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arXiv:1101.0890

Suppressing non-Markovian noises by coupling the qubit to a chaotic device

Jing Zhang, Yu-xi Liu, Wei-Min Zhang, Re-Bing Wu, Tzyh‐Jong Tarn

Published Jan 5, 2011• 0 citations
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Abstract

To suppress decoherence of solid-state qubits which are coupled to the non-Markovian noises, we propose a strategy to couple the qubit with a chaotic device, of which the broad power distribution in the high-frequency domain can be used to freeze the noises just like the dynamical decoupling control (DDC) method. Compared with the DDC, high-frequency components can be generated by the chaotic device even driven by a low-frequency field and we do not need to optimize the control fields to generate complex control pulses. As an application to superconducting circuits, we find that various noises in a wide frequency domain, including low-frequency $1/f$, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator, and the decoherence rate of the qubit is efficiently decreased for about 100 times in magnitude.

DOI
10.48550/arxiv.1101.0890

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To suppress decoherence of solid-state qubits which are coupled to the non-Markovian noises, we propose a strategy to couple the qubit with a chaotic device, of which the broad power distribution in the high-frequency domain can be used to freeze the noises just like the dynamical decoupling control (DDC) method. Compared with the DDC, high-frequency components can be generated by the chaotic device even driven by a low-frequency field and we do not need to optimize the control fields to generate complex control pulses. As an application to superconducting circuits, we find that various noises in a wide frequency domain, including low-frequency 1/f1/f1/f, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator, and the decoherence rate of the qubit is efficiently decreased for about 100 times in magnitude.
To suppress decoherence of solid-state qubits induced by non-Markovian noises, we propose a strategy to couple the qubit with a chaotic device, whose broad power distribution in the high-frequency domain can be used to freeze the noises in the similar way of the dynamical decoupling control (DDC) method. Compared with the DDC, high-frequency components can be generated by the chaotic device even driven by a low-frequency field and thus the control fields do not need any optimization. Thus, our method is easier to be realized in experiments. As an application to superconducting circuits, we find that various noises in a broad band, including low-frequency 1/ƒ, high-frequency Ohmic, sub-Ohmic, and super-Ohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator, and the decoherence rate of the qubit is efficiently decreased by about 100 times in magnitude. Using experimentally realizable parameters, the decoherence time of the superconducting charge qubit can reach 200 µs by our method, which is 10 ∼ 100 times longer in magnitude than that observed in experiments.
We propose a strategy to suppress non-Markovian decoherence of a qubit by coupling the qubit to a deterministic chaotic setup with the broad power distribution in particular in the high-frequency domain. Although it is widely believed that chaos induces decoherence, we find, surprisingly, that the unitary dynamics induced by the chaotic setup can be helpful for the decoherence suppression. Compared with the existing decoherence control methods such as the usual dynamical decoupling, we do not need to impose high-frequency controls, because the high-frequency components in our method are generated by the chaotic setup, and the design of complex optimized control pulses used in the modified dynamical decoupling approaches is also not necessary. Using superconducting quantum circuits as an example, we demonstrate how to realize our general method. We find that various noises in a wide frequency domain, including low-frequency 1/f1/f1/f, high-frequency ohmic, subohmic, and superohmic noises, can be efficiently suppressed by coupling the qubit to a Duffing oscillator acting as the chaotic setup. Significantly, the decoherence time of the qubit is prolonged approximately 100 times in magnitude.
The application of dynamical decoupling pulses to a single qubit interacting with a linear harmonic oscillator bath with 1/f1/f1/f (more generally, strong low-frequency) spectral density is studied, and compared to the Ohmic case. Decoupling pulses that are slower than the fastest bath time scale are shown to drastically reduce the decoherence rate in the 1/f1/f1/f case. Contrary to conclusions drawn from previous studies, this shows that dynamical decoupling pulses do not always have to be ultrafast. Our results explain the recent experiment in which dephasing due to 1/f1/f1/f charge noise affecting a charge qubit in a small superconducting electrode was successfully suppressed using spin-echo-type gate-voltage pulses.
We investigate the capability of dynamical decoupling techniques to reduce decoherence from a realistic environment generating 1/f noise. The predominance of low frequency modes in the noise profile allows for decoherence scenarios where relatively slow control rates suffice for a drastic improvement. However, the actual figure of merit is very sensitive to the details of the dynamics, with decoupling performance which may deteriorate for non-Gaussian noise and/or high frequency working points. Our results are promising for robust solid-state qubits and beyond.
We address the experimentally relevant problem of robust mitigation of dephasing noise acting on a qubit. We first present an extension of the method of Kuopanportti et al. [Phys. Rev. A 77, 032334 (2008)] for representing $1/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$ noise to the efficient representation of arbitrary Markovian noise. We then add qubit control pulses to enable the design of numerically optimized, two-dimensional, bounded amplitude control functions capable of decoupling the qubit from the dephasing effects of a broad variety of Markovian noise spectral densities during one- and two-qubit quantum operations. We illustrate the method with development of numerically optimized control pulse sequences that minimize decoherence due to a combination of $1/\ensuremath{\omega}$ and constant-offset noise sources. Comparison with the performance of standard dynamical decoupling protocols shows that the numerically optimized pulse sequences are considerably more robust with respect to zero-frequency noise. Application to the mitigation of dephasing noise on spin qubits in silicon indicates that high-fidelity quantum gates may, in principle, be implemented for such qubits with the assistance of current pulse-generation technology.
Theoretically understanding and experimentally characterizing and modifying the underlying Hamiltonian of a quantum system is of utmost importance in achieving high-fidelity quantum gates for quantum computing. In this work, we explore the use of dynamical decoupling (DD) in characterizing and suppressing undesired two-qubit couplings as well as the underlying single-qubit decoherence, both significant hurdles to achieving precise quantum control and realizing quantum computing on many hardware prototypes. Through discrete search of DD sequences, we identify sequences that protect against decoherence and selectively target unwanted two-qubit interactions of general form. On a transmon-qubit-based superconducting quantum device, we identify separate white and 1/f1/f1/f noise components underlying the single-qubit decoherence and a static ZZ coupling between pairs of qubits. A family of syncopated DD sequences is found and their efficiency is demonstrated in two-qubit benchmarking experiments. The syncopated decoupling technique significantly boosts performance in a realistic algorithmic quantum circuit.