Estimation of a sparse multi-qubit Hamiltonian via compressed sensing

• URL: http://arxiv.org/abs/2607.04669v1
• Date: Mon, 06 Jul 2026 04:51:30 GMT
• Title: Estimation of a sparse multi-qubit Hamiltonian via compressed sensing
• Abstract summary: Hamiltonian estimation is an effective approach in studying the structure and dynamical evolution of quantum systems.<n>An $N$-qubit Hamiltonian has $4N-1$ unknown parameters, requiring exponentially many equations for information extraction.<n>We develop a method based on compressed sensing to estimate the Hamiltonian of a multi-qubit system.
• Score: 1.6553699564712037
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hamiltonian estimation is an effective approach in studying the structure and dynamical evolution of quantum systems. The difficulty in estimating the Hamiltonian is that an $N$-qubit Hamiltonian has $4^N-1$ unknown parameters, requiring exponentially many equations for information extraction. In this paper we develop a method based on compressed sensing to estimate the Hamiltonian of a multi-qubit system. We identify a problem where as $N$ increases, the common sufficient condition (Restricted Isometry Property) for compressed sensing often fails, obstructing the application of compressed sensing in ($N\geq 3$)-qubit Hamiltonian estimation. To solve this problem, we propose a ``scale transformation" technique to restore RIP and ensure a compressive estimation of a $k$-sparse Hamiltonian using only $O(k\log(4^N/k))$ equations. In the numerical examples, we estimate the Hamiltonians of two 6- and 30-qubit systems, demonstrating the effectiveness of the method.

Related papers

• Practical Estimation of Trotter Error for Hamiltonian Simulation [0.2538121404112091]
  Trotter product formulas are a leading approach for Hamiltonian simulation on quantum computers.<n>We develop new theoretical results, algorithms, and software tools that advance the state-of-the-art in Trottercal error estimation.
  arXiv  Detail & Related papers  (2026-06-29T18:00:06Z)
• Rounding Almost Commuting Hamiltonians [40.02212661155582]
  Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics.<n>We show how to efficiently approximate any almost commuting $2$-local qubit Hamiltonian by a commuting one.
  arXiv  Detail & Related papers  (2026-05-25T17:53:36Z)
• Hamiltonian Decoded Quantum Interferometry [69.7049555871155]
  We introduce Hamiltonian Decoded Quantum Interferometry (HDQI)<n>HDQI utilizes coherent measurements and the symplectic representation of the Pauli group to reduce Gibbs sampling and Hamiltonian Bellians.<n>We show that HDQI efficiently prepares Gibbs states at arbitrary temperatures for a class of physically motivated commuting Hamiltonians.
  arXiv  Detail & Related papers  (2025-10-09T08:06:15Z)
• Lower Bounds for Learning Hamiltonians from Time Evolution [5.118083299467833]
  We consider the problem of learning Hamiltonians from time evolution.<n>We show that any learning algorithm with inverse time resolution requires super-polynomial total evolution time.
  arXiv  Detail & Related papers  (2025-09-25T01:50:55Z)
• Accelerating Fermionic System Simulation on Quantum Computers [1.655267861296594]
  A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems.<n>We introduce a grouping strategy that partitions Hamiltonian terms into $mathcalO(N4)$ groups.<n>We propose a parallel Hamiltonian evolution scheme that reduces the circuit depth of Hamiltonian evolution by a factor of $N$.
  arXiv  Detail & Related papers  (2025-05-13T03:44:07Z)
• SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation [0.0]
  SHARC-VQE significantly reduces computational costs for molecular simulations. measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits.
  arXiv  Detail & Related papers  (2024-07-17T04:01:55Z)
• Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithms [48.869199703062606]
  A fundamental problem in quantum many-body physics is that of finding ground states of local Hamiltonians. We introduce two approaches that achieve a constant sample complexity, independent of system size $n$, for learning ground state properties.
  arXiv  Detail & Related papers  (2024-05-28T18:00:32Z)
• Hamiltonian simulation for low-energy states with optimal time dependence [45.02537589779136]
  We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. We present a quantum algorithm that uses $O(tsqrtlambdaGamma + sqrtlambda/Gammalog (1/epsilon))$ queries to the block-encoding for any $Gamma$.
  arXiv  Detail & Related papers  (2024-04-04T17:58:01Z)
• On the complexity of implementing Trotter steps [2.1369834525800138]
  We develop methods to perform faster Trotter steps with complexity sublinear in number of terms. We also realize faster Trotter steps when certain blocks of Hamiltonian coefficients have low rank. Our result suggests the use of Hamiltonian structural properties as both necessary and sufficient to implement Trotter synthesis steps with lower gate complexity.
  arXiv  Detail & Related papers  (2022-11-16T19:00:01Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• Average-case Speedup for Product Formulas [69.68937033275746]
  Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states. Our results open doors to the study of quantum algorithms in the average case.
  arXiv  Detail & Related papers  (2021-11-09T18:49:48Z)
• Hamiltonian simulation with random inputs [74.82351543483588]
  Theory of average-case performance of Hamiltonian simulation with random initial states. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models.
  arXiv  Detail & Related papers  (2021-11-08T19:08:42Z)

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.