Quantum Science and Technology

Quantum dynamics shaping through fully actuated system representations

Zihao Ren, Lei Wang, Hongye Su, He Kong, Guodong Shi, Guang‐Ren Duan

Published Sep 30, 2026• 0 citations

Abstract

Abstract Quantum control has achieved remarkable success in state transfer, trajectory tracking, and optimal control, yet a fundamental gap remains between trajectory generation and dynamics shaping. Unlike robotic and mechanical systems, where feedback design can directly prescribe transient behaviors such as convergence rates, damping, and robustness, most quantum control methods focus on identifying control fields that achieve a desired evolution without explicitly shaping the dynamics along that evolution. Here we bridge this gap by extending the fully actuated system (FAS) paradigm from classical control to finite-dimensional bilinear quantum systems. We show that controllability does not imply full actuation in quantum dynamics: the Lie-group structure of quantum evolution generally prevents a controllable quantum system from being represented as a FAS. To overcome this limitation, we introduce virtual quantum measurements and construct a local partial FAS representation in the output space, where the highest-order output derivatives are directly assignable by the control Hamiltonians. This representation enables explicit cancellation of nonlinear input–output dynamics and provides a constructive framework for quantum dynamics shaping. The resulting closed-loop behavior can be prescribed through arbitrary pole placement or fixed-time convergence with preassigned settling-time bounds. We further develop an offline closed-loop emulation procedure that converts the feedback law into implementable open-loop control waveforms. Numerical studies on single-qubit and two-qubit systems demonstrate accurate trajectory tracking, fixed-time convergence, prescribed gate-error decay quantified by average gate fidelity, and tunable trade-offs among convergence speed, robustness, and control effort.

DOI: 10.1088/2058-9565/aeae6b

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