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arXiv:2511.14746

Optimization of High-Fidelity Single-Qubit Gates for Fluxoniums Using Single-Flux Quantum Control

Maxime Lapointe-Major, Boyan Torosov, Bohdan Kulchytskyy, Pooya Ronagh

quant-phSubmitted Nov 18, 2025• Announced Nov 19, 2025• 0 citations
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Abstract

We present a gradient-based method to construct memory-efficient, high-fidelity, single-qubit gates for fluxonium qubits. These gates are constructed using a sequence of single-flux quantum (SFQ) pulses that are sent to the qubit through either capacitive or inductive coupling. The schedule of SFQ pulses is constructed with an on-ramp and an off-ramp applied prior to and after a pulse train, where the pulses are spaced at intervals equal to the qubit period. We reduce the optimization problem to the scheduling of a fixed number of SFQ pulses in the on-ramp and solve it by relaxing the discretization constraint of the SFQ clock as an intermediate step, allowing the use of the Broyden-Fletcher-Goldfarb-Shanno optimizer. Using this approach, gate fidelities of 99.99 % can be achieved for inductive coupling and 99.9 % for capacitive coupling, with leakage being the main source of coherent errors for both approaches.

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We present a gradient-based method to construct memory-efficient, high-fidelity, single-qubit gates for fluxonium qubits. These gates are constructed using a sequence of single-flux quantum (SFQ) pulses that are sent to the qubit through either capacitive or inductive coupling. The schedule of SFQ pulses is constructed with an on-ramp and an off-ramp applied prior to and after a pulse train, where the pulses are spaced at intervals equal to the qubit period. We reduce the optimization problem to the scheduling of a fixed number of SFQ pulses in the on-ramp and solve it by relaxing the discretization constraint of the SFQ clock as an intermediate step, allowing the use of the Broyden-Fletcher-Goldfarb-Shanno optimizer. Using this approach, gate fidelities of 99.99 % can be achieved for inductive coupling and 99.9 % for capacitive coupling, with leakage being the main source of coherent errors for both approaches.
In the traditional approach to controlling superconducting qubits using microwave pulses, the field of pulse shaping has emerged in order to assist in the removal of leakage and increase gate fidelity. However, the challenge of scaling microwave control electronics has created an opportunity to explore alternative methods such as single-flux quantum (SFQ) pulses. For qubits controlled by SFQ pulses, high fidelity gates can be achieved by optimizing the binary control sequence. We extend the notion of the derivative removal by adiabatic gate (DRAG) framework a transmon qubit controlled by SFQ drivers. The proposed implementation of SFQ pulse sequences can be stored in 22 bits or fewer, with gate fidelities exceeding 99.99%. This modest memory requirement could help reduce the footprint of the SFQ coprocessors and power dissipation while preserving their inherent advantages of scalability and cost-effectiveness.
We present a gradient-based method to construct high-fidelity, two-qubit quantum gates in a system consisting of two transmon qubits coupled via a tunable coupler. In particular, we focus on single-flux-quantum pulses as a promising and scalable alternative to traditional control schemes that use microwave electronics. We develop a continuous embedding scheme to optimize these discrete pulses, taking advantage of autodifferentiation of our model. This approach allows us to achieve fSim-type gates with average gate fidelities on the order of 99.99% and controlled-ZZZ and controlled-not gates with fidelities above 99.9%. Furthermore, we provide an alternative semianalytical construction of these gates via an exact decomposition using a pair of fSim gates, which leads to the reduction in memory required to store the associated pulse sequences.
We apply the quantum optimal control theory based on the Krotov method to implement single-qubit XXX and ZZZ gates and two-qubit cnot gates for inductively coupled superconducting flux qubits with fixed qubit transition frequencies and fixed off-diagonal qubit-qubit coupling. Our scheme shares an advantage with other direct-coupling schemes in that it requires no additional coupler subcircuit and control lines. The control lines needed are only for the manipulation of individual qubits (e.g., a time-dependent magnetic flux or field applied on each qubit). The qubits are operated at the optimal coherence points and the gate operation times (less than 1 ns for single-qubit gates and $\ensuremath{\sim}2$ ns for cnotgates) are much shorter than the corresponding qubit decoherence time. A cnot gate or other general quantum gates can be implemented in a single run of the pulse sequence rather than being decomposed into several single-qubit and several entangled two-qubit operations in series by composite pulse sequences. Quantum gates constructed via our scheme are all with very high fidelity (very low error) as our optimal control scheme takes into account the fixed qubit detuning and fixed two-qubit interaction as well as all other time-dependent magnetic-field-induced single-qubit interactions and two-qubit couplings. The effect of leakage to higher-energy-level states and the effect of qubit decoherence on the quantum-gate operations are also discussed.
We present theoretical schemes for performing high-fidelity one- and two-qubit pulsed gates for a superconducting flux qubit. The 'IBM qubit' consists of three Josephson junctions, three loops and a superconducting transmission line. Assuming a fixed inductive qubit–qubit coupling, we show that the effective qubit–qubit interaction is tunable by changing the applied fluxes, and can be made negligible, allowing one to perform high-fidelity single qubit gates. Our schemes are tailored to alleviate errors due to 1/ f noise; we find gates with only 1% loss of fidelity due to this source, for pulse times in the range of 20–30 ns for one-qubit gates ( Z rotations, Hadamard) and 60 ns for a two-qubit gate (controlled- Z ). Our relaxation and dephasing time estimates indicate a comparable loss of fidelity from this source. The control of leakage plays an important role in the design of our shaped pulses, preventing shorter pulse times. However, we have found that imprecision in the control of the quantum phase plays a major role in the limitation of the fidelity of our gates.
The fluxonium qubits have emerged as a promising platform for gate-based quantum information processing. However, their extraordinary protection against charge fluctuations comes at a cost: when coupled capacitively, the qubit-qubit interactions are restricted to XX interactions. Consequently, effective ZZ or XZ interactions are only constructed either by temporarily populating higher-energy states, or by exploiting perturbative effects under microwave driving. Instead, we propose and demonstrate an inductive coupling scheme, which offers a wide selection of native qubit-qubit interactions for fluxonium. In particular, we leverage a built-in, flux-controlled ZZ interaction to perform qubit entanglement. To combat the increased flux-noise-induced dephasing away from the flux-insensitive position, we use a continuous version of the dynamical decoupling scheme to perform noise filtering. Combining these, we demonstrate a 20 ns controlled-z gate with a mean fidelity of 99.53%. More than confirming the efficacy of our gate scheme, this high-fidelity result also reveals a promising but rarely explored parameter space uniquely suitable for gate operations between fluxonium qubits.
Abstract. We introduce a binary, relaxed gradient, trust-region method for optimizing pulse sequences for single flux quanta control of a quantum computer. The pulse sequences are optimized with the goal of realizing unitary gate transformations. Each pulse has a fixed amplitude and duration. We model this process as a binary optimal control problem, constrained by Schrödinger’s equation, where the binary variables indicate whether each pulse is on or off. We introduce a first-order trust-region method, which takes advantage of a relaxed gradient to determine an optimal pulse sequence that minimizes the gate infidelity, while also suppressing leakage to higher energy levels. The proposed algorithm has a computational complexity of [Formula: see text], where [Formula: see text] is the number of pulses in the sequence. We present numerical results for the H and X gates, where the optimized pulse sequences give gate fidelities better than 99.9%, in [Formula: see text] trust-region iterations.