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arXiv:2412.05656 · Physical Review A

Robust implicit quantum control of interacting spin chains

Luca Stefanescu, Louis Edwards-Pratt, Jeremy O'Connor, Ezra Tsegaye, Nguyen H. Le, Florian Mintert

Published Jun 23, 2025• 1 citation
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Abstract

Robust quantum control can achieve noise resilience of quantum systems and quantum technological devices. While the need for noise resilience grows with the number of fluctuating quantities, and thus typically with the number of qubits, most numerically exact optimal control techniques are limited to systems of few interacting qubits. This paper exploits quantum control that avoids explicit reference to quantum states in exponentially large Hilbert space. Exemplary control protocols for spin chains are discussed in terms of noise-resilient preparation of highly entangled states.

DOI
10.1103/zmcn-ddkj

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Robust quantum control can achieve noise resilience of quantum systems and quantum technological devices. While the need for noise resilience grows with the number of fluctuating quantities, and thus typically with the number of qubits, most numerically exact optimal control techniques are limited to systems of few interacting qubits. This paper exploits quantum control that avoids explicit reference to quantum states in exponentially large Hilbert space. Exemplary control protocols for spin chains are discussed in terms of noise-resilient preparation of highly entangled states.
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Realising high fidelity entangled states in controlled quantum many-body systems is challenging due to experimental uncertainty in a large number of physical quantities. We develop a robust optimal control method for achieving this goal in finite-size multi-qubit systems despite significant uncertainty in multiple parameters. We demonstrate its effectiveness in the generation of the Greenberger-Horne-Zeilinger state on a star graph of capacitively coupled transmons, and discuss its crucial role for achieving the Heisenberg limit of precision in quantum sensing.
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Abstract A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categories: schemes which extend the robustness to (i) spin or (ii) motional decoherence. We choose to focus on extensions of the σ x ⊗ σ x Mølmer–Sørensen interaction using microwaves and a static magnetic field gradient. Nevertheless, some of the techniques discussed here can be relevant to other trapped ion architectures or physical qubit implementations. Finally, we experimentally realize a proof-of-concept interaction with simultaneous robustness to spin and motional decoherence by combining several quantum control methods presented in this manuscript.
The development of quantum control methods is an essential task for emerging quantum technologies. In general, the process of optimizing quantum controls scales very unfavorably in system size due to the exponential growth of the Hilbert space dimension. Here, I present a scalable subsystem-based method for quantum optimal control on a large quantum system. The basic idea is to cast the original problem as a robust control problem on subsystems with requirement of robustness in respect of inter-subsystem couplings, thus enabling a drastic reduction of problem size. The method is in particular suitable for target quantum operations that are local, e.g., elementary quantum gates. As an illustrative example, I employ it to tackle the demanding task of pulse searching on a 12-spin coupled system, achieving substantial reduction of memory and time costs. This work has significant implications for coherent quantum engineering on near-term intermediate-scale quantum devices.