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Convergence analysis for autonomous adaptive learning applied to quantum architectures

Riddhi Swaroop Gupta, Michael J. Biercuk

Published Nov 13, 2019• 1 citation
OpenAlex

Abstract

We present a formal analysis and convergence proofs for an autonomous adaptive learning algorithm useful for the tuneup and stabilization of quantum computing architectures. We focus on the specific application of spatial noise mapping in a spectator qubit paradigm, in which these qubits act as sensors to provide information useful for decoherence mitigation on proximal data qubits. In earlier work, the authors introduced and experimentally demonstrated this framework, Noise Mapping for Quantum Architectures (NMQA), as applied in autonomous adaptive scheduling of sensor-qubit measurements across multi-qubit architectures. This methodology has several unique features: a classical measurement model that incorporates discretized single-qubit projective measurements, and a two-layered particle filtering structure to facilitate adaptive information sharing between qubits in small spatial regions. In this work, we formalize the NMQA problem definition and build direct links to conventional non-linear filtering theory. Taking into account NMQA's departure from existing literature, we show that NMQA satisfies axioms of theorems for asymptotic convergence in specific parameter regimes. Outside of these parameter regimes, we augment our theoretical analysis with numerical studies to estimate rates of convergence for NMQA. We find that these numerical estimates match our theoretical expectations for a variety of physical configurations. Our work ensures that the methodology encapsulated by NMQA permits comparative analysis with existing filtering techniques in the literature, while highlighting unique directions for future automation of quantum computer tuneup, calibration, and stabilization.

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We present a formal analysis and convergence proofs for an autonomous adaptive learning algorithm useful for the tuneup and stabilization of quantum computing architectures. We focus on the specific application of spatial noise mapping in a spectator qubit paradigm, in which these qubits act as sensors to provide information useful for decoherence mitigation on proximal data qubits. In earlier work, the authors introduced and experimentally demonstrated this framework, Noise Mapping for Quantum Architectures (NMQA), as applied in autonomous adaptive scheduling of sensor-qubit measurements across multi-qubit architectures. This methodology has several unique features: a classical measurement model that incorporates discretized single-qubit projective measurements, and a two-layered particle filtering structure to facilitate adaptive information sharing between qubits in small spatial regions. In this work, we formalize the NMQA problem definition and build direct links to conventional non-linear filtering theory. Taking into account NMQA's departure from existing literature, we show that NMQA satisfies axioms of theorems for asymptotic convergence in specific parameter regimes. Outside of these parameter regimes, we augment our theoretical analysis with numerical studies to estimate rates of convergence for NMQA. We find that these numerical estimates match our theoretical expectations for a variety of physical configurations. Our work ensures that the methodology encapsulated by NMQA permits comparative analysis with existing filtering techniques in the literature, while highlighting unique directions for future automation of quantum computer tuneup, calibration, and stabilization.
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.
New quantum computing architectures consider integrating qubits as sensors to provide actionable information useful for decoherence mitigation on neighboring data qubits. Little work has addressed how such schemes may be efficiently implemented in order to maximize information utilization when noise fields possess long-range correlations. We present an autonomous learning framework, Quantum Simultaneous Localization and Mapping (QSLAM), for adaptive scheduling of sensor-qubit measurements and efficient (in measurement number and time) spatial noise mapping across device architectures. Via a two-layer particle filter, QSLAM 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 QSLAM outperforms brute-force mapping by up-to 181818x (333x) in simulations (experiments), calculated as a reduction in the number of measurements required to map a spatially inhomogeneous magnetic field with a target fidelity. As an early adaptation of robotic control to quantum devices, this work opens up exciting new avenues in quantum computer science.
Performing efficient quantum computer tune-up and calibration is essential for growth in system complexity. In this work we explore the link between facilitating such capabilities and the underlying architecture of the physical hardware. We focus on the specific challenge of measuring (``mapping'') spatially inhomogeneous quasistatic calibration errors using spectator qubits dedicated to the task of sensing and calibration. We introduce an architectural concept for such spectator qubits: arranging them spatially according to prescriptions from optimal two-dimensional approximation theory. We show that this insight allows for efficient reconstruction of inhomogeneities in qubit calibration, focusing on the specific example of frequency errors which may arise from fabrication variances or ambient magnetic fields. Our results demonstrate that optimal interpolation techniques display near optimal error scaling in cases where the measured characteristic (here the qubit frequency) varies smoothly, and we probe the limits of these benefits as a function of measurement uncertainty. For more complex spatial variations, we demonstrate that the noise mapping for quantum architectures formalism for adaptive measurement and noise filtering outperforms optimal interpolation techniques in isolation and, crucially, can be combined with insights from optimal interpolation theory to produce a general purpose protocol.
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.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
The execution of Variational Quantum Algorithms on Noisy Intermediate-Scale Quantum hardware is severely impacted by hardware noise variations over time and decoherence. This work introduces an Adaptive Noise-Aware Variational Quantum Classifier (ANAVQC) that integrates Zero-Noise Extrapolation (ZNE) dynamically into the training loop to counter variations. The framework approximates the instantaneous depolarizing noise from calibration and adapts noise scaling and linear extrapolation to estimate noise-free expectation values at training. A two-qubit parameterized quantum circuit is built and simulated in MATLAB, with the inclusion of stochastic gradient descent coupled with parameter-shift-based gradients. The model is conditioned on a synthetic binary classification data under a time-varying depolarizing noise profile and exhibits improved convergence stability and classification accuracy over non-adaptive methods. The simulation results identify that adaptive ZNE increases model robustness against time-varying noise and offers a scalable route to reliable quantum machine learning on practical NISQ hardware. The current ANAVQC scheme is extendable to multi-qubit platforms and practical quantum backends for the purposes of future experimental testing.