Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering

• URL: http://arxiv.org/abs/2401.09091v3
• Date: Sat, 22 Jun 2024 17:35:29 GMT
• Title: Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
• Authors: Erenay Karacan, Yanbin Chen, Christian B. Mendl,
• Abstract summary: Hamiltonian simulation is a domain where quantum computers have the potential to outperform classical counterparts. One of the main challenges of such quantum algorithms is up-scaling the system size. We present an approach to improve the scalability of eigenspace filtering for the ground state preparation of a given Hamiltonian.
• Score: 0.13108652488669736
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts due to their inherent quantum behavior. One of the main challenges of such quantum algorithms is up-scaling the system size, which is necessary to achieve meaningful quantum advantage. In this work, we present an approach to improve the scalability of eigenspace filtering for the ground state preparation of a given Hamiltonian. Our method aims to tackle limitations introduced by a small spectral gap and high degeneracy of low energy states. It is based on an adaptive sequence of eigenspace filtering through Quantum Eigenvalue Transformation of Unitary Matrices (QETU) followed by spectrum profiling. By combining our proposed algorithm with state-of-the-art phase estimation methods, we achieved good approximations for the ground state energy with local, two-qubit gate depolarizing probability up to $10^{-4}$. To demonstrate the key results in this work, we ran simulations with the transverse-field Ising Model on classical computers using Qiskit. We compare the performance of our approach with the static implementation of QETU and show that we can consistently achieve three to four orders of magnitude improvement in the absolute error rate.

Related papers

• Concurrent VQE for Simulating Excited States of the Schwinger Model [0.0]
  This work explores the application of the concurrent variational quantum eigensolver (cVQE) for computing excited states of the Schwinger model. We show how to efficiently obtain the lowest two, four, and eight eigenstates with one, two, and three ancillary qubits for both vanishing and non-vanishing background electric field cases.
  arXiv  Detail & Related papers  (2024-07-22T13:42:02Z)
• Unleashed from Constrained Optimization: Quantum Computing for Quantum Chemistry Employing Generator Coordinate Method [10.6794560287257]
  Hybrid quantum-classical approaches offer potential solutions for quantum chemistry problems. But they also introduce challenges such as the barren plateau and the exactness of the ansatze. In this work, we highlight the interconnection between constrained optimization and generalized eigenvalue problems.
  arXiv  Detail & Related papers  (2023-12-12T19:36:51Z)
• Simulating non-unitary dynamics using quantum signal processing with unitary block encoding [0.0]
  We adapt a recent advance in resource-frugal quantum signal processing to explore non-unitary imaginary time evolution on quantum computers. We test strategies for optimising the circuit depth and the probability of successfully preparing the desired imaginary-time evolved states. We find that QET-U for non-unitary dynamics is flexible, intuitive and straightforward to use, and suggest ways for delivering quantum advantage in simulation tasks.
  arXiv  Detail & Related papers  (2023-03-10T19:00:33Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations [0.0]
  Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Network. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit.
  arXiv  Detail & Related papers  (2022-08-30T18:00:14Z)
• Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach [0.0]
  We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy. We solve a two-impurity embedded model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.
  arXiv  Detail & Related papers  (2021-08-24T14:58:14Z)
• 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)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)

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.