Improved iterative quantum algorithm for ground-state preparation
- URL: http://arxiv.org/abs/2210.08454v2
- Date: Mon, 24 Oct 2022 07:52:27 GMT
- Title: Improved iterative quantum algorithm for ground-state preparation
- Authors: Jin-Min Liang, Qiao-Qiao Lv, Shu-Qian Shen, Ming Li, Zhi-Xi Wang, and
Shao-Ming Fei
- Abstract summary: We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian system.
Our approach has advantages including the higher success probability at each iteration, the measurement precision-independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.
- Score: 4.921552273745794
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Finding the ground state of a Hamiltonian system is of great significance in
many-body quantum physics and quantum chemistry. We propose an improved
iterative quantum algorithm to prepare the ground state of a Hamiltonian. The
crucial point is to optimize a cost function on the state space via the quantum
gradient descent (QGD) implemented on quantum devices. We provide practical
guideline on the selection of the learning rate in QGD by finding a fundamental
upper bound and establishing a relationship between our algorithm and the
first-order approximation of the imaginary time evolution. Furthermore, we
adapt a variational quantum state preparation method as a subroutine to
generate an ancillary state by utilizing only polylogarithmic quantum
resources. The performance of our algorithm is demonstrated by numerical
calculations of the deuteron molecule and Heisenberg model without and with
noises. Compared with the existing algorithms, our approach has advantages
including the higher success probability at each iteration, the measurement
precision-independent sampling complexity, the lower gate complexity, and only
quantum resources are required when the ancillary state is well prepared.
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) - Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
Quantum computing sets the foundation for new ways of designing algorithms.
New challenges arise concerning which field quantum speedup can be achieved.
Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
arXiv Detail & Related papers (2024-02-26T09:32:07Z) - Sparse Quantum State Preparation for Strongly Correlated Systems [0.0]
In principle, the encoding of the exponentially scaling many-electron wave function onto a linearly scaling qubit register offers a promising solution to overcome the limitations of traditional quantum chemistry methods.
An essential requirement for ground state quantum algorithms to be practical is the initialisation of the qubits to a high-quality approximation of the sought-after ground state.
Quantum State Preparation (QSP) allows the preparation of approximate eigenstates obtained from classical calculations, but it is frequently treated as an oracle in quantum information.
arXiv Detail & Related papers (2023-11-06T18:53:50Z) - 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) - Resource-frugal Hamiltonian eigenstate preparation via repeated quantum
phase estimation measurements [0.0]
Preparation of Hamiltonian eigenstates is essential for many applications in quantum computing.
We adopt ideas from variants of this method to implement a resource-frugal iterative scheme.
We characterise an extension involving a modification of the target Hamiltonian to increase overall efficiency.
arXiv Detail & Related papers (2022-12-01T20:07:36Z) - Quantum Davidson Algorithm for Excited States [42.666709382892265]
We introduce the quantum Krylov subspace (QKS) method to address both ground and excited states.
By using the residues of eigenstates to expand the Krylov subspace, we formulate a compact subspace that aligns closely with the exact solutions.
Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems.
arXiv Detail & Related papers (2022-04-22T15:03:03Z) - Ground state preparation and energy estimation on early fault-tolerant
quantum computers via quantum eigenvalue transformation of unitary matrices [3.1952399274829775]
We develop a tool called quantum eigenvalue transformation of unitary matrices with reals (QET-U)
This leads to a simple quantum algorithm that outperforms all previous algorithms with a comparable circuit structure for estimating the ground state energy.
We demonstrate the performance of the algorithm using IBM Qiskit for the transverse field Ising model.
arXiv Detail & Related papers (2022-04-12T17:11:40Z) - Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees.
Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation.
We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
arXiv Detail & Related papers (2022-03-30T02:02:16Z) - Nearly optimal quantum algorithm for generating the ground state of a
free quantum field theory [0.0]
We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory.
Our algorithm delivers a super-quadratic speedup over the state-of-the-art quantum algorithm for ground-state generation.
arXiv Detail & Related papers (2021-10-12T02:48:46Z) - 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) - Iterative Quantum Assisted Eigensolver [0.0]
We provide a hybrid quantum-classical algorithm for approximating the ground state of a Hamiltonian.
Our algorithm builds on the powerful Krylov subspace method in a way that is suitable for current quantum computers.
arXiv Detail & Related papers (2020-10-12T12:25:16Z)
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.