Best Approximate Quantum Compiling Problems

Madden, Lachlan; Simonetto, Andrea

doi:10.1145/3505181

Cited by 31 publications

(29 citation statements)

References 57 publications

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Section: Introductionmentioning

confidence: 99%

“…Works for the best approximate quantum compilation problems appeared in the literature as [11]- [17]. Here we focus primarily on the recent [12], [17], which formulate the problem as a mathematical optimization program over properly parameterized hardware-compatible circuits. In particular, in [17], one defines a target circuit as a unitary matrix in n qubits, U , and a parametric ansatz V ct (θ) built upon allowed gates and interconnections, and solves (classically) the optimization problem:…”

Section: Introductionmentioning

confidence: 99%

“…Since for near-term applications, the approximate quantum compilation problem will have to be solved classically, we focus here on algorithmic tools to boost its scaling from the current n = 5 (for random targets) in [17] and n = 9 (for short targets) in [12]. In particular, we look at characterizing the landscape properties of (1) and we study computational techniques coming from stochastic gradient descent and sketching [18], [19], which involve fast and efficient computations.…”

Section: Introductionmentioning

confidence: 99%

“…Contributions. Our stepping stone is our previous work [17]. There, we looked at target unitary matrices to be compiled in the space of special unitary matrices of dimension d, SU(d), where d = 2 n and n is the number of qubits.…”

Section: Introductionmentioning

confidence: 99%

“…Considering target matrices from the same structure is also for simplicity--so that we know the minimum of the objective is zero--but it makes sense in a context where we want to compile the target with high precision. Requiring that the number of parameters grows linearly in n allows us to be in a computationally easier setting than the more complete problem we looked at in [17], and therefore allows us to find what scale is achievable for such circuits. This could further guide how to compile circuits with significantly more parameters.…”

Section: Introductionmentioning

confidence: 99%

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Sketching the Best Approximate Quantum Compiling Problem

Madden¹,

Akhriev²,

Simonetto³

2022

Preprint

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This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and consider algorithmic tools to scale it to higher numbers of qubits. We investigate stochastic gradient descent and two sketchand-solve algorithms. For all three algorithms, we compute the gradient efficiently using matrix-vector instead of matrix-matrix computations. Allowing for a runtime on the order of one hour, our implementation using either sketch-and-solve algorithm is able to compile 9 qubit, 27 CNOT circuits; 12 qubit, 24 CNOT circuits; and 15 qubit, 15 CNOT circuits. Without our algorithmic tools, standard optimization does not scale beyond 9 qubit, 9 CNOT circuits, and, beyond that, is theoretically dominated by barren plateaus.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Sketching the Best Approximate Quantum Compiling Problem

Madden¹,

Akhriev²,

Simonetto³

2022

Preprint

Self Cite

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A doubly stochastic matrices-based approach to optimal qubit routing

Mariella

Zhuk

2023

Quantum Inf Process

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Optimal Transport (OT) has fueled machine learning (ML) applications across many domains. In cases where paired data measurements (µ, ν) are coupled to a context variable p i , one may aspire to learn a global transportation map that can be parameterized through a potentially unseen context. Existing approaches utilize Neural OT and largely rely on Brenier's theorem. Here, we propose a first-of-its-kind quantum computing formulation for amortized optimization of contextualized transportation plans. We exploit a direct link between doubly stochastic matrices and unitary operators thus finding a natural connection between OT and quantum computation. We verify our method on synthetic and real data, by predicting variations in cell type distributions parameterized through drug dosage as context. Our comparisons to several baselines reveal that our method can capture dose-induced variations in cell distributions, even to some extent when dosages are extrapolated and sometimes with performance similar to the best classical models. In summary, this is a first step toward learning to predict contextualized transportation plans through quantum. 1 We use "contextual" rather than "conditional" to differentiate from OT on conditional probabilities (Tabak et al., 2021)

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Quarta: quantum supervised and unsupervised learning for binary classification in domain-incremental learning

Loglisci,

Malerba,

Pascazio

2024

Quantum Mach. Intell.

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Quantum machine learning recently gained prominence due to the promise of quantum computers in solving machine learning problems that are intractable on a classical computer. Nevertheless, several studies on problems which remain challenging for classical computing algorithms are emerging. One of these is classifying continuously incoming data instances in incremental fashion, which is studied in this paper through a hybrid computational solution that combines classical and quantum techniques. Hybrid approaches represents one of the current ways for the use of quantum computation in practical applications. In this paper, we show how typical issues of domain-incremental learning can be equally addressed with the properties of quantum mechanics, until to offer often better results. We propose the framework QUARTA to combine algorithms of quantum supervised learning, that is, variational quantum circuits, and techniques used in quantum unsupervised learning, that is, distance estimation. We aim at keeping the classification capabilities, which have learned on previously processed data instances, preserved as much as possible, and then acquiring new knowledge on new data instances. Experiments are performed on real-world datasets with quantum simulators.

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Best Approximate Quantum Compiling Problems

Cited by 31 publications

References 57 publications

Sketching the Best Approximate Quantum Compiling Problem

Sketching the Best Approximate Quantum Compiling Problem

A doubly stochastic matrices-based approach to optimal qubit routing

Quarta: quantum supervised and unsupervised learning for binary classification in domain-incremental learning

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