Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The stabilizer ground state and applications to quantum simulation

Yuping Mao, Chang Chen, Jiaxing Feng, Yimeng Mao, Tim Byrnes

Abstract

The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground state as the stabilizer ground state which has the highest fidelity with the true ground state. This is useful in quantum simulation contexts as it allows for a Clifford circuit approximation of a ground state that can be further refined towards the true ground state. We show how the optimal stabilizer ground state may be evaluated. We show applications of this state in the context of measurement-based deterministic imaginary time evolution (MITE), which converges to the ground state with high efficiency. By classically selecting the optimal stabilizer generator group and employing the stabilizer tableaux formalism, the method prepares the corresponding stabilizer ground state with maximal fidelity. The identification and refinement of this generator group are performed using a genetic algorithm tailored to the structure of the target Hamiltonian. The complexity analysis further demonstrates that algorithm's quantum resource cost scales polynomially with system size, highlighting its high efficiency and potential quantum advantage.

The stabilizer ground state and applications to quantum simulation

Abstract

The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground state as the stabilizer ground state which has the highest fidelity with the true ground state. This is useful in quantum simulation contexts as it allows for a Clifford circuit approximation of a ground state that can be further refined towards the true ground state. We show how the optimal stabilizer ground state may be evaluated. We show applications of this state in the context of measurement-based deterministic imaginary time evolution (MITE), which converges to the ground state with high efficiency. By classically selecting the optimal stabilizer generator group and employing the stabilizer tableaux formalism, the method prepares the corresponding stabilizer ground state with maximal fidelity. The identification and refinement of this generator group are performed using a genetic algorithm tailored to the structure of the target Hamiltonian. The complexity analysis further demonstrates that algorithm's quantum resource cost scales polynomially with system size, highlighting its high efficiency and potential quantum advantage.
Paper Structure (19 sections, 65 equations, 2 figures)

This paper contains 19 sections, 65 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Stabilizer ground state and resource of magic state witness
  3. Stabilizer state
  4. Robustness of Magic
  5. Stabilizer ground state
  6. Optimal stabilizer ground state
  7. Definition
  8. Evaluating the OSGS
  9. Selection of optimal stabilizer generator group for larger systems
  10. Application to quantum simulation
  11. The measurement-based imaginary time evolution method
  12. Using optimal stabilizer ground state
  13. Complexity analysis and convergence error
  14. Numerical simulation
  15. Conclusions
  16. ...and 4 more sections

Figures (2)

  • Figure 1: The schematic plot for preparing optimal stabilizer ground state $|\psi_{OSGS\min}\rangle$
  • Figure 2: Performance of the OSGS-based MITE scheme applied to the transverse-field Ising model at $\lambda=0.6$. (a) Solid curves (in three different colors) show representative evolution trajectories of the random MITE procedure, while the black dashed curve denotes the fidelity averaged over $1000$ independent random MITE trials. (b) Comparison of the averaged fidelity over $1000$ turns for the MITE with and without stabilizer ground state preparation for $5$-qubit and $7$-qubit cases.