Quantum Principal Component Analysis Only Achieves an Exponential Speedup Because of Its State Preparation Assumptions

Tang, Ewin

doi:10.1103/physrevlett.127.060503

Cited by 93 publications

(80 citation statements)

References 32 publications

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“…On the other hand, it is unclear whether such results can be applied to classical datasets [16]. In addition, it has been proved that, with some sampling assumptions, there exist classical algorithms performing as well (up to polynomial factors) as their quantum counterparts when dealing with classical data [55].…”

Section: B Benchmarking Qml Modelsmentioning

confidence: 99%

Entangled Datasets for Quantum Machine Learning

Schatzki¹,

Arrasmith²,

Coles³

et al. 2021

Preprint

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High-quality, large-scale datasets have played a crucial role in the development and success of classical machine learning. Quantum Machine Learning (QML) is a new field that aims to use quantum computers for data analysis, with the hope of obtaining a quantum advantage of some sort. While most proposed QML architectures are benchmarked using classical datasets, there is still doubt whether QML on classical datasets will achieve such an advantage. In this work, we argue that one should instead employ quantum datasets composed of quantum states. For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement. We first show how a quantum neural network can be trained to generate the states in the NTangled dataset. Then, we use the NTangled dataset to benchmark QML models for supervised learning classification tasks. We also consider an alternative entanglement-based dataset, which is scalable and is composed of states prepared by quantum circuits with different depths. As a byproduct of our results, we introduce a novel method for generating multipartite entangled states, providing a use-case of quantum neural networks for quantum entanglement theory.

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Section: B Benchmarking Qml Modelsmentioning

confidence: 99%

Entangled Datasets for Quantum Machine Learning

Schatzki¹,

Arrasmith²,

Coles³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In Equation (11), first term (stage 1) is the leading-order approximation of the quantum circuit depth from existing top-down based algorithms [1,34] for sub-states with s qubits. The exact expression depends on which of the two algorithms is used.…”

Section: Theorem 1 Algorithm 5 Generates a Quantum Circuit With Depthmentioning

confidence: 99%

“…The asymptotic analysis starts by rewriting Eq. (11) and Eq. ( 12) using a more convenient parameterization,…”

Section: Bottom-upmentioning

confidence: 99%

“…For this reason, the most significant quantum speed-ups occur when the quantum algorithm [2][3][4][5][6][7] operates on an input state that is easy to prepare, such as the uniform superposition of all computational basis states. For algorithms that rely on loading data into an arbitrary quantum superposition state, an efficient means to prepare input states is a prerequisite to quantum speed-ups [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…Quantum memories must store a set of samples from a configuration space as a superposition state before the information is retrieved using the algorithm [19]. Quantum linear algebra algorithms operate with a critical assumption that classical data has been efficiently encoded as probability amplitudes of a quantum state without which the quantum speed-up vanishes [8][9][10][11]. All of the above emphasizes the importance of developing efficient quantum state preparation algorithms for broad application of quantum computing techniques on classical data.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Configurable sublinear circuits for quantum state preparation

Araujo¹,

Park²,

Ludermir³

et al. 2021

Preprint

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The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of realworld problems is the cost of loading classical data to a quantum state. Several quantum circuit-based methods have been proposed for encoding classical data as probability amplitudes of a quantum state. However, they require either quantum circuit depth or width to grow linearly with the data size, even though the other dimension of the quantum circuit grows logarithmically. In this paper, we present a configurable bidirectional procedure that addresses this problem by tailoring the resource trade-off between quantum circuit width and depth. In particular, we show a configuration that encodes an Ndimensional state by a quantum circuit with O( √ N ) width and depth and entangled information in ancillary qubits. We show a proof-of-principle on five quantum computers and compare the results.

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JEON, Beomseok (BJ): Seoul/Republic of Korea

Jeon

2019

Leadership in Movement Disorders

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This paper investigates the impact of observations on atmospheric state estimation in weather forecasting systems using graph neural networks (GNNs) and explainability methods. We integrate observation and Numerical Weather Prediction (NWP) points into a meteorological graph, extracting k-hop subgraphs centered on NWP points. Self-supervised GNNs are employed to estimate the atmospheric state by aggregating data within these k-hop radii. The study applies gradient-based explainability methods to quantify the significance of different observations in the estimation process. Evaluated with data from 11 satellite and land-based observations, the results highlight the effectiveness of visualizing the importance of observation types, enhancing the understanding and optimization of observational data in weather forecasting.

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Quantum Principal Component Analysis Only Achieves an Exponential Speedup Because of Its State Preparation Assumptions

Cited by 93 publications

References 32 publications

Entangled Datasets for Quantum Machine Learning

Entangled Datasets for Quantum Machine Learning

Configurable sublinear circuits for quantum state preparation

JEON, Beomseok (BJ): Seoul/Republic of Korea

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