Advances in quantum machine learning

Adcock, Jeremy C.; Allen, Euan J.; Day, Matthew; Frick, Stefan; Hinchliff, Janna; Johnson, Mack; Morley-Short, Sam; Pallister, Sam; Price, Alasdair B.; Stanisic, Stasja

doi:10.48550/arxiv.1512.02900

Cited by 44 publications

(70 citation statements)

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“…We employ the AQCE algorithm to encode separately the quantum state |Ψ (ms) c representing the m s th segment of the picture with the control parameters (M 0 , N, δM ) = (12,100,6) and varying the total number M of two-qubit unitary operators in the quantum circuit Ĉ(ms) . Figures 10(g .…”

Section: Quantum Circuit Encoding Of Classical Datamentioning

confidence: 99%

“…Considering that currently available quantum devices are prone to noise and decoherence, it is highly desirable to find applications that can work effectively with a less number of quantum gates and qubits. Under these conditions, one of the promising and appealing approaches is based on variational quantum algorithms [1] because it can be applied to a wide range of applications including quantum chemistry [2][3][4][5][6][7][8][9] and quantum machine learning [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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Automatic quantum circuit encoding of a given arbitrary quantum state

Shirakawa¹,

Ueda²,

Yunoki³

2021

Preprint

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We propose a quantum-classical hybrid algorithm, named automatic quantum circuit encoding (AQCE), to encode a given arbitrarily quantum state |Ψ onto an optimal quantum circuit Ĉ with a finite number of single-and two-qubit quantum gates. The proposed algorithm employs as an objective function the absolute value of fidelity F = 0| Ĉ † |Ψ , which is maximized iteratively to construct an optimal quantum circuit Ĉ with controlled accuracy. Here, |0 is a trivial product state in the computational basis of a quantum computer. The key ingredient of the algorithm is the sequential determination of a set of optimal two-qubit unitary operators one by one via the singular value decomposition of the fidelity tensor. Once the optimal unitary operators are determined, including the location of qubits on which each unitary operator acts, elementary quantum gates are assigned algebraically. These procedures are deterministic without assuming a quantum circuit ansatz and thus do not introduce any parameter optimization of parametrized quantum gates. With noiseless numerical simulations, we demonstrate the AQCE algorithm to encode a ground state of quantum many-body systems, including the spin-1/2 antiferromagnetic Heisenberg model and the spin-1/2 XY model. The results are also compared with the quantum circuit encoding of the same quantum state onto a quantum circuit in a given circuit structure, i.e., a circuit ansatz, such as Trotter-like and MERA-like circuit structures. Moreover, we demonstrate that the AQCE algorithm can also be applied to construct an optimal quantum circuit for classical data such as a classical image that is represented as a quantum state by the amplitude encoding. This scheme allows us to flexibly vary the required quantum resource. i.e., the number of qubits, by dividing classical data into multiple pieces. Therefore, this is potentially useful for a near-term application in quantum machine learning, e.g, as a state preparation of classical data for an input quantum state to be processed. Finally, we also experimentally demonstrate that a quantum circuit generated by the AQCE algorithm can indeed represent the original quantum state reasonably on a noisy real quantum device.

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Section: Quantum Circuit Encoding Of Classical Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Automatic quantum circuit encoding of a given arbitrary quantum state

Shirakawa¹,

Ueda²,

Yunoki³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…On the one hand, due the low number of qubits and the experimental noise, these devices cannot perform many of the algorithms (or protocols on the communication side) thought to demonstrate exponential speedups over classical algorithms. Thus, the quest for practical applications gained momentum over the last years, especially in the field of quantum machine learning [7,8,9,10,11,12]. On the other hand, NISQ devices are only accessibly via a 'quantum cloud' [13] and hence we need reliable protocols to delegate private computations.…”

Section: Introductionmentioning

confidence: 99%

Probably approximately correct quantum source coding

Angrisani¹,

Coyle²,

Kashefi³

2021

Preprint

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Information-theoretic lower bounds are often encountered in several branches of computer science, including learning theory and cryptography. In the quantum setting, Holevo's and Nayak's bounds give an estimate of the amount of classical information that can be stored in a quantum state. Previous works have shown how to combine information-theoretic tools with a counting argument to lower bound the sample complexity of distribution-free quantum probably approximately correct (PAC) learning. In our work, we establish the notion of Probably Approximately Correct Source Coding and we show two novel applications in quantum learning theory and delegated quantum computation with a purely classical client. In particular, we provide a lower bound of the sample complexity of a quantum learner for arbitrary functions under the Zipf distribution, and we improve the security guarantees of a classically-driven delegation protocol for measurement-based quantum computation (MBQC).

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“…However, the classical LDA algorithm faces the same problem as other classical machine learning algorithms, namely, high time complexity. To optimize it, a range of quantum algorithms have been proposed in machine learning, which achieved exponential acceleration compared with the classical ones [6,7]. In particular, quan-In the application field of quantum dimensionality reduction, the quantum algorithm for PCA has been proposed for unsupervised mode [16,17], the quantum algorithm for A-optimal projection is used in regression tasks [18], and Cong et al gave the quantum LDA algorithm [19].…”

Section: Introductionmentioning

confidence: 99%

Quantum Dimensionality Reduction by Linear Discriminant Analysis

Yu¹,

Guo²,

Song³

2021

Preprint

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Dimensionality reduction (DR) of data is a crucial issue for many machine learning tasks, such as pattern recognition and data classification. In this paper, we present a quantum algorithm and a quantum circuit to efficiently perform linear discriminant analysis (LDA) for dimensionality reduction. Firstly, the presented algorithm improves the existing quantum LDA algorithm to avoid the error caused by the irreversibility of the between-class scatter matrix SB in the original algorithm. Secondly, a quantum algorithm and quantum circuits are proposed to obtain the target state corresponding to the low-dimensional data. Compared with the best-known classical algorithm, the quantum linear discriminant analysis dimensionality reduction (QLDADR) algorithm has exponential acceleration on the number M of vectors and a quadratic speedup on the dimensionality D of the original data space, when the original dataset is projected onto a polylogarithmic low-dimensional space. Moreover, the target state obtained by our algorithm can be used as a submodule of other quantum machine learning tasks. It has practical application value of make that free from the disaster of dimensionality.

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Advances in quantum machine learning

Cited by 44 publications

References 0 publications

Automatic quantum circuit encoding of a given arbitrary quantum state

Automatic quantum circuit encoding of a given arbitrary quantum state

Probably approximately correct quantum source coding

Quantum Dimensionality Reduction by Linear Discriminant Analysis

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