Low-rank optimal control of quantum devices

We demonstrate that the control protocols of quantum information devices can be simulated by assuming a low-rank ansatz for the density matrix. The rationale underlying this assumption is that quantum information protocols, by design, operate in a regime of nearly pure quantum states. Within the low-rank assumption, the simulation of these protocols is considerably faster than solving the full Lindblad master equation. This advantage can be used to increase the accuracy of the simulation by avoiding uncontrolled approximations and to streamline protocol optimization. We benchmark our approach on the optimization of the transmon qubit dispersive readout in a realistic transmon-resonator-filter model. With a Hilbert space dimension <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>N</a:mi> <a:mo>=</a:mo> <a:mn>2000</a:mn> </a:mrow> </a:math> , assuming a rank as low as <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>M</b:mi> <b:mo>=</b:mo> <b:mn>20</b:mn> </b:mrow> </b:math> , we achieve a nearly 100-fold speedup compared to full master equation integration while accurately reproducing all relevant observables. By combining the low-rank approximation with a compact pulse parametrization and gradient-free optimization, we obtain state-of-the-art readout assignment errors <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>ɛ</c:mi> <c:mi>a</c:mi> </c:msub> <c:mo>≈</c:mo> <c:mn>1.2</c:mn> <c:mo>×</c:mo> <c:msup> <c:mn>10</c:mn> <c:mrow> <c:mo>−</c:mo> <c:mn>3</c:mn> </c:mrow> </c:msup> </c:mrow> </c:math> for a 40 ns readout pulse schedule, while comfortably running on a laptop and not relying on the rotating-wave approximation. Our approach is broadly applicable to most quantum control protocols, including quantum gates, state preparation, and fast reset operations. This establishes low-rank methods as a general tool for optimal control across diverse quantum platforms.