Quantum mixed state compiling

Ezzell, Nicholas; Ball, Elliott M.; Siddiqui, Aliza U.; Wilde, Mark M.; Sornborger, Andrew; Coles, Patrick J.; Holmes, Zoë

doi:10.1088/2058-9565/acc4e3

Cited by 16 publications

(3 citation statements)

References 97 publications

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“…Quantum state preparation using quantum algorithms is well-studied for pure states 3,5,6 . However, preparing mixed states requires purification first, followed by the preparation of the pure state 31 . The conventional purification method needs 2N qubits to prepare a mixed state of N qubits.…”

Section: Thermal State Preparation (Tsp)mentioning

confidence: 99%

Multi-target quantum compilation algorithm

Binho,

Hai,

Viet

et al. 2024

Preprint

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In quantum computing, quantum compilation transforms a target unitary into a trainable unitary represented by a quantum circuit. Traditional quantum compilation optimizes circuits for a single target. However, many quantum systems require simultaneous optimization of multiple targets. To address this, we developed a multi-target quantum compilation algorithm to enhance the performance and flexibility of simulating multiple quantum systems. Our benchmarks and case studies demonstrate the algorithm’s effectiveness, highlighting the significance of multi-target optimization in advancing quantum computing. This work establishes the foundation for further development and evaluation of multi-target quantum compilation algorithms.

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Section: Thermal State Preparation (Tsp)mentioning

confidence: 99%

Multi-target quantum compilation algorithm

Binho,

Hai,

Viet

et al. 2024

Preprint

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“…However, validating QPE-based PCA algorithms is technically challenging on near-term quantum computers due to the high requirements for ancillary systems. In a different direction, many efforts have been made to make quantum PCA an accessible application for near-term quantum computers through variational methods [21][22][23][24][25][26][27][28], which are a trainable hybrid quantum-classical framework based on parameterized quantum circuits [29]. These variational methods have become important platforms for demonstrating quantum advantages in the near future.…”

Section: Introductionmentioning

confidence: 99%

Resource-efficient quantum principal component analysis

Wang,

Luo

2024

Quantum Sci. Technol.

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Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum principal component analysis. Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue $\lambda$ with error $\epsilon$ and success probability larger than $\lambda(1-\eta)$ requests a query complexity {$\mathcal{\widetilde{O}}(\epsilon^{-1})$} and a sample complexity {$\mathcal{\widetilde{O}}(\epsilon^{-2}\eta^{-1})$}, respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in $1/\epsilon$ for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum principal component analysis method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.

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“…This latter ability is called generalization and has been intensely studied recently [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Constructing models that generalize well is essential for quantum machine learning tasks such as variational learning of unitaries [18][19][20][21][22][23][24], which is applied to unitary compiling [11,25,26], quantum simulation [10,27,28], quantum autoencoders [29,30] and black-hole recovery protocols [31].…”

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confidence: 99%

Generalization with quantum geometry for learning unitaries

Haug¹,

Kim²

2023

Preprint

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Generalization is the ability of quantum machine learning models to make accurate predictions on new data by learning from training data. Here, we introduce the data quantum Fisher information metric (DQFIM) to determine when a model can generalize. For variational learning of unitaries, the DQFIM quantifies the amount of circuit parameters and training data needed to successfully train and generalize. We apply the DQFIM to explain when a constant number of training states and polynomial number of parameters are sufficient for generalization. Further, we can improve generalization by removing symmetries from training data. Finally, we show that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work opens up new approaches to improve generalization in quantum machine learning.

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Quantum mixed state compiling

Cited by 16 publications

References 97 publications

Multi-target quantum compilation algorithm

Multi-target quantum compilation algorithm

Resource-efficient quantum principal component analysis

Generalization with quantum geometry for learning unitaries

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