Genetic optimization of ansatz expressibility for enhanced variational quantum algorithm performance

TL;DR

This work presents a problem-agnostic, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.

Abstract

Variational quantum algorithms have emerged as a leading paradigm that extracts practical computation from near-term intermediate-scale quantum devices, enabling advances in quantum chemistry simulations, combinatorial optimization, and quantum machine learning. However, the performance of variational quantum algorithms is highly sensitive to the design of the ansatze. To be effective, ansatze must be expressive enough to capture target states but shallow enough to be trainable. We propose a genetic algorithm-inspired framework for designing ansatze that achieve high expressibility while maintaining shallow depth and low parameter count. Our approach evolves ansatze through mutation and selection based on an expressibility metric. The circuit generated by our framework consistently demonstrates high expressibility at any target depth and performs comparably to traditional ansatz design approaches. This work presents a problem-agnostic, scalable solution for ansatz design, producing expressive, low-depth circuits that need to be designed only once and can serve a wide range of applications.

Figures (22)

• Figure 1: There is a trade-off between circuit complexity and expressibility in variational quantum circuits. The diagram shows three important areas in the expressibility-complexity landscape. Region C (red) shows a small search space because the circuit depth is not deep enough, which makes it hard to get close to the target states. The green area in Region B shows the best expressibility zone that our genetic algorithm (GA)-generated ansatz can find. It does this by choosing the best gate configurations at the right depths to balance expressibility and trainability. At high levels of expressibility and complexity, Region A (gray) shows the entire Hilbert space that can be reached. Circuits suffer from the barren plateau phenomenon, which makes them hard to train. Our depth-aware GA framework moves around these areas in real time to create resource-efficient ansatze that are highly expressive and converge quickly across a wide range of problem sizes.
• Figure 2: Overview of the general Genetic Algorithm: parameter initialization, generation of the initial population, iterative fitness evaluation, selection of parents, crossover to produce offspring, mutation for genetic diversity, population replacement, and termination upon meeting the stopping criteria.
• Figure 3: Genetic algorithm framework for ansatz optimization. A population of random quantum circuits is initialized and evaluated using expressibility as the fitness metric. Top-performing circuits are selected as parents for crossover, generating offspring by recombining gate sequences. Offspring undergo mutation to maintain population diversity. The process iterates over generations, yielding an ansatz with maximal expressibility under depth and qubit constraints.
• Figure 5: The plot shows the expressibility metric (y-axis) as a function of the GA framework generations (x-axis) for all gate sets (A-I) on a four-qubit system. A lower metric value indicates better expressibility. All curves show improvement in expressibility through generations, which consistently saturates by generation 10. We additionally verify this by extending the GA framework to 20 generations (see Figure \ref{['fig:20-gen']} in the appendix), which shows that exprressibility gains are minimal, confirming 10 generations as sufficient optimization duration.
• Figure 6: Expressibility saturation with increasing circuit depth. The plot shows the expressibility metric (y-axis) as a function of circuit depth (x-axis) for ansatze constructed using gate set A on systems of 4, 6, 10, and 14 qubits. The expressibility rapidly improves with initial increases in depth before reaching a plateau, which indicates that optimal expressibility is achieved at a circuit depth ( $\approx2n$ depth, where $n$ is the number of qubits) that scales linearly with the number of qubits.