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arXiv:2610.31885

Optimal Control of a Fluxonium Circuit with the Q-PRONTO Numerical Method

John Barta, Brian D. Isakov, Pablo Aramburu Sanchez, Jieqiu Shao, Tamás Kalmár, Trevyn F. Q. Larson, Marco M. Nicotra, András Gyenis

quant-phSubmitted Oct 22, 2026• Announced Oct 26, 2026• 0 citations
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Abstract

Optimizing the control of large quantum systems is a resource-intensive task, where the convergence rate of the underlying iterative schemes is crucial. The recently developed Quantum Projection Operator-Based Newton Method for Trajectory Optimization (Q-PRONTO) offers a unique quadratic convergence for controlling quantum states, while most model-based solvers guarantee only an approximately linear convergence rate. As a proof of concept, here, we design and benchmark single-qubit gates optimized by Q-PRONTO based on the circuit Hamiltonian of a fluxonium superconducting qubit. To ensure that we can apply a long string of arbitrary pulses to the circuit, we modify the firmware associated with the Quantum Instrumentation Control Kit (QICK) by altering its memory allocation. We characterize the performance of the optimal solutions using standard randomized benchmarking and achieve a total error per gate of $6.6\times10^{-4}$.

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Optimizing the control of large quantum systems is a resource-intensive task, where the convergence rate of the underlying iterative schemes is crucial. The recently developed Quantum Projection Operator-Based Newton Method for Trajectory Optimization (Q-PRONTO) offers a unique quadratic convergence for controlling quantum states, while most model-based solvers guarantee only an approximately linear convergence rate. As a proof of concept, here, we design and benchmark single-qubit gates optimized by Q-PRONTO based on the circuit Hamiltonian of a fluxonium superconducting qubit. To ensure that we can apply a long string of arbitrary pulses to the circuit, we modify the firmware associated with the Quantum Instrumentation Control Kit (QICK) by altering its memory allocation. We characterize the performance of the optimal solutions using standard randomized benchmarking and achieve a total error per gate of 6.6×10−46.6\times10^{-4}6.6×10−4.
Quantum optimal control is an important technology that enables fast state preparation and gate design. In the absence of an analytic solution, most quantum optimal control methods rely on an iterative scheme to update the solution estimate. At present, the convergence rate of existing solvers is, at most, superlinear. This paper develops a general-purpose solver for quantum optimal control based on the projection operator Newton method for trajectory optimization, or PRONTO. Specifically, the proposed approach uses a projection operator to incorporate the Schr\"odinger equation directly into the cost function, which is then minimized using Newton's descent method. At each iteration, the descent direction is obtained by computing the analytic solution to a linear-quadratic trajectory-optimization problem. The resulting method guarantees monotonic convergence at every iteration and quadratic convergence in the proximity of the solution. The potential of PRONTO is showcased by solving the optimal state-to-state mapping problem for a qubit and providing comparisons to a state-of-the-art quantum optimal control method.
Quantum optimal control is an important technology that enables fast state preparationand gate design. In the absence of an analytic solution, most quantum optimal control methods rely on an iterative scheme to update the solution estimate. At present, the convergence rate of existing solvers is, at most, superlinear. In this thesis, we develop a new general purpose solver for quantum optimal control, Quantum PRojection Operator-based Newton method for Trajectory Optimization (Q-PRONTO). Specifically, the proposed approach uses a projection operator to incorporate the Schr¨odinger equation directly into the cost function, which is then minimized using a Newton descent method. The resulting method guarantees monotonic convergence at every iteration and quadratic convergence in proximity of the solution. We then implement the method to different quantum applications: the first application is shaken lattice interferometry, which is a novel atom-based interferometry for quantum sensing; the second application is fluxonium qubit, which is a novel superconducting qubit for quantum computing. The potential of Q-PRONTO is showcased by computing an interferometry sequence for shaken lattice interferometry and designing a quantum gate for fluxonium qubit. The encouraging simulation results represent a first step in the development of a new paradigm for both quantum sensing and quantum computing.
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The Quantum Projection Operator-Based Newton Method for Trajectory Optimization (q-pronto) is a numerical method for solving quantum optimal control problems. This paper significantly improves prior versions of the quantum projection operator by introducing a regulator that stabilizes the solution estimate at every iteration. This modification is shown to not only improve the convergence rate of the algorithm, but also steer the solver towards better local minima compared to the unregulated case. Numerical examples showcase how q-pronto can be used to solve multi-input quantum optimal control problems featuring time-varying costs and undesirable populations that ought to be avoided during the transient.
The heavy-fluxonium circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the flux-frustration point. However, the suppressed charge matrix elements and low transition frequency make it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control,and readout that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize higher levels of the fluxonium to read out the qubit state and to initialize the qubit with 97% fidelity corresponding to cooling it to 190 μK. Instead of using standard microwave pulses, we control the qubit only with fast-flux pulses, generating control fields much larger than the qubit frequency. We develop a universal set of gates based on nonadiabatic Landau-Zener transitions that act in 20-60 ns, less than the single-qubit Larmor period. We measure qubit coherence of T1,T2e∼300 μs for a fluxonium in a 2D architecture and realize single-qubit gates with an average gate fidelity of 99.8% as characterized by randomized benchmarking.
Scaling up to a full-scale multi-qubit processor adds complexity to the control signals input requirements which can be addressed by the use of specially designed cryogenic interface circuits. In this paper, we discuss the use of cryogenic classical electronics for control of a fluxonium artificial atom. In recent years, fluxonium has gained notoriety among the superconducting qubit community for exceptionally long coherence times and large anharmonicity - both highly desirable properties when designing the next generation of qubit systems. The feasibility of controlling a fluxonium based quantum processors with a compact control system ultimately enables a highly scalable system; however, the cryogenic environment poses very strict requirements on electronics. Many trade-offs arise in terms of noise, power consumption, and circuit complexity. Addressing these requires comprehensive simulations that account for the physics of fluxonium qubits and the potential impact of control circuits on their performance. This paper focuses on the models and specification derivation for qubit control and explores constraints in fluxonium-based system design. The models and specifications derived enable the design of optimal control circuits targeted for scalable fluxonium quantum processors.