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arXiv:1602.06261 · New Journal of Physics

Dynamical decoupling sequences for multi-qubit dephasing suppression and long-time quantum memory

Gerardo A. Paz-Silva, Seung-Woo Lee, Todd J. Green, Lorenza Viola

Published Jul 11, 2016• 45 citations
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Abstract

We consider a class of multi-qubit dephasing models that combine classical noise sources and linear coupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical decoupling pulses. Building on a general transfer filter-function framework for open-loop control, we provide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian classical and quantum noise statistics, with analytical expressions emerging when all dephasing sources are Gaussian. This exact characterization is used to establish two main results. First, we construct multi-qubit sequences that ensure maximum high-order error suppression in both the time and frequency domain and that can be exponentially more efficient than existing ones in terms of total pulse number. Next, we show how long-time multi-qubit storage may be achieved by meeting appropriate conditions for the emergence of a fidelity plateau under sequence repetition, thereby generalizing recent results for single-qubit memory under Gaussian dephasing. In both scenarios, the key step is to endow multi-qubit sequences with a suitable displacement anti-symmetry property, which is of independent interest for applications ranging from environment-assisted entanglement generation to multi-qubit noise spectroscopy protocols.

DOI
10.1088/1367-2630/18/7/073020

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We consider a class of multi-qubit dephasing models that combine classical noise sources and linear coupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical decoupling pulses. Building on a general transfer filter-function framework for open-loop control, we provide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian classical and quantum noise statistics, with analytical expressions emerging when all dephasing sources are Gaussian. This exact characterization is used to establish two main results. First, we construct multi-qubit sequences that ensure maximum high-order error suppression in both the time and frequency domain and that can be exponentially more efficient than existing ones in terms of total pulse number. Next, we show how long-time multi-qubit storage may be achieved by meeting appropriate conditions for the emergence of a fidelity plateau under sequence repetition, thereby generalizing recent results for single-qubit memory under Gaussian dephasing. In both scenarios, the key step is to endow multi-qubit sequences with a suitable displacement anti-symmetry property, which is of independent interest for applications ranging from environment-assisted entanglement generation to multi-qubit noise spectroscopy protocols.
We introduce open-loop quantum control protocols for characterizing the spectral properties of non-Gaussian noise, applicable to both classical and quantum dephasing environments. By engineering a multidimensional frequency comb via repetition of suitably designed pulse sequences, the desired high-order spectra may be related to observable properties of the qubit probe. We prove that access to a high time resolution is key to achieving spectral reconstruction over an extended bandwidth, overcoming the limitations of existing schemes. Non-Gaussian spectroscopy is demonstrated for a classical noise model describing quadratic dephasing at an optimal point, as well as a quantum spin-boson model out of equilibrium. In both cases, we obtain spectral reconstructions that accurately predict the qubit dynamics in the non-Gaussian regime.
We present novel techniques for modelling and mitigating the effects of time-dependent noise created by interactions between a quantum system and its environment, and by errors in applied controls. Our scope encompasses quantum storage and nontrivial QIP tasks in both single- and multi-qubit systems, with a particular focus on control operations applied to trapped-ion qubits. The work begins with the introduction of a computationally efficient approach to characterizing the impact of time-dependent noise in single-qubit systems, in terms of the spectral characteristics of the noise and a set of generalized control filter functions. In conjunction with brute-force numerical simulation, we show that this novel analytical technique can used to model the evolution of a noisy single-qubit system subject to an arbitrary piecewise-constant control sequence, and to accurately predict the effects of experimentally engineered noise in single-qubit trapped ion systems. We also obtain a number of new and important results that extend the range of utility of state-preserving dynamical decoupling control sequences. These device-independent results provide a means to create a practically useful high-fidelity, long-time quantum memory in both single- and multi-qubit systems. We go on to explain how, given the freedom to arbitrarily and quasi-instantaneously change the phase of the interaction between a system of qubits and a finite collection of oscillators, frequency-specific phase modulation protocols can be implemented that decouple the qubits from targeted oscillator modes at pre-determined times. This technique can be used to generate fast, high-fidelity multi-qubit entangling operations in, for example, ion trap QIP devices.
In this paper, we study how to preserve entanglement and nonlocality under dephasing produced by classical noise with large low-frequency components, such as 1/f1/f1/f noise, using dynamical decoupling techniques. We first show that quantifiers of entanglement and nonlocality satisfy a closed relation valid for two independent qubits locally coupled to a generic environment under pure dephasing and starting from a general class of initial states. This result allows us to assess the efficiency of pulse-based dynamical decoupling for protecting nonlocal quantum correlations between two qubits subject to pure-dephasing local random telegraph and 1/f1/f1/f noise. We investigate the efficiency of an ``entanglement memory'' element under two-pulse echo and under sequences of periodic, Carr-Purcell, and Uhrig dynamical decoupling. The Carr-Purcell sequence is shown to outperform the other sequences in preserving entanglement against both random telegraph and 1/f1/f1/f noise. For typical 1/f1/f1/f flux-noise figures in superconducting nanocircuits, we show that entanglement and its nonlocal features can be efficiently stored up to times one order of magnitude longer than natural entanglement disappearance times employing pulse timings of current experimental reach.
We introduce multipulse quantum noise spectroscopy protocols for spectral estimation of the noise affecting multiple qubits coupled to Gaussian dephasing environments including both classical and quantum sources. Our protocols are capable of reconstructing all the noise auto- and cross-correlation spectra entering the multiqubit dynamics, providing access, in particular, to the asymmetric spectra associated with nonclassical environments. Our result relies on (i) an exact analytic solution for the reduced multiqubit dynamics that holds in the presence of an arbitrary Gaussian environment and dephasing-preserving control; (ii) the use of specific timing symmetries, which allow for a frequency comb to be engineered for all filter functions of interest, and for the spectra to be related to experimentally accessible observables. We show that quantum spectra have distinctive dynamical signatures, which we explore in two paradigmatic open-system models describing spin and charge qubits coupled to bosonic environments. Complete noise spectroscopy is demonstrated numerically in a realistic setting consisting of two-exciton qubits coupled to a phonon bath. The estimated spectra allow us to accurately predict the exciton dynamics as well as extract the temperature and spectral density of the quantum environment.
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.
Dynamical decoupling (DD) emerges as a promising tool to suppress decoherence of quantum systems by eliminating the system-environment coupling. We investigate its power in combating pure dephasing of a qubit under random classical noise. Interestingly, the decoherence rate can be viewed as the interplay between noise spectrum and a controllable filter function. More specifically, the filter function is determined by the DD sequence we employed. Here we take Uhrig DD (UDD) as a benchmark sequence to illustrate the filtering process. We find that UDD sequence works as a perfect dynamical filter for low-frequency noise. For spectrum with hard cutoff, UDD increases the performance order by order with linearly increased number of pulses. However, for noise spectrum with soft cutoff, the required pulse number grows exponentially.