Computation of operator exponentials using the Dunford-Cauchy integral

• URL: http://arxiv.org/abs/2509.08600v1
• Date: Wed, 10 Sep 2025 13:58:16 GMT
• Title: Computation of operator exponentials using the Dunford-Cauchy integral
• Authors: Alexander Tsirulev,
• Abstract summary: We consider an n-qubit quantum system with a Hamiltonian, defined by an expansion in the Pauli basis, and propose a new algorithm for classical computing the exponential of the Hamiltonian.<n>The algorithm is based on the representation of the exponential by the Dunford-Cauchy integral, followed by an efficient computation of the resolvent, and is suitable for Hamiltonians that are sparse in the Pauli basis.
• Score: 51.56484100374058
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider an n-qubit quantum system with a Hamiltonian, defined by an expansion in the Pauli basis, and propose a new algorithm for classical computing the exponential of the Hamiltonian. The algorithm is based on the representation of the exponential by the Dunford-Cauchy integral, followed by an efficient computation of the resolvent, and is suitable for Hamiltonians that are sparse in the Pauli basis. The practical efficiency of the algorithm is demonstrated by two illustrative examples.

Related papers

• Computing Green's functions and improving ground state energy estimation on quantum computers with Liouvillian recursion [35.18016233072556]
  We present a quantum-classical hybrid implementation of the Liouvillian recursion method compute many-body Green functions using a quantum computer.<n>From an approximate ground state preparation circuit, this algorithm produces the local ($r=r'$) and inter-site ($rneq r'$) Green's functions.
  arXiv  Detail & Related papers  (2026-03-05T16:28:48Z)
• Optimization of the quantization of dense neural networks from an exact QUBO formulation [33.03114296244325]
  This work introduces a post-training quantization (PTQ) method for dense neural networks via a novelROUND-based QUBO formulation.<n>The approach is evaluated on MNIST, FashionMNIST, EMNIST, and CIFAR-108 across integer precisions from int to int1 and compared with a round-to-nearest traditional quantization methodology.
  arXiv  Detail & Related papers  (2025-10-17T09:57:28Z)
• Classical optimization algorithms for diagonalizing quantum Hamiltonians [0.0]
  This paper introduces classical optimization algorithms for diagonalization by simulating a Hamiltonian.<n>We pinpoint a class of Hamiltonians that highlights severe drawbacks of existing methods, including exponential per-iteration, exponential circuit depth, or convergence to optima.<n>Our approach overcomes these shortcomings, achieving cost-time efficiency while avoiding spurious points.<n>On the practical side, we also present a randomized-coordinate variant that achieves a more efficient per-iteration cost than the deterministic counterpart.
  arXiv  Detail & Related papers  (2025-06-22T03:17:56Z)
• Quantum circuit for exponentiation of Hamiltonians: an algorithmic description based on tensor products [1.1786249372283566]
  Exponentiation of Hamiltonians refers to a mathematical operation to a Hamiltonian operator, where H is the Hamiltonian and t is a time parameter.<n>In quantum algorithms, such as Adiabatic methods and QAOA, exponentiation enables efficient simulation of a system dynamics.<n>We demonstrate a straightforward and efficient method to construct compact circuits that are easy to implement.
  arXiv  Detail & Related papers  (2025-01-29T17:14:45Z)
• Quantum Algorithms for Stochastic Differential Equations: A Schrödingerisation Approach [29.662683446339194]
  We propose quantum algorithms for linear differential equations.<n>The gate complexity of our algorithms exhibits an $mathcalO(dlog(Nd))$ dependence on the dimensions.<n>The algorithms are numerically verified for the Ornstein-Uhlenbeck processes, Brownian motions, and one-dimensional L'evy flights.
  arXiv  Detail & Related papers  (2024-12-19T14:04:11Z)
• A probabilistic imaginary-time evolution quantum algorithm for advection-diffusion equation: Explicit gate-level implementation and comparisons to quantum linear system algorithms [0.0]
  We propose a quantum algorithm for solving the advection-diffusion-reaction equation.<n>Our algorithm achieves an exponential speedup regarding the matrix size at the cost of a worse dependence on the error bound.
  arXiv  Detail & Related papers  (2024-09-27T08:56:21Z)
• QuOp: A Quantum Operator Representation for Nodes [0.0]
  We derive an intuitive and novel method to represent nodes in a graph with quantum operators. This method does not require parameter training and is competitive with classical methods on scoring similarity between nodes.
  arXiv  Detail & Related papers  (2024-07-19T13:10:04Z)
• Convergence rate of algorithms for solving linear equations by quantum annealing [0.0]
  We consider various iterative algorithms for solving the linear equation $ax=b$ using a quantum computer. The application of this approach to algorithms using both an infinite number of qubits and a small number of qubits is discussed.
  arXiv  Detail & Related papers  (2023-10-24T01:23:00Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Iterative Qubit Coupled Cluster using only Clifford circuits [36.136619420474766]
  An ideal state preparation protocol can be characterized by being easily generated classically. We propose a method that meets these requirements by introducing a variant of the iterative qubit coupled cluster (iQCC) We demonstrate the algorithm's correctness in ground-state simulations and extend our study to complex systems like the titanium-based compound Ti(C5H5)(CH3)3 with a (20, 20) active space.
  arXiv  Detail & Related papers  (2022-11-18T20:31:10Z)
• Partition Function Estimation: Quantum and Quantum-Inspired Algorithms [1.7510560590853574]
  We present two algorithms, one quantum and one classical, for estimating partition functions of quantum spin Hamiltonians. The former is a DQC1 (Deterministic quantum computation with one clean qubit) algorithm, and the first such for complex temperatures.
  arXiv  Detail & Related papers  (2022-08-01T15:29:06Z)

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.