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arXiv:2603.09914

Qubit reset beyond the Born-Markov approximation: optimal driving to overcome polaron formation

Carlos Ortega-Taberner, Eoin O'Neill, Paul Eastham

quant-phcond-mat.stat-mechSubmitted Mar 10, 2026• Announced Mar 11, 2026• 0 citations
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Abstract

Qubits are typically reset into a known state by coupling them to a low-temperature environment. When treated in the Born-Markov approximation such couplings produce exponential relaxation to equilibrium, giving high reset fidelities limited only by temperature. We investigate qubit reset beyond this approximation, using numerically exact tensor network methods and the time-dependent variational principle, focussing on a spin-boson model describing a transmon qubit coupled to a resistor. Beyond the Born-Markov approximation the reset fidelity becomes limited by the buildup of system-environment correlations which corresponds to the formation of a polaron. We implement numerical optimal control to find time-dependent qubit Hamiltonians which overcome this limitation by steering the dynamics of the correlated system-environment state. The optimal controls becomes more effective when the environment is filtered to span a smaller spectral range, and remain effective when the multilevel nature of the transmon is considered. A related paper [C. Ortega-Taberner, E. O'Neill and P. R. Eastham, arXiv:XXXX.XXXX] addresses the complementary case of control via a time-dependent system-environment coupling. Our results show how limitations on reset speed and fidelity can be overcome, and how time-dependent driving can steer system-environment correlations and reverse polaron formation.

Comments
11 pages, 6 figures

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Qubits are typically reset into a known state by coupling them to a low-temperature environment. When treated in the Born-Markov approximation such couplings produce exponential relaxation to equilibrium, giving high reset fidelities limited only by temperature. We investigate qubit reset beyond this approximation, using numerically exact tensor network methods and the time-dependent variational principle, focussing on a spin-boson model describing a transmon qubit coupled to a resistor. Beyond the Born-Markov approximation the reset fidelity becomes limited by the buildup of system-environment correlations which corresponds to the formation of a polaron. We implement numerical optimal control to find time-dependent qubit Hamiltonians which overcome this limitation by steering the dynamics of the correlated system-environment state. The optimal controls becomes more effective when the environment is filtered to span a smaller spectral range, and remain effective when the multilevel nature of the transmon is considered. A related paper [C. Ortega-Taberner, E. O'Neill and P. R. Eastham, arXiv:XXXX.XXXX] addresses the complementary case of control via a time-dependent system-environment coupling. Our results show how limitations on reset speed and fidelity can be overcome, and how time-dependent driving can steer system-environment correlations and reverse polaron formation.
Qubit reset is crucial in quantum technology and is typically achieved by coupling the qubit to a dissipative environment. However, the achievable speed and fidelity are limited by qubit-environment entanglement. We use exact tensor-network simulations and a time-dependent variational approach to investigate these effects for transmon qubits with a time-dependent system-environment coupling. We show that they are due to the formation of a polaron state and how this can be reversed using a time-dependent coupling. Coupling protocols are identified which achieve reset with an excited-state population of 10−610^{-6}10−6 in 101010 ns. A related paper [C. Ortega-Taberner, E. O'Neill and P. R. Eastham, arXiv:XXXX.XXXX] addresses the complementary case of control via a time-dependent Hamiltonian. Our work shows how the dynamics of the environment of an open quantum system can be controlled to design effective quantum processes in non-Markovian systems.
Fast qubit reset is essential for qubit reuse in the noisy intermediate-scale quantum computing era, yet it conflicts with the weak decoherence required for high-fidelity computation. We solve the time-optimal reset problem for a frequency-tunable qubit coupled to a structural environment under realistic spectral and control constraints. The optimal strategy consists of a switch--restore--switch sequence, where the qubit is moved from a low-decoherence computational configuration to a high-decoherence restoring configuration and then returned for reuse. For superconducting qubits in four representative environments, this strategy reduces the reset time from typically $\gtrsim\SI{100}{\nano\second}$ to $\SI{20}{\nano\second}$, about 40%40\%40% of a typical two-qubit gate time, while achieving a reset precision of 10−510^{-5}10−5. Our results identify environmental spectral structure as a practical resource for rapid, high-fidelity qubit reset and provide a design principle for qubit reuse on qubit-limited processors.
We present a framework that combines the adjoint-state method together with reverse-time backpropagation to solve prohibitively large open-system quantum control problems. Our approach enables the optimization of arbitrary cost functions with fully general controls applied on large open quantum systems described by a Lindblad master equation. It is scalable, computationally efficient, and has a low-memory footprint. We apply this framework to optimize two inherently dissipative operations in superconducting qubits which lag behind in terms of fidelity and duration compared to other unitary operations: the dispersive readout and all-microwave reset of a transmon qubit. Our results show that while standard pulses for dispersive readout are nearly optimal, adding a transmon drive during the protocol can yield 2× improvements in fidelity and duration. We further demonstrate a 2× improvement in reset fidelity and duration through pulse shaping, indicating significant potential for enhancement in reset protocols. Our approach can readily be applied to optimize quantum controls in a vast range of applications such as reservoir engineering, autonomous quantum error correction, and leakage-reduction units.
While the quantum regression theorem (QRT) is the standard tool for computing multi-time correlation functions in open quantum systems, it relies on system-bath separability and an environment that remains in equilibrium, assumptions that are violated once dynamical correlations develop. Using the projection operator formalism, we derive an extension to the QRT that explicitly incorporates these correlation-induced corrections, enabling us to capture multi-time correlation functions in non-Markovian regimes. We apply this framework to the variational polaron master equation for the spin-boson model in ohmic and super-ohmic regimes, where the polaron transformation mixes system-bath degrees of freedom to produce a non-thermal effective environment. Benchmarking against numerically exact tensor-network simulations, we demonstrate quantitative agreement for single- and two-time observables, including linear-response spectra, even at strong coupling. Our approach broadens the reach of analytic master equations to multi-time observables in strong-coupling and non-Markovian regimes, where environmental memory effects and system-bath correlations are crucial.
Fast and reliable reset of a qubit is a key prerequisite for any quantum technology. For real world open quantum systems undergoing non-Markovian dynamics, reset implies not only purification, but in particular erasure of initial correlations between qubit and environment. Here, we derive optimal reset protocols using a combination of geometric and numerical control theory. For factorizing initial states, we find a lower limit for the entropy reduction of the qubit as well as a speed limit. The time-optimal solution is determined by the maximum coupling strength. Initial correlations, remarkably, allow for faster reset and smaller errors. Entanglement is not necessary.
Abstract We determine how to optimally reset a superconducting qubit which interacts with a thermal environment in such a way that the coupling strength is tunable. Describing the system in terms of a time-local master equation with time-dependent decay rates and using quantum optimal control theory, we identify temporal shapes of tunable level splittings which maximize the efficiency of the reset protocol in terms of duration and error. Time-dependent level splittings imply a modification of the system-environment coupling, varying the decay rates as well as the Lindblad operators. Our approach thus demonstrates efficient reservoir engineering employing quantum optimal control. We find the optimized reset strategy to consist in maximizing the decay rate from one state and driving non-adiabatic population transfer into this strongly decaying state.