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Fundamental bounds on qubit reset

Daniel Basilewitsch, Jonas Fischer, Daniel M. Reich, Dominique Sugny, Christiane P. Koch

Published Jan 1, 2021• 14 citations

Abstract

Qubit reset is a key task in the operation of quantum devices which, for many quantum hardware platforms, presently limits device clock speed. While it is known that coupling the qubit to an ancilla on demand allows for the fastest qubit reset, the limits on reset accuracy and speed due to the choice of ancilla have not yet been identified-despite the great flexibility in device design for most quantum hardware platforms. Here, we derive bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. For two-level ancillas, we find a provably time-optimal protocol which consists of purity exchange between qubit and ancilla brought into resonance. The globally minimal time can only be realized for specific choices of coupling and control which we identify. When increasing the size of the ancilla Hilbert space, the maximally achievable fidelity increases, whereas the reset time remains constant. Our results translate into device design principles for realizing, in a given quantum architecture, the fastest and most accurate protocol for qubit reset.

DOI: 10.17169/refubium-30036

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Qubit reset is a key task in the operation of quantum devices which, for many quantum hardware platforms, presently limits device clock speed. While it is known that coupling the qubit to an ancilla on demand allows for the fastest qubit reset, the limits on reset accuracy and speed due to the choice of ancilla have not yet been identified-despite the great flexibility in device design for most quantum hardware platforms. Here, we derive bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. For two-level ancillas, we find a provably time-optimal protocol which consists of purity exchange between qubit and ancilla brought into resonance. The globally minimal time can only be realized for specific choices of coupling and control which we identify. When increasing the size of the ancilla Hilbert space, the maximally achievable fidelity increases, whereas the reset time remains constant. Our results translate into device design principles for realizing, in a given quantum architecture, the fastest and most accurate protocol for qubit reset.

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\%

of a typical two-qubit gate time, while achieving a reset precision of

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.

Landauer's principle shows that the minimum energy cost to reset a classical bit in a bath with temperature T is k_{B}Tln2 in the infinite time. However, the task to reset the bit in finite time has posted a new challenge, especially for quantum bit (qubit) where both the operation time and controllability are limited. We design a shortcut-to-isothermal scheme to reset a qubit in finite time τ with limited controllability. The energy cost is minimized with the optimal control scheme with and without bound. This optimal control scheme can provide a reference to realize qubit reset with minimum energy cost for the limited time.

The Landauer principle sets a lower bound on the thermodynamic cost of qubit reset, which is only attainable for the quasistatic process. In this Letter, we explore the collective advantage of qubit reset of coherent qubits in three aspects. First, for the quasistatic process, the thermodynamic cost of collective reset is remarkably lower than parallel reset because of the reduced Hilbert space dimension due to entanglement effects. Second, for the finite-time qubit reset, we prove that the error probability fades away and per-qubit heat production tends the Landauer bound for initially continuous protocols in the thermodynamic limit. Third, we show that qubit reset performance enhances with the increase in the number of qubits. Our results, illustrated by different protocols, provide a blueprint for future quantum device fabrication.

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.

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.