A Quantum-Centric Super-Krylov Diagonalization Method

• URL: http://arxiv.org/abs/2412.17289v2
• Date: Wed, 14 May 2025 15:24:10 GMT
• Title: A Quantum-Centric Super-Krylov Diagonalization Method
• Authors: Adam Byrne, William Kirby, Kirk M. Soodhalter, Sergiy Zhuk,
• Abstract summary: We present a Krylov quantum diagonalization (KQD) method that uses only real-time evolutions and recovery probabilities.<n>We also propose a classical post-processing derivative estimation algorithm.
• Score: 0.562479170374811
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The problem of estimating the ground-state energy of a quantum system is ubiquitous in chemistry and condensed matter physics. Krylov quantum diagonalization (KQD) methods have emerged as a promising approach for this task, although many existing methods rely on subroutines - particularly the Hadamard test - that are challenging to implement on near-term quantum computers. We present a KQD method that uses only real-time evolutions and recovery probabilities, making it very well adapted for existing quantum hardware. Additionally, we propose a classical post-processing derivative estimation algorithm. Under assumptions on the spectrum of the Hamiltonian, we prove that our algorithm converges exponentially quickly to the ground-state energy. Finally, we provide classical numerical simulations for the transverse-field Ising model on 100 qubits.

Related papers

• Real-Time Scattering on Quantum Computers via Hamiltonian Truncation [0.0]
  We present a quantum computational framework using Hamiltonian Truncation (HT) simulating for real-time scattering processes.<n>HT approximates the quantum field theory Hilbert space by truncating the energy eigenbasis of a solvable reference Hamiltonian.<n>Our findings suggest that Hamiltonian Truncation offers a promising strategy for quantum simulations of quantum field theories.
  arXiv  Detail & Related papers  (2025-05-06T18:00:01Z)
• Quantum-Centric Algorithm for Sample-Based Krylov Diagonalization [0.6512657417859998]
  We introduce a quantum diagonalization algorithm which combines two key ideas on quantum subspaces.<n>We prove that our algorithm converges under working assumptions of Krylov quantum diagonalization and sparseness of ground state.<n>We then show numerical investigations of lattice Hamiltonians, which indicate that our method can outperform existing Krylov quantum diagonalization in presence of shot noise.
  arXiv  Detail & Related papers  (2025-01-16T17:56:19Z)
• Bayesian Quantum Amplitude Estimation [49.1574468325115]
  We introduce BAE, a noise-aware Bayesian algorithm for quantum amplitude estimation. We show that BAE achieves Heisenberg-limited estimation and benchmark it against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions [39.58317527488534]
  We propose a variational strategy based on symmetry-preserving cost functions to iteratively construct a reduced subspace for extraction of low-lying energy states.<n>As a proof of concept, we test the proposed algorithms on H4 chain and ring, targeting both the ground-state energy and the charge gap.
  arXiv  Detail & Related papers  (2024-11-25T20:33:47Z)
• Quantum Boltzmann machine learning of ground-state energies [3.187381965457262]
  Esting the ground-state energy of Hamiltonians is a fundamental task for which quantum computers can be helpful. We analyze the performance of quantum Boltzmann machines for this task. Our algorithm estimates the gradient of the energy function efficiently by means of a novel quantum circuit construction.
  arXiv  Detail & Related papers  (2024-10-16T18:22:03Z)
• A quantum implementation of high-order power method for estimating geometric entanglement of pure states [39.58317527488534]
  This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states. It is executable on current (hybrid) quantum hardware and does not depend on quantum memory. We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel.
  arXiv  Detail & Related papers  (2024-05-29T14:40:24Z)
• 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)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• Solving the Lipkin model using quantum computers with two qubits only with a hybrid quantum-classical technique based on the Generator Coordinate Method [0.0]
  We discuss the possibility of using the generator coordinate method (GCM) using hybrid quantum-classical algorithms with reduced quantum resources. We show that, ultimately, only two qubits is enough to solve the problem regardless of the particle number. As an alternative to this technique, we also explored how the quantum state deflation method can be adapted to the GCM problem.
  arXiv  Detail & Related papers  (2023-12-07T21:18:27Z)
• Fighting noise with noise: a stochastic projective quantum eigensolver [0.0]
  We present a novel approach to estimating physical observables which leads to a two order of magnitude reduction in the required sampling of the quantum state. The method can be applied to excited-state calculations and simulation for general chemistry on quantum devices.
  arXiv  Detail & Related papers  (2023-06-26T09:22:06Z)
• Quantum Thermal State Preparation [39.91303506884272]
  We introduce simple continuous-time quantum Gibbs samplers for simulating quantum master equations. We construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time.
  arXiv  Detail & Related papers  (2023-03-31T17:29:56Z)
• Calculating the many-body density of states on a digital quantum computer [58.720142291102135]
  We implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18bits.
  arXiv  Detail & Related papers  (2023-03-23T17:46:28Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Exact and efficient Lanczos method on a quantum computer [0.0]
  We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space. The construction is exact in the sense that the Krylov space is identical to that of the Lanczos method.
  arXiv  Detail & Related papers  (2022-08-01T01:57:23Z)
• 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)
• Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation [50.591267188664666]
  Quantum chemistry and materials is one of the most promising applications of quantum computing. Much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them.
  arXiv  Detail & Related papers  (2022-03-14T16:51:36Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Schr\"odinger-Heisenberg Variational Quantum Algorithms [1.9887498823918806]
  Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits. The extremely high accuracy needed to surpass classical computers poses a critical demand to the circuit depth. Here, we propose a paradigm of Schr"odinger-Heisenberg variational quantum algorithms to resolve this problem.
  arXiv  Detail & Related papers  (2021-12-15T04:53:01Z)
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments [5.774827369850958]
  Recent efforts highlight the development of quantum algorithms based upon quantum computed Hamiltonian moments. This tutorial review focuses on the typical ways of computing Hamiltonian moments using quantum hardware and improving the accuracy of the estimated state energies.
  arXiv  Detail & Related papers  (2021-09-27T04:24:19Z)
• 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)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)

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.