[Paper Review] Diabatic quantum annealing by counter-diabatic driving

Luise Prielinger, Andreas Hartmann+4 more|arXiv (Cornell University)|Nov 5, 2020

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proposes a two-parameter counter-diabatic driving protocol for quantum annealing in the transverse-field Ising model, accelerating convergence to the ground state by simulating unconventional diabatic control of longitudinal and transverse fields. It achieves significantly higher ground-state fidelity and lower residual energy than traditional and single-parameter methods, with a demonstrated scaling advantage in time-to-solution for the p=3 p-spin model.

ABSTRACT

We introduce a two-parameter approximate counter-diabatic term into the Hamiltonian of the transverse-field Ising model for quantum annealing to accelerate convergence to the solution, generalizing an existing single-parameter approach. The protocol is equivalent to unconventional diabatic control of the longitudinal and transverse fields in the transverse-field Ising model and thus makes it more feasible for experimental realization than an introduction of new terms such as non-stoquastic catalysts toward the same goal of performance enhancement. We test the idea for the $p$-spin model with $p=3$, which has a first-order quantum phase transition, and show that our two-parameter approach leads to significantly larger ground-state fidelity and lower residual energy than those by traditional quantum annealing as well as by the single-parameter method. We also find a scaling advantage in terms of the time to solution as a function of the system size in a certain range of parameters as compared to the traditional methods.

Motivation & Objective

• To accelerate convergence in quantum annealing for systems with first-order quantum phase transitions.
• To overcome limitations of single-parameter counter-diabatic approaches in enhancing ground-state fidelity and reducing residual energy.
• To make performance-enhancing control more experimentally feasible by avoiding non-stoquastic terms.
• To investigate scaling advantages in time-to-solution for larger system sizes.

Proposed method

• Introduces a two-parameter approximate counter-diabatic term into the transverse-field Ising model Hamiltonian.
• Generalizes the single-parameter counter-diabatic approach to allow independent control over longitudinal and transverse field dynamics.
• Maps the counter-diabatic protocol to unconventional diabatic control of the longitudinal and transverse fields, avoiding the need for non-stoquastic catalysts.
• Applies the method to the p=3 p-spin model, a system with a first-order quantum phase transition, to test performance.
• Uses numerical simulations to evaluate ground-state fidelity and residual energy as performance metrics.
• Analyzes time-to-solution scaling with system size to assess computational advantage.

Experimental results

Research questions

• RQ1 Can a two-parameter counter-diabatic approach outperform traditional quantum annealing in ground-state fidelity and residual energy for first-order phase transition systems?
• RQ2 Does the proposed method offer a scaling advantage in time-to-solution compared to single-parameter and conventional quantum annealing?
• RQ3 Is the two-parameter protocol experimentally more feasible than non-stoquastic counter-diabatic approaches?
• RQ4 How does the performance of the two-parameter method vary with parameter tuning in the p=3 p-spin model?

Key findings

• The two-parameter method achieves significantly higher ground-state fidelity than both traditional quantum annealing and the single-parameter approach in the p=3 p-spin model.
• Residual energy is substantially lower under the two-parameter protocol, indicating better convergence to the true ground state.
• A scaling advantage in time-to-solution is observed for certain parameter ranges, suggesting improved efficiency with increasing system size.
• The method enables effective diabatic control without introducing non-stoquastic terms, enhancing experimental feasibility.