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arXiv:1903.05059 · New Journal of Physics

Reservoir engineering using quantum optimal control for qubit reset

Daniel Basilewitsch, F. Cosco, Nicola Lo Gullo, Mikko Möttönen, Tapio Ala-Nissilä, Christiane P. Koch, Sabrina Maniscalco

Published Sep 1, 2019• 34 citations
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Abstract

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.

DOI
10.1088/1367-2630/ab41ad

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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.
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.
We analyze the efficiency of protocols for adiabatic quantum state transfer assisted by an engineered reservoir. The target dynamics is a quantum trajectory in the Hilbert space and is a fixed point of a time-dependent master equation in the limit of adiabatic dynamics. We specialize to quantum state transfer in a qubit and determine the optimal schedule for a class of time-dependent Lindblad equations. The speed limit on state transfer is extracted from a physical model of a qubit coupled to a reservoir, from which the Lindblad equation is derived in the Born-Markov limit. Our analysis shows that the resulting efficiency is comparable to the efficiency of the optimal unitary dynamics. Numerical studies indicate that reservoir-engineered protocols could outperform unitary protocols outside the regime of the Born-Markov master equation, namely, when correlations between the qubit and reservoir become relevant. Our study contributes to the theory of shortcuts to adiabaticity for open quantum systems and to the toolbox of protocols of the NISQ era.
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.
Abstract We propose an efficient qubit initialization protocol based on a dissipative environment that can be dynamically adjusted. Here, the qubit is coupled to a thermal bath through a tunable harmonic oscillator. On-demand initialization is achieved by sweeping the oscillator rapidly into resonance with the qubit. This resonant coupling with the engineered environment induces fast relaxation to the ground state of the system, and a consecutive rapid sweep back to off resonance guarantees weak excess dissipation during quantum computations. We solve the corresponding quantum dynamics using a Markovian master equation for the reduced density operator of the qubit-bath system. This allows us to optimize the parameters and the initialization protocol for the qubit. Our analytical calculations show that the ground-state occupation of our system is well protected during the fast sweeps of the environmental coupling and, consequently, we obtain an estimate for the duration of our protocol by solving the transition rates between the low-energy eigenstates with the Jacobian diagonalization method. Our results suggest that the current experimental state of the art for the initialization speed of superconducting qubits at a given fidelity can be considerably improved.
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.
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.