Leakage Suppression in Quantum Control via Static Parameter Offsets

Abstract

High-fidelity quantum operations require the system dynamics to be strictly confined to the computational subspace. In practice, however, control fields inevitably couple to leakage levels, giving rise to quantum state leakage that significantly reduces the fidelity of the operation. To address this challenge, we propose a general strategy for actively suppressing leakage errors by applying small, static offsets to tunable system parameters. This approach systematically mitigates leakage's detrimental impact on quantum control, without modifying the original control framework or incurring additional time overhead. By avoiding the need for extra suppression pulses or complex optimization procedures altogether, it offers a streamlined solution for leakage compensation while remaining fully compatible with subsequent optimal control techniques. Numerical validation conducted on superconducting quantum circuits demonstrates effective leakage suppression, enabling high-fidelity single-qubit gates, precise control of two-qubit interactions, and perfect state transfer in multi-level systems. Moreover, when integrated with optimal control techniques, our approach also allows for the cooperative suppression of both leakage errors and residual crosstalk. Therefore, this work provides a feasible technical pathway toward the low error thresholds required for fault-tolerant quantum computation.

Figures (10)

• Figure 1: (a) The nonequidistant energy-spectrum diagram for a driven superconducting transmon-type qubit, in which $\{|0\rangle,~|1\rangle\}$ and $\{|2\rangle,~|3\rangle\}$ are taken as the computational subspace (blue box) and leakage subspace (red box), respectively. The dotted gray line indicates the positions the energy level would be at if the system was a harmonic oscillator. (b) Energy level diagram for two capacitively coupled transmon qubits, which can be used to implement the iSWAP gates. The dashed line indicates leakage errors between energy levels. (c) Two independent pulses are applied between energy levels $\{|0\rangle, |1\rangle\}$ (red) and $\{|1\rangle, |2\rangle\}$ (blue), thereby driving the target energy level transitions. (d) The dashed lines indicate leakage errors between energy levels outside the target energy level, with each color representing leakage errors caused by different pulse drivers.
• Figure 2: The approximate solutions from calculations (dashed lines) and exact solutions from numerical simulations (solid lines) for gate fidelity as functions of small, static offsets of coupling strength $\delta_\Omega$, phase $\delta_\phi$ and detuning $\delta_\Delta$, respectively, for NOT (above column) and Hadamard (below column) gates. $\Delta F^G$ denotes the enhancement in fidelity achieved by introducing offsets, as compared to without offsets.
• Figure 3: Comparison of the gate fidelity obtained with the optimized parameters under the small, static offsets (SSO) scheme and those uncorrected (UC). Figures (a) and (b) correspond to the NOT and Hadamard gates considering decoherence, respectively. The state population for NOT gate (c) and Hadamard gate (d) with the optimized parameters under the small, static offsets (SSO) scheme and those uncorrected (UC) while considering decoherence effect. The initial state of both gates is $|0\rangle$.
• Figure 4: The approximate solutions from calculations (dashed lines) and exact solutions from numerical simulations (solid lines) for gate fidelity as functions of small, static offsets of coupling strength $\delta_\Omega$, phase $\delta_\phi$ and detuning $\delta_\Delta$, respectively, for $i$SWAP gate. $\Delta F^G$ denotes the enhancement in fidelity achieved by introducing offsets, as compared to without offsets.
• Figure 5: Figure (a) compares the fidelity of the $i$SWAP gate using optimized parameters under the small, static offsets (SSO) scheme and uncorrected (UC), taking into account decoherence effects. Figure (b) shows the state population for $i$SWAP gate which the initial state is $|01\rangle$, similarly considering decoherence effects.