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Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers

Alejandro Perdomo-Ortiz, Marcello Benedetti, John Realpe-Gómez, Rupak Biswas

arXiv:1708.09757v2quant-phcs.ET

TL;DR

The paper addresses the disconnect between quantum ML proposals, practitioner needs, and near-term hardware capabilities. It proposes targeting difficult generative-learning tasks and quantum-like datasets with hybrid quantum-classical methods, illustrated through the QAHM framework. The paper reports a cognitive-science example where a quantum model is more parsimonious than classical alternatives.

  • Problem

    Existing quantum ML proposals often target tractable supervised tasks, while difficult generative-learning problems and potentially quantum-like classical datasets remain important opportunities for near-term quantum enhancement.

  • Method

    The paper develops a hybrid quantum-classical perspective using quantum sampling, quantum-like model selection, and the quantum-assisted Helmholtz machine for high-dimensional data.

  • Results

    P(G|W) = 0.69, P(G|L) = 0.59, and P(G) = 0.39 in a gambling experiment violated the law of total probability, and a quantum model fit the results more parsimoniously than classical alternatives.

  • Takeaways & Limitations

    Near-term quantum ML may be most promising when quantum devices address hard sampling steps or represent quantum-like correlations in classical data.

Abstract

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With quantum computing technologies nearing the era of commercialization and quantum supremacy, machine learning (ML) appears as one of the promising "killer" applications. Despite significant effort, there has been a disconnect between most quantum ML proposals, the needs of ML practitioners, and the capabilities of near-term quantum devices to demonstrate quantum enhancement in the near future. In this contribution to the focus collection on "What would you do with 1000 qubits?", we provide concrete examples of intractable ML tasks that could be enhanced with near-term devices. We argue that to reach this target, the focus should be on areas where ML researchers are struggling, such as generative models in unsupervised and semi-supervised learning, instead of the popular and more tractable supervised learning techniques. We also highlight the case of classical datasets with potential quantum-like statistical correlations where quantum models could be more suitable. We focus on hybrid quantum-classical approaches and illustrate some of the key challenges we foresee for near-term implementations. Finally, we introduce the quantum-assisted Helmholtz machine (QAHM), an attempt to use near-term quantum devices to tackle high-dimensional datasets of continuous variables. Instead of using quantum computers to assist deep learning, as previous approaches do, the QAHM uses deep learning to extract a low-dimensional binary representation of data, suitable for relatively small quantum processors which can assist the training of an unsupervised generative model. Although we illustrate this concept on a quantum annealer, other quantum platforms could benefit as well from this hybrid quantum-classical framework.

I. INTRODUCTION

The paper argues that near-term quantum ML should target genuinely difficult ML problems and datasets with quantum-like correlations, using hybrid quantum-classical designs to address hardware constraints.

  • I. INTRODUCTION: Near-term quantum ML should prioritize generative models in unsupervised and semi-supervised learning, where current ML methods face difficult intractable tasks.The authors contrast these targets with popular supervised techniques that already scale efficiently.
  • I. INTRODUCTION: Datasets with intrinsic quantum-like correlations could yield compact quantum representations and significant advantages with 50-100 qubit devices.Cognitive-science datasets are suggested as one possible domain for finding such correlations.
  • I. INTRODUCTION: Hybrid algorithms are presented as a possible way to make near-term quantum assistance practical by combining classical processing with quantum computation.The proposed focus is on executing the intractable step of an ML pipeline on quantum hardware.
  • I. INTRODUCTION: The paper surveys viable near-term ML opportunities, discusses implementation challenges, and introduces the quantum-assisted Helmholtz machine for industrial-scale datasets.Its illustrations include demonstrations on quantum annealers, with insights intended to apply across quantum-computing paradigms.

A. Quantum devices for sampling applications

Sampling complex probability distributions is identified as a computational bottleneck in generative ML, where quantum devices may assist inference and training through hybrid approaches.

  • A. Quantum devices for sampling applications: Most collected data is unlabeled, making unsupervised methods important for discovering patterns and learning useful representations without task-specific labels.Such representations can reduce the labeled data needed for supervised generalization.
  • A. Quantum devices for sampling applications: Generative models learn joint probability distributions, enabling inference of marginal and conditional distributions and generation of data resembling the training set.Deep hidden-variable models can represent multimodal distributions over high-dimensional data.
  • A. Quantum devices for sampling applications: Quantum devices may assist classical and quantum generative models by sampling Gibbs distributions as an alternative to computationally costly MCMC methods.The proposed use targets more efficient inference and training in models such as Boltzmann machines.
  • A. Quantum devices for sampling applications: Sampling complex probability distributions is an intractable step in many ML frameworks with potential impact across science and engineering.The paper connects this opportunity to inference and learning in graphical models and probabilistic programming.
  • A. Quantum devices for sampling applications: Near-term implementations may require gray-box hybrid architectures that tolerate noisy, partially characterized quantum distributions while classical components bypass hardware limitations.The approach is called quantum-assisted.

B. Datasets with native quantum-like correlations

The paper proposes identifying real-world classical datasets whose quantum-like statistical structure makes quantum models substantially simpler than classical alternatives.

  • B. Datasets with native quantum-like correlations: The central challenge is to find non-quantum real-life datasets where quantum models are substantially simpler under standard model-comparison criteria.The Akaike information criterion is given as one possible evaluation tool.
  • B. Datasets with native quantum-like correlations: Cognitive-science data may contain interference, entanglement, or contextuality-like features that make quantum models useful mathematical descriptions.Prior work is cited as evidence for this possibility.
  • B. Datasets with native quantum-like correlations: In a gambling experiment, participants chose to replay with probabilities P(G|W) = 0.69, P(G|L) = 0.59, and P(G) = 0.39, violating the law of total probability.The reported behavior was fit by a quantum model more parsimonious than classical alternatives under Bayesian model comparison.
  • B. Datasets with native quantum-like correlations: The authors argue that finding datasets with intrinsically quantum characteristics could create unique near-term commercial niches rather than simply competing with mature classical technologies.They identify possible quantum advantage even at 50-100 qubits.

III. CHALLENGES IN QAML

Near-term QAML should target computationally intractable ML steps through hybrid quantum-classical algorithms, while addressing hardware and model-compatibility challenges.

  • III. CHALLENGES IN QAML: Near-term QAML proposals should focus on algorithms with potent intractable steps rather than quantum versions of popular ML methods.The paper argues that popular methods would require millions or billions of qubits for industrial-scale applications.
  • III. CHALLENGES IN QAML: Hybrid algorithms use classical computers for tractable subroutines and quantum computers to assist only the intractable steps.In generative models, quantum sampling can approximate functions needed for parameter updates or predictions.
  • III. CHALLENGES IN QAML: Near-term QAML implementations face limited connectivity, finite parameter dynamic range, and intrinsic device noise.These effects can cause qubit decoherence and uncertainty in programmable parameters.

A. Issue of classical and quantum model compatibility

Hybrid QAML requires precise information exchange between classical and quantum components, especially when their samples contribute to the same model update.

  • A. Issue of classical and quantum model compatibility: RBM and DBN training combines a tractable classical positive phase with an intractable quantum-assisted negative phase.The two terms are subtracted in the same stochastic-gradient update.
  • A. Issue of classical and quantum model compatibility: Classical and quantum probability distributions must match their defining parameters so that samples from both components represent the same model.Mismatch can break communication between the two architectures.
  • A. Issue of classical and quantum model compatibility: Unknown device temperature can break communication between classical and quantum components because it changes the sampled Gibbs distribution.Estimating temperature enables restart techniques that continue learning on the quantum device after classical training.

B. Robustness to noise in programmable parameters of the quantum device

Noise and parameter misspecification can make quantum samples deviate from the intended distribution, motivating gray-box models that emphasize sample quality over exact device parameters.

  • B. Robustness to noise in programmable parameters of the quantum device: Quantum Gibbs-state preparation is difficult because programmable-parameter noise and annealer dynamics can produce non-equilibrium distributions.Such deviations challenge RBM and DBN training, which requires reliable samples from a classical Boltzmann distribution.
  • B. Robustness to noise in programmable parameters of the quantum device: Quantum samples can seed classical Gibbs samplers, but this solution forces the model into a specific form and may shift efficiency burdens to post-processing.The drawback is greatest when the device distribution differs substantially from the assumed distribution.
  • B. Robustness to noise in programmable parameters of the quantum device: Gray-box models use first- and second-moment statistics without complete knowledge of implemented parameters, potentially improving resilience to hardware perturbations.Their emphasis is the quality and data-closeness of quantum samples.
  • B. Robustness to noise in programmable parameters of the quantum device: A gray-box quantum-assisted Helmholtz machine samples hidden variables from a D-Wave device while coping with intrinsic noise and parameter misspecification.The resulting model is tailored to the quantum device used during training.

C. The curse of limited connectivity

Limited connectivity creates a combined embedding and parameter-setting problem: mapping logical models onto hardware can add resources while distorting the desired sampling distribution.

  • C. The curse of limited connectivity: Missing physical interactions require embedding or swap operations, increasing the computational resources needed to realize the logical model.Annealers incur qubit overhead through embedding, while gate-model devices require swaps between distant qubits.
  • C. The curse of limited connectivity: For quantum annealers, embedding is only half the challenge because additional interactions require parameters that accurately represent the intended model.No optimal parameter-setting solution is known, although heuristic strategies exist.
  • C. The curse of limited connectivity: Machine-learning training can implicitly solve the embedded device's parameter-setting problem while learning arbitrary pairwise connectivity.The paper identifies training the whole device, rather than embedding alone, as the difficult task.
  • C. The curse of limited connectivity: The curse of limited connectivity includes both logical-to-physical mapping and setting embedding parameters so the device samples from the desired distribution.Gate-model implementations must also weigh connectivity against computation quality and resource overhead.

D. Representation of complex ML datasets into near-term devices

Near-term quantum ML must represent high-dimensional, often continuous datasets despite limited qubit counts and difficult state preparation. The paper proposes semantic binarization and hybrid classical-quantum architectures to address these constraints.

  • Continuous observables are possible in principle, but most available quantum computers operate with qubits while industrial datasets are commonly non-binary.
  • Industrial datasets often contain many non-binary variables, making naive binarization impractical for devices with 100–1000 qubits.Amplitude encoding offers compact representation but arbitrary state preparation and full readout remain problematic on near-term hardware.
  • Semantic binarization stochastically maps continuous variables into abstract binary representations suitable for near-term quantum sampling.The approach targets quantum probability distributions that may capture correlations difficult for conventional classical ML models.
  • Hybrid architectures can implement visible variables classically and hidden variables quantum mechanically, but model compatibility and posterior sampling remain challenges.Sampling a binarization for each data point may add further implementation difficulty.

IV. THE QUANTUM-ASSISTED HELMHOLTZ MACHINE

The QAHM is a hybrid generative framework that uses classical networks for high-dimensional data and a quantum device for compact, abstract hidden representations. A preliminary MNIST demonstration produced novel digit-like samples, though they remained blurry and below state-of-the-art ML.

  • The framework is designed to cope with continuous variables, limited qubit counts, and repeated quantum state preparation and measurement.
  • The generator models P(v) by combining a classical conditional distribution P(v|u) with a quantum distribution PQC(u) over hidden variables.The visible variables may be continuous, discrete, or other data types.
  • A classical recognition network approximates the hidden-variable posterior to avoid quantum state preparation and measurement for every training datum and iteration.Restricting recognition to classical computation is presented as an option for accelerating learning with serial quantum devices.
  • The QAHM architecture performs bottom-up recognition from raw data and top-down generation from quantum-sampled hidden variables.The quantum device supplies the deepest representation, while the classical generator transforms it into visible samples.
  • The MNIST demonstration used 266 visible variables, hidden layers of 120 and 60 variables, and mapped the deepest layer to 1644 D-Wave 2000Q qubits.Training used 1000 wake-sleep iterations.
  • QAHM uses a quantum computer to model the deepest hidden layers, where a low-dimensional representation can capture abstract data correlations.This compact representation is intended for near-term annealers or gate-model quantum computers.
  • Generated samples often resembled human-written digits and showed variation rather than copying nearest training images, although they were blurry and below state-of-the-art ML.The comparison used training images closest in Euclidean distance to generated samples.

V. SUMMARY

The paper argues that near-term quantum ML should target difficult generative and correlation-modeling problems rather than tractable popular applications. It presents hybrid algorithms, including QAHM, as a strategy while emphasizing hardware and model-complexity constraints.

  • Existing quantum ML proposals lack concrete benchmarks showing that they could outperform conventional classical ML in near-term implementations.
  • Near-term applications should prioritize highly desirable ML problems that are currently intractable, especially generative modeling and complex probability distributions.
  • Datasets with quantum-like correlations may provide opportunities where quantum distributions naturally fit the data and could support quantum advantage on smaller devices.The paper identifies cognitive sciences as a potential source of such datasets.
  • Limited qubit connectivity creates qubit overhead in adiabatic models and gate-operation overhead in gate-model architectures.Hardware model complexity may also significantly affect the ML task.
  • Hybrid quantum-classical algorithms are proposed to exploit complementary strengths and bypass limitations of near-term quantum hardware.The QAHM is introduced as a framework implementing this strategy.
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