Identification of topological phases using classically-optimized variational quantum eigensolver

• URL: http://arxiv.org/abs/2202.02909v2
• Date: Fri, 11 Feb 2022 01:39:06 GMT
• Title: Identification of topological phases using classically-optimized variational quantum eigensolver
• Authors: Ken N. Okada, Keita Osaki, Kosuke Mitarai, Keisuke Fujii
• Abstract summary: Variational quantum eigensolver (VQE) is regarded as a promising candidate of hybrid quantum-classical algorithm for quantum computers. We propose classically-optimized VQE (co-VQE), where the whole process of the optimization is efficiently conducted on a classical computer. In co-VQE, we only use quantum computers to measure nonlocal quantities after the parameters are optimized.
• Score: 0.6181093777643575
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational quantum eigensolver (VQE) is regarded as a promising candidate of hybrid quantum-classical algorithm for the near-term quantum computers. Meanwhile, VQE is confronted with a challenge that statistical error associated with the measurement as well as systematic error could significantly hamper the optimization. To circumvent this issue, we propose classically-optimized VQE (co-VQE), where the whole process of the optimization is efficiently conducted on a classical computer. The efficacy of the method is guaranteed by the observation that quantum circuits with a constant (or logarithmic) depth are classically tractable via simulations of local subsystems. In co-VQE, we only use quantum computers to measure nonlocal quantities after the parameters are optimized. As proof-of-concepts, we present numerical experiments on quantum spin models with topological phases. After the optimization, we identify the topological phases by nonlocal order parameters as well as unsupervised machine learning on inner products between quantum states. The proposed method maximizes the advantage of using quantum computers while avoiding strenuous optimization on noisy quantum devices. Furthermore, in terms of quantum machine learning, our study shows an intriguing approach that employs quantum computers to generate data of quantum systems while using classical computers for the learning process.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Bias-field digitized counterdiabatic quantum optimization [39.58317527488534]
  We call this protocol bias-field digitizeddiabatic quantum optimization (BF-DCQO) Our purely quantum approach eliminates the dependency on classical variational quantum algorithms. It achieves scaling improvements in ground state success probabilities, increasing by up to two orders of magnitude.
  arXiv  Detail & Related papers  (2024-05-22T18:11:42Z)
• Unveiling quantum phase transitions from traps in variational quantum algorithms [0.0]
  We introduce a hybrid algorithm that combines quantum optimization with classical machine learning. We use LASSO for identifying conventional phase transitions and the Transformer model for topological transitions. Our protocol significantly enhances efficiency and precision, opening new avenues in the integration of quantum computing and machine learning.
  arXiv  Detail & Related papers  (2024-05-14T09:01:41Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Variational Quantum Approximate Spectral Clustering for Binary Clustering Problems [0.7550566004119158]
  We introduce the Variational Quantum Approximate Spectral Clustering (VQASC) algorithm. VQASC requires optimization of fewer parameters than the system size, N, traditionally required in classical problems. We present numerical results from both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-09-08T17:54:42Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage [43.3054117987806]
  We introduce a scalable procedure for harnessing classical computing resources to provide pre-optimized initializations for quantum circuits. We show this method significantly improves the trainability and performance of PQCs on a variety of problems. By demonstrating a means of boosting limited quantum resources using classical computers, our approach illustrates the promise of this synergy between quantum and quantum-inspired models in quantum computing.
  arXiv  Detail & Related papers  (2022-08-29T15:24:03Z)
• Fundamental limitations on optimization in variational quantum algorithms [7.165356904023871]
  A leading paradigm to establish such near-term quantum applications is variational quantum algorithms (VQAs) We prove that for a broad class of such random circuits, the variation range of the cost function vanishes exponentially in the number of qubits with a high probability. This result can unify the restrictions on gradient-based and gradient-free optimizations in a natural manner and reveal extra harsh constraints on the training landscapes of VQAs.
  arXiv  Detail & Related papers  (2022-05-10T17:14:57Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices [0.0]
  Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources. We develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics.
  arXiv  Detail & Related papers  (2020-08-12T13:49:29Z)
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices [0.0]
  We introduce a quantum solver of contracted eigenvalue equations, the quantum analogue of classical methods for the energies. We demonstrate the algorithm though computations on both a quantum simulator and two IBM quantum processing units.
  arXiv  Detail & Related papers  (2020-04-23T18:35:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.