Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility

Abstract

Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus" phenomenon is particularly prominent. In such cases, the loss function concentrates exponentially with increasing system size, thereby hindering effective parameter optimization. To address this challenge, we propose a general and hardware-efficient method for eliminating barren plateaus in an arbitrary PQC. Specifically, our approach achieves this by inserting a layer of easily implementable quantum channels into the original PQC, each channel requiring only one ancilla qubit and four additional gates, yielding a modified PQC (MPQC) that is provably at least as expressive as the original PQC and, under mild assumptions, is guaranteed to be free from barren plateaus. Furthermore, by appropriately adjusting the structure of MPQCs, we rigorously prove that any parameter in the original PQC can be made trainable. Importantly, the absence of barren plateaus in MPQCs is robust against realistic noise, making our approach directly applicable to near-term quantum hardware. Numerical simulations demonstrate that MPQC effectively eliminates barren plateaus in PQCs for preparing thermal states of systems with up to 100 qubits and 2400 layers. Furthermore, in end-to-end simulations, MPQC significantly outperforms PQC in finding the ground-state energy of a complex Hamiltonian.