Circuit-Based Quantum Random Access Memory for Classical Data With Continuous Amplitudes

Veras, Tiago Mendonça Lucena de; Araujo, Ismael C. S.; Park, Daniel K.; Silva, Adenilton J. da

doi:10.1109/tc.2020.3037932

Cited by 35 publications

(19 citation statements)

References 17 publications

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“…( 7), with known, classical description of |𝐷 𝑘 ∈ C 2 . A naive protocol is to digitize |𝐷 𝑘 [28,41] with 𝐷 𝑘 |𝐷 ⊥ 𝑘 = 0, Eq. (S-21) is equivalent to Eq.…”

Section: Parallel Hamiltonian Simulation Based On Quantum Walkmentioning

confidence: 99%

“…In practice, the data may behave with a certain structure. Indeed, if the one imposes certain restrictions on the target quantum states, the circuit depth and the ancillary qubit number might be further reduced [25][26][27][28][29][30]. A typical scenario that has both theoretical and practical relevance is the sparse data structure, such as sparse classical data, Hamiltonians of physics systems, etc.…”

mentioning

confidence: 99%

“…A typical scenario that has both theoretical and practical relevance is the sparse data structure, such as sparse classical data, Hamiltonians of physics systems, etc. Using a constant number of ancillary qubits, arbitrary 𝑑-sparse quantum states (with 𝑑 non-zero entries) can be prepared using a circuit depth of 𝑂 (𝑑𝑛) [25][26][27][28]. However, it was unclear if the sparse preparation procedure could be further sped up with more (polynomial with 𝑛) ancillary qubits.…”

mentioning

confidence: 99%

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Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Zhang¹,

Li²,

Yuan³

2022

Preprint

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Quantum state preparation is an important subroutine for quantum computing. We show that any 𝑛-qubit quantum state can be prepared with a Θ(𝑛)-depth circuit using only single-and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with 𝑑 2 nonzero entries, we can reduce the circuit depth to Θ(log(𝑛𝑑)) with 𝑂 (𝑛𝑑 log 𝑑) ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.

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“…( 7), with known, classical description of |𝐷 𝑘 ∈ C 2 . A naive protocol is to digitize |𝐷 𝑘 [28,41] with 𝐷 𝑘 |𝐷 ⊥ 𝑘 = 0, Eq. (S-21) is equivalent to Eq.…”

Section: Parallel Hamiltonian Simulation Based On Quantum Walkmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Zhang¹,

Li²,

Yuan³

2022

Preprint

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“…Machine learning has been considered as a promising domain for which quantum computing can shine [10][11][12][13][14][15]. Quantum advantages in machine learning are expected, since quantum computers can in principle store and manipulate the amount of classical information that scales exponentially with the number of qubits [16][17][18]. Moreover, quantum computers can reduce the computational cost exponentially for solving certain basic linear algebra problems [19,20] that often appear as basic subroutines in machine learning tasks, such as in support vector machine [21] and principal component analysis [22].…”

Section: Introductionmentioning

confidence: 99%

Compact quantum distance-based binary classifier

Blank,

da Silva,

de Albuquerque

et al. 2022

Preprint

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Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by engineering the quantum interference effect to carry out the kernel evaluation in parallel. For practical applications of these quantum machine learning methods, an important issue is to minimize the size of quantum circuits. We present the simplest quantum circuit for constructing a kernel-based binary classifier. This is achieved by generalizing the interference circuit to encode data labels in the relative phases of the quantum state and by introducing compact amplitude encoding, which encodes two training data vectors into one quantum register. When compared to the simplest known quantum binary classifier, the number of qubits is reduced by two and the number of steps is reduced linearly with respect to the number of training data. The two-qubit measurement with post-selection required in the previous method is simplified to single-qubit measurement. Furthermore, the final quantum state has a smaller amount of entanglement than that of the previous method, which advocates the cost-effectiveness of our method. Our design also provides a straight-forward way to handle an imbalanced data set, which is often encountered in many machine learning problems.

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“…¶ Equal contribution ©2021 IEEE Quantum advantages in machine learning are expected naturally since quantum computers can reduce the computational cost exponentially for solving certain basic linear algebra problems [13], [4] that often appear as basic subroutines in machine learning tasks. Moreover, quantum computers can achieve exponential compression of data [14], [15], [16]. Full comprehension of which machine learning problems can be solved more efficiently with quantum algorithms remains as an important open problem.…”

Section: Introductionmentioning

confidence: 99%

Robust quantum classifier with minimal overhead

Park,

Blank,

Petruccione

2021

Preprint

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To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the potential to significantly enhance existing classical machine learning methods, and several quantum algorithms for binary classification based on the kernel method have been proposed. These algorithms rely on estimating an expectation value, which in turn requires an expensive quantum data encoding procedure to be repeated many times. In this work, we calculate explicitly the number of repetition necessary for acquiring a fixed success probability and show that the Hadamard-test and the swap-test circuits achieve the optimal variance in terms of the quantum circuit parameters. The variance, and hence the number of repetition, can be further reduced only via optimization over data-related parameters. We also show that the kernel-based binary classification can be performed with a single-qubit measurement regardless of the number and the dimension of the data. Finally, we show that for a number of relevant noise models the classification can be performed reliably without quantum error correction. Our findings are useful for designing quantum classification experiments under limited resources, which is the common challenge in the noisy intermediate-scale quantum era.

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Circuit-Based Quantum Random Access Memory for Classical Data With Continuous Amplitudes

Cited by 35 publications

References 17 publications

Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications

Compact quantum distance-based binary classifier

Robust quantum classifier with minimal overhead

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