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A simple method for seniority-zero quantum state preparation

Michal Krompiec, Josh J. M. Kirsopp, Antonio Márquez Romero, Vicente Perez Soloviev

TL;DR

The paper presents oo-pCCD-UpCCD, a non-variational, low-depth state preparation method for singlet electronic states that leverages leading oo-pCCD amplitudes within an UpCCD circuit. It demonstrates high overlaps with ground states across Hubbard and bond-dissociation models, even at stretched geometries, while requiring shallow quantum circuits (8–10 gates) unlike deep QRAM-based alternatives. The approach improves the success probability of Quantum Phase Estimation for dissociated molecules and achieves near-CASCI fidelity, underscoring its potential for practical quantum simulations of strongly correlated systems. Overall, the work establishes a solid theoretical and computational link between non-unitary and unitary paired-double CC methods and provides a scalable path for QPE-ready state preparation in challenging electronic structure problems.

Abstract

Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of electronic systems using a quantum computer. It requires, however, to be warm--started from an initial state with sufficiently high overlap with the ground state. For strongly-correlated states, where QPE is expected to have advantage over classical methods, preparation of such initial states requires deep quantum circuits and/or expensive hybrid quantum-classical optimization. It is well-known that orbital-optimized paired Coupled Cluster Doubles (oo-pCCD) method can describe the static correlation features of many strongly correlated singlet states. We show that pCCD and its unitary counterpart, UpCCD, become equivalent in the limit of small amplitudes or if the number of large amplitudes is below 5. We demonstrate that substituting leading oo-pCCD amplitudes into the UpCCD Ansatz allows to prepare high-fidelity singlet states for models of multiple-bond dissociation in ethene, ethyne and dinitrogen, as well as for 1D Hubbard models at half-filling, with very shallow circuits. We envisage our method to be of general use for approximate preparation of singlet states for Quantum Phase Estimation and related algorithms.

A simple method for seniority-zero quantum state preparation

TL;DR

The paper presents oo-pCCD-UpCCD, a non-variational, low-depth state preparation method for singlet electronic states that leverages leading oo-pCCD amplitudes within an UpCCD circuit. It demonstrates high overlaps with ground states across Hubbard and bond-dissociation models, even at stretched geometries, while requiring shallow quantum circuits (8–10 gates) unlike deep QRAM-based alternatives. The approach improves the success probability of Quantum Phase Estimation for dissociated molecules and achieves near-CASCI fidelity, underscoring its potential for practical quantum simulations of strongly correlated systems. Overall, the work establishes a solid theoretical and computational link between non-unitary and unitary paired-double CC methods and provides a scalable path for QPE-ready state preparation in challenging electronic structure problems.

Abstract

Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of electronic systems using a quantum computer. It requires, however, to be warm--started from an initial state with sufficiently high overlap with the ground state. For strongly-correlated states, where QPE is expected to have advantage over classical methods, preparation of such initial states requires deep quantum circuits and/or expensive hybrid quantum-classical optimization. It is well-known that orbital-optimized paired Coupled Cluster Doubles (oo-pCCD) method can describe the static correlation features of many strongly correlated singlet states. We show that pCCD and its unitary counterpart, UpCCD, become equivalent in the limit of small amplitudes or if the number of large amplitudes is below 5. We demonstrate that substituting leading oo-pCCD amplitudes into the UpCCD Ansatz allows to prepare high-fidelity singlet states for models of multiple-bond dissociation in ethene, ethyne and dinitrogen, as well as for 1D Hubbard models at half-filling, with very shallow circuits. We envisage our method to be of general use for approximate preparation of singlet states for Quantum Phase Estimation and related algorithms.

Paper Structure

This paper contains 14 sections, 8 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theory
  3. Seniority-zero methods for singlet states
  4. Coupled Cluster methods in Quantum Circuits
  5. Exact relations between CC, disentangled UCC and CI
  6. Relations between pCCD and UpCCD
  7. Calculations
  8. Numerical results and discussion
  9. 1-D Hubbard Model
  10. Bond dissociation in ethene, ethyne and dinitrogen
  11. Bond dissociation: 20-qubit models
  12. State fidelity in all-electron calculations
  13. Application to Quantum Phase Estimation
  14. Conclusions and Outlook

Figures (5)

  • Figure 1: Overlaps of UpCCD and pCCD wave functions sharing the same amplitudes, for different numbers of non-zero amplitudes and various interactions between excitations (see text)
  • Figure 2: Overlaps of UpCCD (solid lines) and Hartree-Fock (dashed lines) states with CASCI states, for 6-, 10- and 12-site Hubbard models at half filling
  • Figure 3: Overlaps of UpCCD (solid lines) and Hartree-Fock (dashed lines) states with CASCI states, for 20-qubit models of C2H2, C2H4 and N2, vs. C-C or N-N distances (see text)
  • Figure 4: Effect of the initial state on the outcome of Canonical Quantum Phase Estimation applied to singlet state of dissociated C2H4
  • Figure 5: Effect of the initial state on the outcome of Canonical Quantum Phase Estimation applied to singlet state of dissociated C2H4: histogram of energies (2000 samples)