[Paper Review] Greedy Gradient-free Adaptive Variational Quantum Algorithms on a Noisy Intermediate Scale Quantum Computer

César Feniou, Muhammad Hassan+5 more|arXiv (Cornell University)|Jun 29, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper introduces Greedy Gradient-free Adaptive VQE (GGA-VQE), a noise-resilient variational quantum algorithm that uses analytic, gradient-free optimization to iteratively build system-tailored ansatz circuits on noisy intermediate-scale quantum (NISQ) devices. It demonstrates improved robustness to statistical sampling noise and successfully computes the ground state of a 25-body Ising model on a 25-qubit error-mitigated quantum processor, achieving accurate results via noiseless wavefunction emulation of the final ansatz.

ABSTRACT

Hybrid quantum-classical adaptive Variational Quantum Eigensolvers (VQE) hold the potential to outperform classical computing for simulating many-body quantum systems. However, practical implementations on current quantum processing units (QPUs) are challenging due to the noisy evaluation of a polynomially scaling number of observables, undertaken for operator selection and high-dimensional cost function optimization. We introduce an adaptive algorithm using analytic, gradient-free optimization, called Greedy Gradient-free Adaptive VQE (GGA-VQE). In addition to demonstrating the algorithm's improved resilience to statistical sampling noise in the computation of simple molecular ground states, we execute GGA-VQE on a 25-qubit error-mitigated QPU by computing the ground state of a 25-body Ising model. Although hardware noise on the QPU produces inaccurate energies, our implementation outputs a parameterized quantum circuit yielding a favorable ground-state approximation. We demonstrate this by retrieving the parameterized operators calculated on the QPU and evaluating the resulting ansatz wave-function via noiseless emulation (i.e., hybrid observable measurement).

Motivation & Objective

• To address the challenge of statistical noise in gradient-based operator selection and optimization in variational quantum eigensolvers (VQEs) on NISQ hardware.
• To develop a gradient-free, analytic optimization strategy that reduces reliance on noisy gradient measurements during ansatz construction.
• To improve resilience to measurement noise in both operator selection and parameter optimization steps in adaptive VQE algorithms.
• To demonstrate the feasibility of computing accurate ground states for strongly correlated systems on current noisy quantum processors using a greedy, adaptive ansatz-building approach.

Proposed method

• Proposes a greedy, gradient-free adaptive VQE (GGA-VQE) that selects the next unitary operator from a pre-defined pool based on the largest change in the energy expectation value, avoiding gradient computation.
• Employs analytic, one-dimensional landscape functions to compute the optimal parameter for each newly added unitary, enabling noise-resilient optimization without numerical derivatives.
• Uses a sequential reoptimization protocol that alternately reoptimizes parameters from the first to the last and back, enhancing convergence under noisy conditions.
• Applies a hybrid measurement strategy: quantum device measures observable expectations, while the final ansatz is evaluated via noiseless classical simulation to verify ground-state fidelity.
• Introduces a two-phase algorithm: (1) greedy operator selection via energy sensitivity, and (2) iterative reoptimization of all parameters to refine the ansatz.
• Validates the method on both molecular systems (H2O, LiH) and a 25-body Ising model using real quantum hardware and noiseless emulation.

Experimental results

Research questions

• RQ1 Can a gradient-free, analytic optimization strategy outperform gradient-based methods in the presence of statistical sampling noise on NISQ devices?
• RQ2 How does the GGA-VQE algorithm perform in constructing accurate, system-specific ansatz circuits for strongly correlated many-body quantum systems?
• RQ3 Does sequential reoptimization improve convergence and accuracy in noisy quantum simulations compared to single-pass optimization?
• RQ4 Can GGA-VQE achieve chemical accuracy in ground state energy estimation despite noisy measurements on current quantum processors?
• RQ5 How does GGA-VQE compare to ADAPT-VQE and Frozen-ADAPT-VQE in terms of noise resilience and convergence speed under realistic noise conditions?

Key findings

• GGA-VQE achieves better energy convergence than gradient-based ADAPT-VQE under statistical noise, demonstrating superior noise resilience in both H2O and LiH simulations.
• The algorithm successfully computes the ground state of a 25-body Ising model on a 25-qubit error-mitigated quantum processor, producing a favorable ground-state approximation despite hardware noise.
• Noiseless emulation of the final ansatz wavefunction confirms high fidelity, showing that the quantum device output is a valid approximation of the true ground state.
• Sequential reoptimization significantly improves convergence and accuracy, especially under noisy conditions, outperforming single-pass optimization strategies.
• Frozen-ADAPT-VQE, which uses local optimization, outperforms standard ADAPT-VQE under noise, suggesting that global optimization is less effective when measurement noise is present.
• BFGS optimizer fails to converge under shot noise, confirming the unsuitability of gradient-based optimizers for noisy NISQ environments, thus validating the choice of COBYLA and GGA-VQE's approach.