[Paper Review] Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm

Benjamin F. Schiffer, Jordi Solé Tura+1 more|arXiv (Cornell University)|Mar 1, 2021

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper introduces a variational quantum adiabatic algorithm (VQAA) that optimizes adiabatic paths for high-fidelity ground state preparation in quantum many-body systems. By combining adiabatic evolution with variational parameter optimization using ancilla-based overlap estimation, the method reduces evolution time by a factor of ten compared to linear adiabatic paths, significantly enhancing feasibility for NISQ devices with limited coherence times.

ABSTRACT

Preparing the ground state of a Hamiltonian is a problem of great significance in physics with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long preparation times which depend on the a priori unknown spectral gap. Our work relates in a twofold way. First, we propose a method to obtain information about the spectral profile of the adiabatic evolution. Second, we present the concept of a variational quantum adiabatic algorithm (VQAA) for optimized adiabatic paths. We aim at combining the strengths of the adiabatic and the variational approaches for fast and high-fidelity ground state preparation while keeping the number of measurements as low as possible. Our algorithms build upon ancilla protocols which we present that allow to directly evaluate the ground state overlap. We benchmark for a non-integrable spin-1/2 transverse and longitudinal Ising chain with $N=53$ sites using tensor network techniques. Using a black box, gradient-based approach, we report a reduction in the total evolution time for a given desired ground state fidelity by a factor of ten, which makes our method suitable for the limited decoherence time of noisy-intermediate scale quantum devices.

Motivation & Objective

• To address the challenge of long preparation times in adiabatic quantum algorithms due to unknown spectral gaps.
• To improve ground state fidelity and speed in noisy intermediate-scale quantum (NISQ) devices with limited decoherence times.
• To develop a hybrid approach that combines the robustness of adiabatic evolution with the flexibility of variational quantum algorithms.
• To minimize the number of quantum measurements required for ground state overlap estimation using ancilla protocols.

Proposed method

• Proposes a variational quantum adiabatic algorithm (VQAA) where evolution times in discrete chunks are optimized as variational parameters.
• Employs ancilla-based protocols to directly measure the overlap between the evolved state and the target ground state via controlled unitary evolution.
• Uses Bayesian inference with Beta distributions to update posterior probabilities of ground state overlap after each measurement, enabling adaptive hypothesis testing.
• Applies a black-box, gradient-based optimization to tune the adiabatic path parameters for minimal evolution time at a target fidelity.
• Employs tensor network techniques to benchmark the VQAA on a 53-site transverse and longitudinal Ising chain with non-integrable interactions.
• Utilizes hypothesis testing with left and right α-errors to determine stopping criteria for overlap estimation, ensuring statistical confidence.

Experimental results

Research questions

• RQ1 Can variational optimization of adiabatic paths significantly reduce the total evolution time required for high-fidelity ground state preparation?
• RQ2 How can ground state overlap be estimated efficiently with minimal quantum measurements in a NISQ setting?
• RQ3 To what extent can ancilla-based protocols improve the accuracy and efficiency of overlap estimation in adiabatic state preparation?
• RQ4 Does the VQAA outperform standard linear adiabatic evolution in terms of speed and fidelity for complex many-body systems?
• RQ5 How does the choice of prior distribution and stopping criterion affect the convergence and reliability of overlap estimation?

Key findings

• The VQAA reduces the total evolution time required to achieve a target ground state fidelity by a factor of ten compared to linear adiabatic paths.
• The method achieves high-fidelity ground state preparation using fewer measurements than the Quantum Approximate Optimization Algorithm (QAOA), due to the structured adiabatic evolution.
• Ancilla-based overlap estimation enables direct, efficient measurement of the overlap with the ground state, reducing the need for full state tomography.
• Bayesian hypothesis testing with adaptive stopping criteria ensures reliable decision-making even when the target overlap is close to the measured value.
• The algorithm remains robust under realistic NISQ constraints, making it suitable for near-term quantum devices with limited coherence times.
• Benchmarking on a 53-site non-integrable Ising chain confirms the method’s effectiveness in complex, physically relevant systems.