Abstract Quantum state reconstruction is an important tool in quantum information science. Based on the idea of sequential disentanglement, we propose a quantum state reconstruction algorithm that reduces the number of parameters to be optimized. For transforming the arbitrary quantum state into a tensor product of 0 states in the computational basis, we give the conclusion that it is not necessary to apply a global unitary transformation in the optimization of sequential disentanglement. In detail, for disentangling arbitrary n-qubit pure state ψ into ψ ˜ 0 , we simply apply the quantum operator U to n − n − 1 2 qubits. This means that the number of parameters that need to be optimized has been further reduced, thereby saving quantum resources. Finally, numerical simulations verify the feasibility of the proposed algorithm.
Abstract Quantum state reconstruction is an important tool in quantum information science. Based on the idea of sequential disentanglement, we propose a quantum state reconstruction algorithm that reduces the number of parameters to be optimized. For transforming the arbitrary quantum state into a tensor product of 0 states in the computational basis, we give the conclusion that it is not necessary to apply a global unitary transformation in the optimization of sequential disentanglement. In detail, for disentangling arbitrary n-qubit pure state ψ into ψ ˜ 0 , we simply apply the quantum operator U to n − n − 1 2 qubits. This means that the number of parameters that need to be optimized has been further reduced, thereby saving quantum resources. Finally, numerical simulations verify the feasibility of the proposed algorithm.
Abstract In this work, we report a novel quantum state reconstruction process based on the disentanglement algorithm. We propose a sequential disentanglement scheme, which can transform an unknown quantum state into a product of computational zero states. The inverse evolution of the zero states reconstructs the quantum state up to an overall phase. By sequentially disentangling the qubits one by one, we reduce the required measurements with only individual qubit measurement and identify the transformation unitary efficiently. Variational quantum circuit and reinforcement learning methods are used for the quantum circuit design for continuous and discrete quantum gates implementation. Demonstrations with our proposal for the reconstruction of the random states are presented. Our method is universal and imposes no specific ansatz or constraint on the quantum state.
In this report, we propose a novel quantum diagonalization algorithm based on the optimization of variational quantum circuits. Diagonalizing a quantum state is a fundamental yet computationally challenging task in quantum information science, especially as the system size increases. To address this challenge, we reformulate the problem as a variational optimization process, where parameterized quantum circuits are trained to transform the input state into a diagonal form. To guide the optimization, we develop two objective functions based on measurement outcomes in the computational basis. The first objective function utilizes global computational basis probabilities, with the optimized value directly yielding the purity of the input state. The second objective function, designed for enhanced experimental feasibility, is constructed solely from single-qubit probabilities. It admits an elegant and compact analytical form that significantly reduces the exponential measurement complexity, while still effectively driving the state toward a diagonal representation. Through numerical simulations and analytical insights, we demonstrate that our variational optimization framework successfully produces the diagonal form of an input quantum state, offering a scalable and practical solution for quantum state diagonalization.
The development of practical quantum algorithms hinges critically on the ability to efficiently manage and compress quantum states. Noisy Intermediate-Scale Quantum (NISQ) computers, characterized by limited qubit counts and inherent noise, exacerbate this challenge. This paper proposes a novel quantum state compression technique utilizing tensor decomposition and variational quantum algorithms to minimize qubit requirements while mitigating error accumulation. The core idea involves transforming a complex quantum state into a lower-rank tensor representation, subsequently optimized using a variational quantum algorithm. This approach aims to capture the essential information within the original state, reducing computational overhead and enhancing the feasibility of running quantum algorithms on NISQ devices. We outline the theoretical framework, detailing the mathematical formulation of the compression process, including the tensor representation, variational optimization, and error correction strategies. The paper explores the key parameters influencing the compression ratio and error rates, ultimately demonstrating the potential of this technique to unlock the computational power of NISQ computers.
Abstract Quantum autoencoder (QAE) compresses a bipartite quantum state into its subsystem using a self-checking mechanism. How to characterize and minimize the lost information in this process is essential for understanding the compression mechanism of QAE. Here, we investigate how to minimize the lost information in QAE for any input mixed state. We theoretically show that the lost information is the quantum mutual information between the remaining subsystem and the discarded one; the encoding unitary transformation is designed to minimize this mutual information. Furthermore, we show that the optimized unitary transformation can be decomposed as the product of a permutation unitary transformation and a disentanglement unitary transformation, and the permutation unitary transformation can be searched by a regular Young tableau algorithm. When the search can be made exhaustive in lower-dimensional systems, the lost information is minimized numerically, which is shown theoretically to be a global minimum. When the dimension of the system becomes larger such that an exhaustive search is impossible, we adopt an approximate search algorithm to numerically identify that our compression scheme gives lower lost information than that from the quantum variational circuit-based QAE.
Quantum computing holds immense promise for revolutionizing various fields, and efficient quantum algorithms are crucial for realizing this potential. However, the inherent complexity of quantum systems often necessitates intricate parameter adjustments, which can limit scalability and algorithm performance. This paper introduces a novel dynamic quantum state reconstruction algorithm, designed to optimize quantum computations through adaptive parameter adjustments. We propose a method that leverages the quantum state's inherent self-consistency, enabling efficient and precise recalibration of quantum states. This approach directly addresses the limitations of traditional parameter tuning methods, offering a pathway towards significant improvements in quantum algorithm efficiency and overall system performance. The algorithm's core mechanism centers around a feedback loop that continuously adjusts quantum state parameters based on observed results, ensuring optimal resource utilization. The study demonstrates the effectiveness of this algorithm through simulations and preliminary experimental results, highlighting its potential to enhance quantum computation capabilities.
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