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The European Physical Journal B

Implementation of one-qubit gates using optimal control theory for a dissipative system

Hamza Jirari

Published Oct 1, 2021• 5 citations
Publisher
DOI
10.1140/epjb/s10051-021-00221-9

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Based on the exact non-Markovian master equation for two interacting two-level atoms coupled to a dissipative zero-temperature bonsonic environment, we extend the results of Tai [Phys. Rev. A 89, 062310 (2014)], in which optimal control approach is used to implement one-qubit gates within the same environment, to two-qubit gate implementations with the help of Krotov's iterative method for optimal control. Furthermore, for practical applications, the realization of a quantum circuit comprising cascaded quantum gates is considered.
Quantum systems are inherently sensitive to environmental noise and imperfections in external control fields, which pose a significant challenge for the practical implementation of quantum technologies. These noise sources degrade the fidelity of quantum gates, making their mitigation a key requirement for realizing reliable quantum computing. In this study, we apply Optimal Control Theory (OCT) within a thermodynamically consistent Markovian framework to design high-fidelity quantum gates in the presence of thermal relaxation. Such a description is essential for realistic modeling and optimization of noisy quantum gates in near-term quantum technologies, where strong control fields and thermal environments act simultaneously. Our approach combines OCT with a control-dependent dissipative generator derived from the non-adiabatic master equation framework based on time-dependent invariants of the free evolution. As a result, the driving fields modify both the unitary and dissipative parts of the evolution. We implement the scheme for one- and two-qubit gates embedded in larger Hilbert spaces and compare direct-control and ancilla-assisted architectures. Using logical-subspace-resolved diagnostics, we quantify how the optimized dynamics redistributes the dissipative action between logical and ancillary sectors in the model systems studied here. In particular, we show that ancilla-assisted control can reduce the effective thermal-noise burden on the logical subspace in the relevant parameter regime, while direct control remains the most effective route when available. High-precision propagation of the full open-system dynamics reveals substantial fidelity improvements, in some cases by orders of magnitude, while clarifying the limits of mitigation at large relaxation rates and temperatures.
Superconducting circuits are one of the leading architectures in quantum computing. To undertake quantum computing one must be able to perform quantum gates; however, two-qubit gates are still limited in fidelity and gate time. The cross-resonance gate is a two-qubit gate that uses direct microwave drives and has seen much success in its implementation; but, there are theoretical indications that it has not yet reached the coherence limited fidelity value and its gate time is still relatively long compared with other quantum gate methods. Quantum optimal control theory is a powerful tool in the design of controls for quantum operations and has shown the capability to improve gate fidelities and reduce gate times. Robust quantum optimal control methodologies have further built on this to develop high fidelity quantum gates that are robust to uncertainties and noise in the system. In this thesis we use robust quantum optimal control theory to achieve these goals for the cross-resonance gate in a variety of superconducting qubit architectures. First, we investigate two superconducting qubits embedded in a common 3D microwave cavity in which the control drive is implemented via the common cavity mode of the cavity. We determine pulse shapes that implement the cross-resonance gate that are robust to uncertainty in the qubit transition frequencies for both a strictly two-level superconducting qubit and a three-level qubit. Second, we look at the cross-resonance gate with direct drives on each qubit, finding the minimal time to perform the cross-resonance gate with pulses that are robust to uncertainty in a measured system parameter for three cases: two three-level qubits with no drive crosstalk, two three-level qubits with some drive crosstalk, and two two-level qubits. Lastly, we report on simulations undertaken towards implementing a robust, high fidelity cross-resonance gate in a novel superconducting quantum device known as the coaxmon.