Towards determining the presence of barren plateaus in some chemically inspired variational quantum algorithms

TL;DR

This paper investigates whether chemically inspired variational quantum algorithms, specifically UCC-based circuits, can avoid barren plateaus, and finds that they may not, raising concerns about their scalability and trainability.

Contribution

The study provides theoretical and numerical evidence that UCC-inspired circuits may not escape barren plateau issues, challenging assumptions about their effectiveness in quantum chemistry applications.

Findings

Alternated dUCC and relaxed Trotterized UCC ansätze show exponential concentration in energy landscapes.

One-body terms in UCC lead to polynomially concentrated landscapes, while two-body terms cause exponential concentration.

Numerical simulations suggest UCCSD ansätze may not scale effectively due to barren plateau problems.

Abstract

In quantum chemistry, the variational quantum eigensolver (VQE) is a promising algorithm for molecular simulations on near-term quantum computers. However, VQEs using hardware-efficient circuits face scaling challenges due to the barren plateau problem. This raises the question of whether chemically inspired circuits from unitary coupled cluster (UCC) methods can avoid this issue. Here we provide theoretical evidence indicating they may not. By examining alternated dUCC ans\"atze and relaxed Trotterized UCC ans\"atze, we find that in the infinite depth limit, a separation occurs between particle-hole one- and two-body unitary operators. While one-body terms yield a polynomially concentrated energy landscape, adding two-body terms leads to exponential concentration. Numerical simulations support these findings, suggesting that popular 1-step Trotterized unitary coupled-cluster with singles and doubles (UCCSD) ans\"atze may not scale. Our results emphasize the link between trainability and circuit expressiveness, raising doubts about VQEs' ability to surpass classical methods.