Quantum machine learning of large datasets using randomized measurements

Haug, Tobias; Self, Chris N.; Kim, M. S.

doi:10.48550/arxiv.2108.01039

Cited by 11 publications

(12 citation statements)

References 43 publications

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“…This problem has been tackled before with quantum hardware. In [13], dimensionality reduction techniques (such as principal component analysis) are used to reduce the dimensionality of the digits to a feature vector small enough to fit on their 8 qubit machine. Similarly, in [14] handwritten digits are classified on an 8 qubit machine, in this instance the size of the data is not reduced, the full data is carefully encoded into the quantum computer, first with amplitude encoding, and then by using 11 layers of parameterised gates.…”

Section: Related Workmentioning

confidence: 99%

“…Our approach is fundamentally different from either of these. We use the same sized data (8×8 pixels) but do not apply dimensionality reduction as in [13], or reuse qubits for multiple data points as in [14]. We follow a simple encoding: giving each pixel its own qubit, which we can achieve as we are approximating a 64 qubit machine, while only using an 8 qubit machine.…”

Section: Related Workmentioning

confidence: 99%

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High Dimensional Quantum Machine Learning With Small Quantum Computers

C.¹,

Casper²,

Dunjko³

2022

Preprint

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Quantum computers hold great promise to enhance machine learning, but their current qubit counts restrict the realisation of this promise. In an attempt to placate this limitation techniques can be applied for evaluating a quantum circuit using a machine with fewer qubits than the circuit naively requires. These techniques work by evaluating many smaller circuits on the smaller machine, that are then combined in a polynomial to replicate the output of the larger machine. This scheme requires more circuit evaluations than are practical for general circuits. However, we investigate the possibility that for certain applications many of these subcircuits are superfluous, and that a much smaller sum is sufficient to estimate the full circuit. We construct a machine learning model that may be capable of approximating the outputs of the larger circuit with much fewer circuit evaluations. We successfully apply our model to the task of digit recognition, using simulated quantum computers much smaller than the data dimension. The model is also applied to the task of approximating a random 10 qubit PQC with simulated access to a 5 qubit computer, even with only relatively modest number of circuits our model provides an accurate approximation of the 10 qubit PQCs output, superior to a neural network attempt. The developed method might be useful for implementing quantum models on larger data throughout the NISQ era.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

High Dimensional Quantum Machine Learning With Small Quantum Computers

C.¹,

Casper²,

Dunjko³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For the second question, we consider the solution of QPL using quantum computers. Among different applications of quantum computing [22][23][24][25][26][27][28][29][30][31][32], a variety of quantum machine learning algorithms [20,[33][34][35][36][37][38][39][40][41][42] have been developed for different problems and demonstrated the potential for solving classically intractable problems, using parameterized circuits and classical optimization of noisy-intermediate-scale-quantum devices. Using a quantum computer, we propose the quantum kernel Alphatron algorithm to efficiently solve the QPL problem.…”

Section: Introductionmentioning

confidence: 99%

Provable Advantage in Quantum Phase Learning via Quantum Kernel Alphatron

Wu¹,

Wu²,

Wang³

et al. 2021

Preprint

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Can we use a quantum computer to speed up classical machine learning in solving problems of practical significance? Here, we study this open question focusing on the quantum phase learning problem, an important task in many-body quantum physics. We prove that, under widely believed complexity theory assumptions, quantum phase learning problem cannot be efficiently solved by machine learning algorithms using classical resources and classical data. Whereas using quantum data, we theoretically prove the universality of quantum kernel Alphatron in efficiently predicting quantum phases, indicating quantum advantages in this learning problem. We numerically benchmark the algorithm for a variety of problems, including recognizing symmetry-protected topological phases and symmetry-broken phases. Our results highlight the capability of quantum machine learning in efficient prediction of quantum phases.

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“…Quantum machine learning (QML) has recently emerged as a new research field aiming to take advantage of quantum computing for machine learning (ML) tasks. It has been shown that embedding data into gate-based quantum circuits can be used to produce kernels for ML models by quantum measurements [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A major question that remains open is whether quantum kernels thus produced can outperform classical kernels for practical ML applications.…”

mentioning

confidence: 99%

Compositional optimization of quantum circuits for quantum kernels of support vector machines

Torabian¹,

Krems²

2022

Preprint

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While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate an algorithm for constructing quantum kernels for support vector machines that adapts quantum gate sequences to data. The algorithm includes three essential ingredients: greedy search in the space of quantum circuits, Bayesian information criterion as circuit selection metric and Bayesian optimization of the parameters of the optimal quantum circuit identified. The performance of the resulting quantum models for classification problems with a small number of training points significantly exceeds that of optimized classical models with conventional kernels. In addition, we illustrate the possibility of mapping quantum circuits onto molecular fingerprints and show that performant quantum kernels can be isolated in the resulting chemical space. This suggests that methods developed for optimization and interpolation of molecular properties across chemical spaces can be used for building quantum circuits for quantum machine learning with enhanced performance.

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Quantum machine learning of large datasets using randomized measurements

Cited by 11 publications

References 43 publications

High Dimensional Quantum Machine Learning With Small Quantum Computers

High Dimensional Quantum Machine Learning With Small Quantum Computers

Provable Advantage in Quantum Phase Learning via Quantum Kernel Alphatron

Compositional optimization of quantum circuits for quantum kernels of support vector machines

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