Trotterized Variational Quantum Control for Spin-Chain State Transfer

TL;DR

This paper introduces a hybrid variational quantum control method using Trotterization for high-fidelity state transfer in spin chains, demonstrating robustness and scalability for NISQ devices.

Contribution

It develops a novel variational framework with two parameterizations for quantum control, showing near-unit fidelities and noise robustness in spin chain simulations.

Findings

Both parameterizations achieve high fidelity in noiseless conditions.

The global scheme offers better noise robustness.

The approach reveals an expressivity-stability trade-off.

Abstract

We present a hybrid variational framework for quantum optimal control aimed at high-fidelity state transfer in spin chains. The system dynamics are discretized and compiled into a parameterized circuit, where deterministic two-qubit blocks implement the drift interactions, while trainable on-site RZ rotations encode the control inputs. We study two parameterizations: a compact global scheme with a small number of shared parameters per slice, and a local scheme with site-wise angles. Using a Sequential Least Squares Quadratic Programming (SLSQP) optimization to minimize infidelity, simulations on XXZ spin chains show that both parameterizations can achieve near-unit fidelities in the noiseless regime. Under depolarizing noise, the global scheme provides improved robustness for comparable circuit depth and iteration budgets. The results make explicit an expressivity-stability trade-off and suggest a scalable route to Noisy Intermediate-Scale Quantum (NISQ) compatible control synthesis.