Low-depth quantum state preparation

Zhang, Xiao‐Ming; Yung, Man‐Hong; Yuan, Xiao

doi:10.1103/physrevresearch.3.043200

Cited by 48 publications

(20 citation statements)

References 41 publications

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“…Remarkably, recent work has produced new ways to prepare arbitrary quantum states using shallow quantum circuits [33], by using additional ancillary qubits [34,35], by training parametrised quantum circuits in the so-called quantum machine learning setup [24,36,37], or even by implementing tensor-network inspired gradient-free optimisation techniques [38].…”

Section: Multi-qubit Quantum State Preparationmentioning

confidence: 99%

Optimisation-free Classification and Density Estimation with Quantum Circuits

Vargas-Calderón,

González,

Vinck-Posada

2022

Preprint

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We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification and probability density estimation using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of the new data sample. Remarkably, the implementation of our framework on a real quantum device does not require any optimisation of quantum circuit parameters. Nonetheless, we discuss a variational quantum circuit approach that could leverage quantum advantage for our framework.

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Section: Multi-qubit Quantum State Preparationmentioning

confidence: 99%

Optimisation-free Classification and Density Estimation with Quantum Circuits

Vargas-Calderón,

González,

Vinck-Posada

2022

Preprint

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“…Without ancillary qubit, an exponential circuit depth is inevitable to prepare an arbitrary quantum state [6][7][8][9][10][11][12][13][14][15][16] and the optimal result Θ(2 𝑛 /𝑛) is recently obtained by Sun et al [17]. Leveraging ancillary qubits, the circuit depth could be reduced to be sub-exponential scaling [17][18][19][20], yet in the worse case with an exponential number of ancillas. Very recently, the optimal circuit depth Θ(𝑛) was achieved by [17,20] with 𝑂 (2 𝑛 ) [17] and Õ (2 𝑛 ) [20] ancillary qubits.…”

mentioning

confidence: 99%

“…Our method saturates the circuit depth lower bound Ω(𝑛) [17,18]. Below we sketch our protocol with five stages and refer to [31] for the formal description.…”

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confidence: 99%

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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“…Previous works [1], [46] have also included divide-andconquer strategies for preparing arbitrary quantum states with reduced circuit depth.…”

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confidence: 99%