitals on the quantum computer and execute the algorithm using sparse Hamiltonian simulation [18].…”

Section: Introductionmentioning

confidence: 99%

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Compact Molecular Simulation on Quantum Computers via Combinatorial Mapping and Variational State Preparation

Chamaki¹,

Metcalf²,

Jong³

2022

Preprint

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Compact representations of fermionic Hamiltonians are necessary to perform calculations on quantum computers that lack error-correction. A fermionic system is typically defined within a subspace of fixed particle number and spin while unnecessary states are projected out of the Hilbert space. We provide a bijective mapping using combinatoric ranking to bijectively map fermion basis states to qubit basis states and express operators in the standard spin representation. We then evaluate compact mapping using the Variational Quantum Eigensolver (VQE) with the unitary coupled cluster singles and doubles excitations (UCCSD) ansatz in the compact representation. Compactness is beneficial when the orbital filling is well away from half, and we show at 30 spin orbital H2 calculation with only 8 qubits. We find that the gate depth needed to prepare the compact wavefunction is not much greater than the full configuration space in practice. A notable observation regards the number of calls to the optimizer needed for the compact simulation compared to the full simulation. We find that the compact representation converges faster than the full representation using the ADAM optimizer in all cases. Our analysis demonstrates the effect of compact mapping in practice.

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Section: Mapping Electronic Structure Hamiltonians To Quantum Computersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compact Molecular Simulation on Quantum Computers via Combinatorial Mapping and Variational State Preparation

Chamaki¹,

Metcalf²,

Jong³

2022

Preprint

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“…We found that the apparent violation of the variational principle does pose a serious problem to the applicability of the VQE algorithm to the calculations of the electronic properties of spin defects in materials. The severity of this problem also depends on the chosen Fermion-to-qubit transformation, which in turn determines the extent to which the qubit Hilbert space differs from the configuration state space spanned by the Fermionic Hamiltonian [103].…”

Section: B Calculation Of the Ground State Using A Quantum Computermentioning

confidence: 99%

Simulating the electronic structure of spin defects on quantum computers

Huang,

Govoni,

Galli

2021

Preprint

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We present calculations of the ground and excited state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical/quantum protocol. We focus on the negatively charged nitrogen vacancy center in diamond and on the double vacancy in 4H-SiC, which are of interest for the realization of quantum technologies. We employ a recently developed firstprinciple quantum embedding theory to describe point defects embedded in a periodic crystal, and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation. We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation. We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground and excited state properties of spin defects.

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“…To obtain the qubit Hamiltonian for QEE of the hydrogen laser-atom system, one can start from the secondary quantized Hamiltonian in Eq. 16, and rewrite the excitation operators as [51]:…”

Section: Compact Encodingmentioning

confidence: 99%