[Paper Review] A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver

Arthur G. Rattew, Shaohan Hu+3 more|arXiv (Cornell University)|Oct 21, 2019

Quantum Computing Algorithms and Architecture36 references45 citations

TL;DR

EVQE uses evolutionary programming to automatically generate and optimize quantum circuit variational forms that are domain-agnostic, hardware-aware, and more noise-resistant than fixed VQE forms, achieving shallower circuits with fewer CX gates and good performance on real quantum hardware.

ABSTRACT

Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms---the quantum circuits that implement ansatzes ---are either crafted heuristically or by encoding domain-specific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardware-efficient ansatzes. In molecular simulations, the variational forms generated by EVQE are up to $18.6 imes$ shallower and use up to $12 imes$ fewer CX gates than those obtained by VQE with a unitary coupled cluster ansatz. EVQE demonstrates significant noise-resistance properties, obtaining results in noisy simulation with at least $3.6 imes$ less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5-qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for general-purpose optimization on the quantum computers of the present and near future.

Motivation & Objective

• Address the limitations of fixed variational forms in VQE by enabling automatic generation and optimization of circuit structures.
• Develop a domain-agnostic variational algorithm applicable across chemistry, optimization, finance, and AI.
• Improve hardware efficiency and noise resilience by evolving shallow circuits tailored to hardware connectivity and noise profiles.
• Demonstrate empirical advantages over traditional VQE/UCCSD in molecular problems and benchmark problems, including real quantum hardware.

Proposed method

• Represent quantum circuits as genomes where each gene encodes a circuit layer with gates drawn from a set {I, U3, CU3}.
• Evolve circuit forms via asexual mutation (topological, parameter, and removal mutations) to progressively grow or prune layers.
• Use identity initialization for new gates so added gates do not change the current energy evaluation, enabling smooth improvement.
• Apply speciation based on a genetic ancestry tree to maintain diverse, niche solutions and protect against noise disruption.
• Evaluate fitness as energy expectation value plus small penalties for circuit depth and two-qubit gates to promote shallow, hardware-efficient circuits (f_i = <ψ_i|H|ψ_i> + α|g_i| + β·CU3(g_i)).
• Population-level exploration uses fitness sharing and speciation with a distance metric defined by shared genes to maintain multiple optima.

Experimental results

Research questions

• RQ1 Can a domain-agnostic evolutionary process generate efficient variational circuit forms that compete with domain-specific VQE variants?
• RQ2 Do EVQE-generated circuits exhibit enhanced noise resilience and reduced depth/gate counts on both simulated and real quantum hardware?
• RQ3 How does an asexual, speciation-enabled evolutionary approach mitigate barren-plateau issues in variational quantum optimization?
• RQ4 Are EVQE-generated circuits able to achieve chemical accuracy for molecular Hamiltonians with fewer CX gates and reduced depth compared to UCCSD-based VQE?

Key findings

• EVQE generates significantly shallower circuits and uses fewer CX gates than VQE/UCCSD in LiH and BeH2 benchmarks (up to 18.6× shallower and up to 12× fewer CX gates for BeH2).
• In LiH, EVQE circuits are 5.0–15.2× shallower and use 3.5–5.0× fewer CX gates than VQE/UCCSD for ground-state energy estimation.
• EVQE shows substantial noise resistance, achieving at least 3.6× less error than VQE across tested ansatz configurations in noisy simulations.
• EVQE achieves successful ground-state energy estimation on a real 5-qubit IBMQ quantum processor, demonstrating hardware feasibility.
• On Max-Cut and vehicle-routing problems, EVQE produces efficient and more consistent results than VQE.
• In state-vector simulations, both LiH and BeH2 cases reach chemical accuracy, with EVQE performing competitively or better across distances and configurations.