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arXiv:2112.14524 · Physical Review Research

Automatic quantum circuit encoding of a given arbitrary quantum state

Tomonori Shirakawa, Hiroshi Ueda, Seiji Yunoki

Published Oct 3, 2024• 22 citations
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Abstract

We introduce an quantum-classical hybrid algorithm, named automatic quantum circuit encoding (AQCE), that is designed to encode an arbitrary quantum state | Ψ 〉 onto an optimal quantum circuit C ̂ composed of a finite set of single- and two-qubit quantum gates. The algorithm employs an objective function based on the absolute value of fidelity, F = 〈 0 | C ̂ † | Ψ 〉 , which is iteratively maximized to construct an optimal quantum circuit C ̂ with controlled accuracy. Here, | 0 〉 denotes a trivial product state in the computational basis of a quantum computer. The core of this algorithm lies in the sequential determination of an optimal set of two-qubit unitary operators, identified one by one through the singular value decomposition of the fidelity tensor. Once an optimal set of operators is determined, including the location of qubits on which each operator acts, elementary quantum gates are assigned algebraically to these two-qubit unitary operators. Importantly, these procedures are deterministic without assuming any quantum circuit ansatz and therefore eliminate the need for parameter optimization of parametrized quantum gates. Through noiseless numerical simulations, we demonstrate the effectiveness of the AQCE algorithm in encoding ground states of quantum many-body systems, including the spin-1/2 antiferromagnetic Heisenberg model and the spin-1/2 X Y model. We also compare these results with quantum circuit encoding employing predefined circuit structures such as Trotter-like and MERA-like circuit ansatze. Furthermore, our algorithm extends to classical data, for instance, classical images represented as quantum states using amplitude encoding. The adaptability enables us to adjust the quantum resource requirement, i.e., the number of qubits, by partitioning classical data into multiple distinct segments. This feature holds potential for near-term applications in quantum machine learning, such as a state preparation of classical data for an input quantum state to be processed. Finally, using a real quantum device provided by IBM Quantum, we experimentally validate that a quantum circuit generated by the AQCE algorithm can indeed reasonably represent the original quantum state. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043008

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We introduce an quantum-classical hybrid algorithm, named automatic quantum circuit encoding (AQCE), that is designed to encode an arbitrary quantum state | Ψ 〉 onto an optimal quantum circuit C ̂ composed of a finite set of single- and two-qubit quantum gates. The algorithm employs an objective function based on the absolute value of fidelity, F = 〈 0 | C ̂ † | Ψ 〉 , which is iteratively maximized to construct an optimal quantum circuit C ̂ with controlled accuracy. Here, | 0 〉 denotes a trivial product state in the computational basis of a quantum computer. The core of this algorithm lies in the sequential determination of an optimal set of two-qubit unitary operators, identified one by one through the singular value decomposition of the fidelity tensor. Once an optimal set of operators is determined, including the location of qubits on which each operator acts, elementary quantum gates are assigned algebraically to these two-qubit unitary operators. Importantly, these procedures are deterministic without assuming any quantum circuit ansatz and therefore eliminate the need for parameter optimization of parametrized quantum gates. Through noiseless numerical simulations, we demonstrate the effectiveness of the AQCE algorithm in encoding ground states of quantum many-body systems, including the spin-1/2 antiferromagnetic Heisenberg model and the spin-1/2 X Y model. We also compare these results with quantum circuit encoding employing predefined circuit structures such as Trotter-like and MERA-like circuit ansatze. Furthermore, our algorithm extends to classical data, for instance, classical images represented as quantum states using amplitude encoding. The adaptability enables us to adjust the quantum resource requirement, i.e., the number of qubits, by partitioning classical data into multiple distinct segments. This feature holds potential for near-term applications in quantum machine learning, such as a state preparation of classical data for an input quantum state to be processed. Finally, using a real quantum device provided by IBM Quantum, we experimentally validate that a quantum circuit generated by the AQCE algorithm can indeed reasonably represent the original quantum state. Published by the American Physical Society 2024
Converting classical information into a quantum circuit is an inevitable step in utilizing quantum computing. Current quantum computers are referred to as NISQ devices, which have a high level of noise without error correction, imposing strict limitations on the number of qubits and quantum gates. Therefore, when constructing quantum circuits, it becomes crucial to generate shallower circuits. Specifically, when amplitude encoding is employed for classical-quantum information conversion, analytical methods often necessitate an exponential number of quantum gates relative to the number of qubits, rendering them unsuitable for current NISQ devices. Here, we explore a method for constructing an approximately improved circuit for amplitude encoding, considering classical information from an array composed of floating-point numbers. In our method, we optimize the matrix elements of a two-qubit unitary gate using a technique similar to that used in the tensor network method. We then analytically decompose the obtained unitary matrix into a product of elementary unitary gates. Furthermore, using this as an element of the basic optimization technique, we explore a method for selectively adapting better quantum gates. We apply this method to the problem of constructing a circuit that approximately generates the ground state of the quantum spin model. Consequently, we find that better circuits can be automatically constructed without prior knowledge of classical information.
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Emerging quantum algorithms that process data require that classical input data be represented as a quantum state. These data-processing algorithms often follow the gate model of quantum computing-which requires qubits to be initialized to a basis state, typically| 0 〉-and thus often employ state generation circuits to transform the initialized basis state to a data-representation state. There are many ways to encode classical data in a qubit, and the oft-applied approach of basis encoding does not allow optimization to the extent that other variants do. In this work, we thus consider automatic synthesis of addressable, quantum read-only memory (QROM) circuits, which act as data-encoding state-generation circuits. We investi-gate three data encoding approaches, one of which we introduce to provide improved dynamic range and precision. We present experimental results that compare these encoding methods for QROM synthesis to better understand the implications of and applications for each.
Abstract Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups often predicated on access to an efficient data-loading oracle. In practice, constructing a circuit to prepare a generic n-qubit quantum state typically demands computational efforts scaling as O ( 2 n ) , posing a significant challenge for quantum algorithms to outperform their classical counterparts. To address this critical issue, various hybrid quantum–classical approaches have been proposed. However, many of these solutions favor simplistic circuit architectures, which are susceptible to substantial optimization challenges. In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we propose a framework called Adaptive Circuit Learning of Born Machine, which dynamically expands the ansatz circuit. Our algorithm is designed to selectively integrate two-qubit entangled gates that best capture the intricate entanglement present within the target state. Empirical experiments underscore the efficacy of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by prior research.
A central challenge in quantum machine learning is the state preparation bottleneck that describes the prohibitive computational cost of loading high-dimensional classical data into a quantum state. Although amplitude encoding can represent 2n2^n2n-dimensional data using only nnn qubits in principle, preparing arbitrary states remains computationally expensive, typically requiring variational optimization of a parameterized quantum circuit for each individual data instance. In this work, we propose a method that avoids iterative optimization by training a classical neural network to map input data directly to the continuous parameters of a fixed quantum circuit. We demonstrate the generation of quantum image states with high fidelity on data not seen during training. Since all optimization is performed once during training, the resulting model encodes new inputs in a single inference step, providing a scalable pathway for data loading in near-term quantum algorithms. We validate our method on the MNIST and Fashion-MNIST datasets, achieving fidelities up to 0.992 on unseen images and reducing the per-data-instance runtime by more than 5000-fold.