Hardware-efficient ansatz without barren plateaus in any depth

TL;DR

This paper introduces two parameter conditions for hardware-efficient ansatz circuits that prevent barren plateaus regardless of circuit depth, enhancing trainability for quantum applications.

Contribution

It proposes novel parameter conditions ensuring barren plateau-free training in hardware-efficient ansatz circuits at any depth, supported by theoretical proofs and phenomenological models.

Findings

Gradient bounds are maintained at any depth under the proposed conditions.

Initializing parameters according to these conditions improves performance in many-body Hamiltonian problems.

Barren plateaus are mitigated by smart parameter initialization, not circuit depth or expressivity.

Abstract

Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge potential, the practical usefulness of those circuits beyond tens of qubits is largely questioned. One of the major problems is the so-called barren plateaus phenomenon. Quantum circuits with a random structure often have a flat cost-function landscape and thus cannot be trained efficiently. In this paper, we propose two novel parameter conditions in which the hardware-efficient ansatz (HEA) is free from barren plateaus for arbitrary circuit depths. In the first condition, the HEA approximates to a time-evolution operator generated by a local Hamiltonian. Utilizing a recent result by [Park and Killoran, Quantum 8, 1239 (2024)], we prove a constant lower bound of gradient magnitudes in any depth both for local and global observables. On the other hand, the HEA is within the many-body localized (MBL) phase in the second parameter condition. We argue that the HEA in this phase has a large gradient component for a local observable using a phenomenological model for the MBL system. By initializing the parameters of the HEA using these conditions, we show that our findings offer better overall performance in solving many-body Hamiltonians. Our results indicate that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial.