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arXiv:1904.07225 · npj Quantum Information

Adaptive characterization of spatially inhomogeneous fields and errors in qubit registers

Riddhi Swaroop Gupta, Claire Edmunds, Alistair R. Milne, Cornelius Hempel, Michael J. Biercuk

Published Jun 12, 2020• 13 citations
arXivHTMLPDF

Abstract

Abstract New quantum computing architectures consider integrating qubits as sensors to provide actionable information useful for calibration or decoherence mitigation on neighboring data qubits, but little work has addressed how such schemes may be efficiently implemented in order to maximize information utilization. Techniques from classical estimation and dynamic control, suitably adapted to the strictures of quantum measurement, provide an opportunity to extract augmented hardware performance through automation of low-level characterization and control. In this work, we present an adaptive learning framework, Noise Mapping for Quantum Architectures (NMQA), for scheduling of sensor–qubit measurements and efficient spatial noise mapping (prior to actuation) across device architectures. Via a two-layer particle filter, NMQA receives binary measurements and determines regions within the architecture that share common noise processes; an adaptive controller then schedules future measurements to reduce map uncertainty. Numerical analysis and experiments on an array of trapped ytterbium ions demonstrate that NMQA outperforms brute-force mapping by up to 20× (3×) in simulations (experiments), calculated as a reduction in the number of measurements required to map a spatially inhomogeneous magnetic field with a target error metric. As an early adaptation of robotic control to quantum devices, this work opens up exciting new avenues in quantum computer science.

DOI
10.1038/s41534-020-0286-0

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Decoherence remains a major challenge in Near term, Intermediate scale Noisy Quantum (NISQ) computers. This thesis proposes techniques for characterizing classical noise correlations and performance variations in NISQ devices using single-qubit projective measurements. The central tasks of qubit state estimation and prediction are considered for measurements that are either temporally or spatially correlated. Firstly, this thesis focuses on timeseries prediction for single-qubit measurement outcomes. Focusing on repeated Ramsey measurements performed on a single qubit subject to temporally correlated dephasing, the key challenge is to predict qubit state dynamics by learning temporal noise correlations in a real-time stream of incoming measurements. Autoregressive or Fourier-based Kalman Filtering (KF) protocols are investigated for maximizing the forward prediction horizon and autoregressive approaches demonstrate superior predictive capabilities. Secondly, this thesis investigates the utility of nonlinear stochastic methods to characterize quantum systems using spatially correlated single-qubit projective measurements, via particle filters. A novel likelihood function is presented and incorporated into conventional particle filters. An adaptive procedure, `NMQA', is proposed to characterize a spatially inhomogeneous dephasing field in 2D by allocating measurements on a multi-qubit array. NMQA outperforms brute-force mapping in simulations and using experimental data. Finally, spatial prediction in 2D is compared with bivariate interpolation on a geometric arrangement of points known as the Padua points. By measuring a spatially inhomogeneous dephasing field on dedicated `sensor qubits', the objective is to predict the value of the field on unmeasured, proximal `data qubits'. The number and arrangement of sensor qubits relative to a fixed lattice of data qubits is investigated, providing insights for a general purpose predictive mapping protocol.
Abstract Quantum Error Mitigation (QEM) enables the extraction of high-quality results from the presently-available noisy quantum computers. In this approach, the effect of the noise on observables of interest can be mitigated using multiple measurements without additional hardware overhead. Unfortunately, current QEM techniques are limited to weak noise or lack scalability. In this work, we introduce a QEM method termed ‘Adaptive KIK’ that adapts to the noise level of the target device, and therefore, can handle moderate-to-strong noise. The implementation of the method is experimentally simple — it does not involve any tomographic information or machine-learning stage, and the number of different quantum circuits to be implemented is independent of the size of the system. Furthermore, we have shown that it can be successfully integrated with randomized compiling for handling both incoherent as well as coherent noise. Our method handles spatially correlated and time-dependent noise which enables us to run shots over the scale of days or more despite the fact that noise and calibrations change in time. Finally, we discuss and demonstrate why our results suggest that gate calibration protocols should be revised when using QEM. We demonstrate our findings in the IBM quantum computers and through numerical simulations.