A Variational Surrogate Approach to Finite-Horizon Quantum Control via Hardware-Efficient Ansatz

Research Approach

This paper introduces a variational quantum framework for finite-horizon optimal control. Instead of the traditional approach of synthesizing time-dependent control fields based on a known system Hamiltonian, the authors reformulate the control task as a variational optimization problem. They employ a hardware-efficient ansatz—a parameterized quantum circuit consisting of alternating layers of single-qubit rotations and entangling gates—to act as a surrogate for the terminal evolution of the quantum system. By optimizing the parameters of this circuit using classical routines, the system can be steered from an initial state to a target state while remaining compatible with near-term noisy intermediate-scale quantum (NISQ) hardware.

The researchers evaluated their framework using multi-qubit state-transfer benchmarks, specifically focusing on transferring a single excitation across a qubit register. Their numerical experiments demonstrate that the proposed method successfully achieves high-fidelity state transfer. The results highlight a clear trade-off: while increasing circuit depth enhances the expressive capacity of the ansatz, it simultaneously increases the complexity of the optimization landscape. As the number of qubits grows, the optimization process becomes more challenging, leading to slower convergence and increased sensitivity to initial parameter values.

Conventional quantum optimal control methods often require detailed physical models and explicit control field synthesis, which can be computationally demanding and difficult to implement on current quantum devices. By shifting to a variational surrogate approach, this framework provides a flexible, implementation-friendly alternative that bypasses the need for explicit Hamiltonian modeling. This makes it a promising candidate for practical applications in quantum information transfer and state preparation on near-term hardware, provided that the challenges of optimization scalability are managed.