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arXiv:1608.04292 · Physical Review A

Spectral investigation of the noise influencing multiqubit states

Deepak Khurana, Govind Unnikrishnan, T. S. Mahesh

Published Dec 27, 2016• 11 citations
arXivHTMLPDF

Abstract

Characterizing and understanding noise affecting quantum states has immense benefits in spectroscopy as well as in realizing quantum devices. Transverse relaxation times under a set of dynamical decoupling (DD) sequences with varying interpulse delays were earlier used for obtaining the noise spectral densities of single-qubit coherences. In this work, using a pair of homonuclear spins and NMR techniques, we experimentally characterize noise in certain decoherence-free subspaces. We also explore the noise of similar states in a heteronuclear spin pair. Further, using a 10-qubit system, we investigate noise profiles of various multiqubit coherences and study the scaling of noise with respect to the coherence order. Finally, using the experimentally obtained noise spectrum of the 10-qubit NOON state, we predict the performance of a Uhrig DD sequence and verify it experimentally.

DOI
10.1103/physreva.94.062334

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Characterizing and understanding noise affecting quantum states has immense benefits in spectroscopy as well as in realizing quantum devices. Transverse relaxation times under a set of dynamical decoupling (DD) sequences with varying interpulse delays were earlier used for obtaining the noise spectral densities of single-qubit coherences. In this work, using a pair of homonuclear spins and NMR techniques, we experimentally characterize noise in certain decoherence-free subspaces. We also explore the noise of similar states in a heteronuclear spin pair. Further, using a 10-qubit system, we investigate noise profiles of various multiqubit coherences and study the scaling of noise with respect to the coherence order. Finally, using the experimentally obtained noise spectrum of the 10-qubit NOON state, we predict the performance of a Uhrig DD sequence and verify it experimentally.
One of the simplest and least resource-intensive methods to suppress decoherence for qubit operations, namely, dynamical decoupling (DD), is investigated for a broad range of realistic noise sources with time-retarded feedback. By way of example, the Carr-Purcell-Meiboom-Gill sequence is analyzed in a numerically rigorous manner accounting also for correlations between qubits and environments. Since experimentally noise sources are characterized through spectral densities, we adopt the spin-boson model as a suitable framework to describe the qubit dynamics under DD for a given spectral density J ( ω ) ∝ ω s . Motivated by the situation for superconducting qubits, the spectral exponent s is varied from s = 1 (Ohmic bath) to a substantially small value 0 < s ≪ 1 (deep sub-Ohmic bath), in order to investigate the impact of time-nonlocal back action on DD performances for enhanced coherence times. As reference to the DD schemes, dynamics of a single qubit subject to Ramsey sequences without any pules and Hahn echo sequences are also investigated.
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.
Decoherence induced by laser frequency noise is one of the most important obstacles in quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to $(2\ensuremath{\pi})530$ kHz by monitoring the transverse relaxation from an initial state +X+X+X, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by encoding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth is assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise.
Abstract Dynamical decoupling (DD) is a quantum error-mitigation technique based on applying sequences of control pulses to suppress decoherence. Here we perform a numerical study to compare different DD protocols, namely Carr-Purcell-Meiboom-Gill (CPMG), Periodic Dynamical Decoupling (PDD), Concatenated Dynamical Decoupling (CDD) and Uhrig Dynamical Decoupling (UDD) applied to three commonly used noise power spectral densities: (i) white, (ii) 1/f, (iii) 1/f 2 and their hybrid combinations. By ignoring qubit relaxation, we simulate these protocols focusing purely on dephasing noise. We then consider independent multi-axial noise with uniaxial control pulses. The effective coherence times T2,eff are extracted for each case and compared with the baseline free induction decay T ∗ 2 [6]. In all these simulations, the time-domain decoherence profiles follow a stretched exponential form ∼ exp −(t/T2,eff) β with the effective coherence times dependent on the noise spectrum considered, the strength of the noise, and the DD sequence employed. An exception is observed for the UDD under specific noise conditions where it cannot be described by a simple stretched exponential decay form.
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral density at many different frequencies. Here we describe an alternative approach to noise spectroscopy, which requires fewer resources, and relies on direct measurement of arbitrary linear functionals of the noise spectral density. This method uses random pulse sequences with carefully controlled correlations, which are chosen using algorithms for phase retrieval. These measurements allow us to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum, compared to conventional dynamical decoupling approaches.
Characterizing and understanding the environment affecting quantum systems is critical to elucidate its physical properties and engineer better quantum devices. We develop an approach to reduce the quantum environment causing single-qubit dephasing to a simple yet predictive noise model. Our approach, inspired by quantum noise spectroscopy, is to define a ``self-consistent'' classical noise spectrum, that is, compatible with all observed decoherence under various qubit dynamics. We demonstrate the power and limits of our approach by characterizing, with nanoscale spatial resolution, the noise experienced by two electronic spins in diamond that, despite their proximity, surprisingly reveal the presence of a complex quantum spin environment, both classically reducible and not. Our results overcome the limitations of existing noise spectroscopy methods and highlight the importance of finding predictive models to accurately characterize the underlying environment. Extending our work to multiqubit systems would enable spatially resolved quantum sensing of complex environments and quantum device characterization, notably to identify correlated noise between qubits, which is crucial for practical realization of quantum error correction.