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Optimal Clock Speed of Single-Qubit Operations

Nilanjana Chanda, Rangeet Bhattacharyya

Published Aug 1, 2019• 0 citations
OpenAlex

Abstract

Efficient implementation of quantum algorithms requires single- or multi-qubit gates with high fidelity. We use a recently reported thermal fluctuation-regulated quantum master equation to estimate the fidelity of single-qubit gates on open quantum systems. We show that the fidelity is a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves non-monotonically with the drive-amplitude. The calculated fidelity is found to have a maximum corresponding to an optimum value of the drive-amplitude. Therefore, the highest fidelity of the single-qubit operations on open quantum systems would require an optimal clock speed. The arguments are also extended to multi-qubit systems.

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Efficient implementation of quantum algorithms requires single- or multi-qubit gates with high fidelity. We use a recently reported thermal fluctuation-regulated quantum master equation to estimate the fidelity of single-qubit gates on open quantum systems. We show that the fidelity is a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves non-monotonically with the drive-amplitude. The calculated fidelity is found to have a maximum corresponding to an optimum value of the drive-amplitude. Therefore, the highest fidelity of the single-qubit operations on open quantum systems would require an optimal clock speed. The arguments are also extended to multi-qubit systems.
Efficient implementation of quantum algorithms requires single- or multiple-qubit gates with high fidelity. Here we report that the fidelity of gate operations on open quantum systems has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To demonstrate this, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The fidelity is found to be a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves nonmonotonically with the drive amplitude. The existence of an optimum drive amplitude implies that the qubit gate operations on open quantum systems would have an optimal clock speed. We demonstrate the universality of the results for the gate operations on single- and multiple-qubit gates.
We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.
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.
Quantum communications require efficient implementations of quantum state transportation with high fidelity. Here, we consider the transport of entanglement along a chain of qubits. A series of SWAP operations involving successive pairs of qubits can transport entanglement along the chain. We report that the fidelity of the abovementioned gate has a maximum value corresponding to an optimum value of the drive amplitude in the presence of drive-induced decoherence. To incorporate environmental effect, we use a previously reported fluctuation-regulated quantum master equation [A. Chakrabarti and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The existence of an optimum drive amplitude implies that these series of SWAP operations on open quantum systems would have an optimal transfer speed of the entanglement.
An efficient optimal-control theory based on the Krotov method is introduced for a non-Markovian open quantum system with a time-nonlocal master equation in which the control parameter and the bath correlation function are correlated. This optimal-control method is developed via a quantum dissipation formulation that transforms the time-nonlocal master equation to a set of coupled linear time-local equations of motion in an extended auxiliary Liouville space. As an illustration, the optimal-control method is applied to find the control sequences for high-fidelity ZZZ gates and identity gates of a qubit embedded in a non-Markovian bath. ZZZ gates and identity gates with errors less than ${10}^{\ensuremath{-}5}$ for a wide range of bath decoherence parameters can be achieved for the non-Markovian open qubit system with control over only the ${\ensuremath{\sigma}}_{z}$ term. The control-dissipation correlation and the memory effect of the bath are crucial in achieving the high-fidelity gates.
Quantum gates based on resonant Rabi oscillations are inherently slow for small-frequency qubits. They are also prone to errors due to counter-rotating terms. However, when the anharmonicity is sufficiently high, as in the fluxonium architecture, alternative manipulation protocols can outperform standard resonant driving. In this work, we implement fast, high-fidelity quantum gates based on a one-period Landau-Zener-Stückelberg-Majorana (LZSM) driving protocol. We derive analytical expressions that simplify the exploration of the parameter space while accounting for the multi-level structure of the circuit. Furthermore, we analyze the role of leakage, discussing strategies to mitigate it and identifying regimes in which it becomes the dominant source of error. Finally, to evaluate the impact of dissipation on gate fidelity, we develop a robust formalism suitable for analyzing the open-system performance of quantum gates in the strong driving regime.