[论文解读] Improving the accuracy of quantum computational chemistry using the transcorrelated method

Sam McArdle, David P. Tew|arXiv (Cornell University)|Jun 19, 2020

Quantum Computing Algorithms and Architecture参考文献 2被引用 32

一句话总结

本文研究使用 transcorrelated (TC) method 提高量子计算化学的精度，并展示如何将 ansatz-based imaginary time evolution 应用于非厄米 TC 哈密顿量，以在量子计算机上估算基态。

ABSTRACT

Accurately treating electron correlation in the wavefunction is a key challenge for both classical and quantum computational chemistry. Classical methods have been developed which explicitly account for this correlation by incorporating inter-electronic distances into the wavefunction. The transcorrelated method transfers this explicit correlation from the wavefunction to a transformed, non-Hermitian Hamiltonian, whose right-hand eigenvectors become easier to obtain than those of the original Hamiltonian. In this work, we show that the transcorrelated method can reduce the resources required to obtain accurate energies from electronic structure calculations on quantum computers. We overcome the limitations introduced by the non-Hermitian Hamiltonian by using quantum algorithms for imaginary time evolution.

研究动机与目标

• Motivate and review explicit correlation approaches for reducing dynamic correlation errors in electronic structure calculations.
• Introduce and analyze the transcorrelated (TC) method as a way to transform the Hamiltonian rather than the wavefunction.
• Propose and justify using ansatz-based quantum imaginary time evolution to find ground states of the non-Hermitian TC Hamiltonian.
• Discuss practical implications for quantum algorithms given non-Hermitian Hamiltonians and measurement challenges.

提出的方法

• Present the transcorrelated transformation H' = e^{-g} H e^{g} and its BCH expansion truncating at second order to obtain H' = H + [H,g] + 1/2 [[H,g],g].
• Explain that the TC transformation introduces two- and three-body terms, altering the spectral properties and left/right eigenvectors.
• Propose an ansatz-based quantum imaginary time evolution (QITE) scheme to approximate ground states of H' by evolving a parameterized circuit state via McLachlan’s variational principle.
• Derive parameter update rules A dot theta = -C for imaginary-time evolution within a unitary ansatz manifold.
• Outline measurement strategies to estimate energy and metric components A_{ij}, C_i on a quantum device, including Hadamard-test-style circuits.

实验结果

研究问题

• RQ1 Can the non-Hermitian transcorrelated Hamiltonian be efficiently solved on a quantum computer using ansatz-based imaginary time evolution?
• RQ2 Does applying a TC transformation before basis projection yield energies closer to the basis-set limit compared to the untransformed Hamiltonian in quantum simulations?
• RQ3 What are the practical measurement and accuracy implications of non-Hermiticity for observables and left/right eigenvectors in TC quantum simulations?
• RQ4 How does the TC approach compare with Hermitian approximations (e.g., canonical TC, UCC-downfolding) for enabling near-term quantum algorithms?

主要发现

• Demonstrate, via numerical simulations, that an ansatz-based QITE approach can converge to ground states of the non-Hermitian TC Hamiltonian in model systems.
• Argue that TC can make right-hand eigenvectors more compact, potentially reducing resources needed for accurate energies when sampling with quantum algorithms.
• Highlight that left-hand eigenvectors acquire additional dynamic correlation under TC, complicating the calculation of observables beyond energy.
• Discuss that measuring energies under TC is feasible by mapping to a weighted sum of Pauli operators, despite non-Hermiticity.
• Contextualize the work as complementary to emergent Hermitian TC approaches, illustrating a path for integrating TC with variational quantum algorithms.