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arXiv:2408.00119 · Academia quantum.

Pulse family optimization for parameterized quantum gates using spectral clustering

Robert de Keijzer, Jurgen Snijders, Andre R. R. Carvalho, S. J. J. M. F. Kokkelmans

Published Oct 23, 2024• 4 citations
arXivHTMLPDF

Abstract

Parameterized gate circuits are used in many applications in the current Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing. These parameterized gates are mainly implemented using analytically found pulse protocols, often yielding suboptimal gate times, and consequently, fidelities. Alternatively, gate optimization algorithms are designed to construct high-fidelity pulses for individual fixed points in a continuous parameter space. Gates for intermediate parameters can subsequently be found by some form of interpolation between previously constructed pulses. Nevertheless, it is not guaranteed (as with analytic protocols) that the pulses found by the optimization algorithms belong to the same family of solutions and thus resemble each other. Interpolation of two pulses from different solution families often leads to high infidelities, as the pulse strays away from the minimum in the parameter/fidelity landscape. This work introduces a spectral clustering method to sort high-fidelity, optimized pulses in families and interpolate solely between pulses of the same family. Accordingly, interpolations will always approach maximal fidelity. Furthermore, as more than one pulse family is constructed, the parameter space can be partitioned, and according to this partition, a family prevails fidelity-wise. This work provides a meticulous demonstration of our constitutive continuous gate family construction by applying it to a universal gate set for Rydberg and Cat qubits under noise.

DOI
10.20935/acadquant7374

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Parameterized gate circuits are used in many applications in the current Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing. These parameterized gates are mainly implemented using analytically found pulse protocols, often yielding suboptimal gate times, and consequently, fidelities. Alternatively, gate optimization algorithms are designed to construct high-fidelity pulses for individual fixed points in a continuous parameter space. Gates for intermediate parameters can subsequently be found by some form of interpolation between previously constructed pulses. Nevertheless, it is not guaranteed (as with analytic protocols) that the pulses found by the optimization algorithms belong to the same family of solutions and thus resemble each other. Interpolation of two pulses from different solution families often leads to high infidelities, as the pulse strays away from the minimum in the parameter/fidelity landscape. This work introduces a spectral clustering method to sort high-fidelity, optimized pulses in families and interpolate solely between pulses of the same family. Accordingly, interpolations will always approach maximal fidelity. Furthermore, as more than one pulse family is constructed, the parameter space can be partitioned, and according to this partition, a family prevails fidelity-wise. This work provides a meticulous demonstration of our constitutive continuous gate family construction by applying it to a universal gate set for Rydberg and Cat qubits under noise.
We present a general method to quickly generate high-fidelity control pulses for any continuously-parameterized set of quantum gates after calibrating a small number of reference pulses. We find that interpolating between optimized control pulses for different quantum operations does not immediately yield a high-fidelity intermediate operation. To solve this problem, we propose a method to optimize control pulses specifically to provide good interpolations. We pick several reference operations in the gate family of interest and optimize pulses that implement these operations, then iteratively re-optimize the pulses to guide their shapes to be similar for operations that are closely related. Once this set of reference pulses is calibrated, we can use a straightforward linear interpolation method to instantly obtain high-fidelity pulses for arbitrary gates in the continuous operation space. We demonstrate this procedure on the three-parameter Cartan decomposition of two-qubit gates to obtain control pulses for any arbitrary two-qubit gate (up to single-qubit operations) with consistently high fidelity. Compared to previous neural network approaches, the method is 7.7x more computationally efficient to calibrate the pulse space for the set of all single-qubit gates. Our technique generalizes to any number of gate parameters and could easily be used with advanced pulse optimization algorithms to allow for better translation from simulation to experiment.
Control synthesis for continuously-parameterized families of quantum gates can enable critical advantages for mid-sized quantum computing applications in advance of fault-tolerance. We combine quantum optimal control with physics-informed machine learning to efficiently synthesize control surfaces that interpolate among continuously-parameterized gate families. Using optimal control as an active learning strategy to guide pretraining, we bootstrap a physics-informed neural network to achieve rapid convergence to nonlinear control surfaces sufficient for our desired gates. We find our approach is critical for enabling an expressiveness beyond linear interpolation, which is important in cases of hard quantum control. We show in simulation that by adapting our pretraining to use a few reference pulse calibrations, we can apply transfer learning to quickly calibrate our learned control surfaces when devices fluctuate over time. We demonstrate synthesis for one and two qubit gates with one or two parameters, focusing on gate families for variational quantum algorithm (VQA) ansatz. By avoiding the inefficient decomposition of VQA ansatz into basis gate sets, continuous gate families are a potential method to improve the noise robustness of VQAs in the near term. Our framework shows how accessible optimal control tools can be combined with simple machine learning to enable practitioners to achieve 3x speedups for their algorithms by going beyond the standard gate sets.
Control synthesis for continuously-parameterized families of quantum gates can enable critical advantages for mid-sized quantum computing applications in advance of fault-tolerance. We combine quantum optimal control with physics-informed machine learning to efficiently synthesize control surfaces that interpolate among continuously-parameterized gate families. Using optimal control as an active learning strategy to guide pretraining, we bootstrap a physics-informed neural network to achieve rapid convergence to nonlinear control surfaces sufficient for our desired gates. We find our approach is critical for enabling an expressiveness beyond linear interpolation, which is important in cases of hard quantum control. We show in simulation that by adapting our pretraining to use a few reference pulse calibrations, we can apply transfer learning to quickly calibrate our learned control surfaces when devices fluctuate over time. We demonstrate synthesis for one and two qubit gates with one or two parameters, focusing on gate families for variational quantum algorithm (VQA) ansatz. By avoiding the inefficient decomposition of VQA ansatz into basis gate sets, continuous gate families are a potential method to improve the noise robustness of VQAs in the near term. Our framework shows how accessible optimal control tools can be combined with simple machine learning to enable practitioners to achieve 3x speedups for their algorithms by going beyond the standard gate sets.
ABSTRACT: Recent research has tackled the problem of mitigating noise present in quantum computers in the Noisy Intermediate-Scale Quantum (NISQ) era to enable precise computations and to benefit from the intrinsic properties of quantum mechanics. For this matter, an important task is the characterization of qubits available in quantum devices so as to provide insights on how to reduce noise on the final output of a quantum circuit. Characterization comprises analysis of noise sources and this information can be used to reduce noise with methods such as Cycle Benchmarking, Quantum Error Mitigation, Quantum Error Correction and others. Here, we study optimization of pulses through Quantum Optimal Control (QOC) to obtain higher gate fidelity. We will explore an algorithm that performs calibration on specific quantum gates by implementing optimized pulse schedules to subsequently use the algorithm for analysis of noise sources. Using calibrated gates as input, several benchmarking protocols, including pulse noise extrapolation, leakage analysis from quantum optimal control, and machine learning based classification of qubit readout, will be tested to extract precise information on how noise influences the analyzed qubits. We will explain and discuss different techniques for obtaining properties of qubits and quantum computers. We will implement state discrimination with a Machine Learning (ML) focus to analyze readout errors caused by factors such as cross-talk and leakage into higher quantum states. We will perform noise fitting of optimized pulses and evaluate the effectiveness of important quantum algorithms at the pulse level.
In the near-term noisy intermediate-scale quantum (NISQ) era, high noise will significantly reduce the fidelity of quantum computing. What's worse, recent works reveal that the noise on quantum devices is not stable, that is, the noise is dynamically changing over time. This leads to an imminent challenging problem: At run-time, is there a way to efficiently achieve a consistent high-fidelity quantum system on unstable devices? To study this problem, we take quantum learning (a.k.a., variational quantum algorithm) as a vehicle, which has a wide range of applications, such as combinatorial optimization and machine learning. A straightforward approach is to optimize a variational quantum circuit (VQC) with a parameter-shift approach on the target quantum device before using it; however, the optimization has an extremely high time cost, which is not practical at run-time. To address the pressing issue, in this paper, we proposed a novel quantum pulse-based noise adaptation framework, namely QuPAD. In the proposed framework, first, we identify that the CNOT gate is the fidelity bottleneck of the conventional VQC, and we employ a more robust parameterized multi-qubit gate (i.e., Rzx gate) to replace CNOT gate. Second, by benchmarking Rzx gate with different parameters, we build a fitting function for each coupling qubit pair, such that the deviation between the theoretic output of Rzx gate and its on-device output under a given pulse amplitude and duration can be efficiently predicted. On top of this, an evolutionary algorithm is devised to identify the pulse amplitude and duration of each Rzx gate (i.e., calibration) and find the quantum circuits with high fidelity. Experiments show that the runtime on quantum devices of QuPAD with 8–10 qubits is less than 15 minutes, which is up to 270 x faster than the parameter-shift approach. In addition, compared to the vanilla VQC as a baseline, QuPAD can achieve 59.33% accuracy gain on a classification task, and average 66.34% closer to ground state energy for molecular simulation.
The performance of quantum processors in the noisy intermediate-scale quantum (NISQ) era is severely constrained by environmental noise and other uncertainties. While the recently proposed quantum control robustness landscape (QCRL) offers a powerful framework for generating robust control pulses for parametric gate families, its application has been practically restricted to quasi-static noise. To address the spectrally complex, time-varying noise prevalent in reality, we propose filter function-enhanced QCRL (FF-QCRL), which integrates filter function formalism into the QCRL framework. The resulting FF-QCRL algorithm minimizes a generalized robustness metric that faithfully encodes the impact of stochastic processes, enabling robust pulse-family generation for parametric gates under realistic time-varying noise. Numerical validation in a representative single-qubit setting confirms the effectiveness of the proposed method.