Efficient calculation of Green's functions on quantum computers via simultaneous circuit perturbation

• URL: http://arxiv.org/abs/2505.05563v1
• Date: Thu, 08 May 2025 18:00:03 GMT
• Title: Efficient calculation of Green's functions on quantum computers via simultaneous circuit perturbation
• Authors: Samuele Piccinelli, Francesco Tacchino, Ivano Tavernelli, Giuseppe Carleo,
• Abstract summary: We propose a novel, ancilla-free algorithm to compute Retarded Green's Functions (RGFs) on quantum computers.<n>We benchmark the protocol on the one-dimensional Heisenberg and Fermi-Hubbard models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel, ancilla-free algorithm to compute Retarded Green's Functions (RGFs) on quantum computers. Our proposal is based on real-time evolution and specifically designed circuit components, which we refer to as circuit perturbations, acting as a direct representation of the external perturbative force within the quantum circuit in a linear response framework. First, we establish a direct analytical connection between the evaluation of circuit derivatives and the computation of RGFs. We then build on this connection to devise a new approach involving multiple simultaneous time perturbations. Our method does not require long-range connections and is efficient in terms of circuit calls, allowing us to compute the RGFs at different times simultaneously. We benchmark the protocol on the one-dimensional Heisenberg and Fermi-Hubbard models, comparing the resulting dynamical correlations and spectral functions with exact diagonalization. The results demonstrate good quantitative agreement with the predicted solutions even under realistic noise models, highlighting the practical potential of our method for studying complex dynamical phenomena on near-term quantum devices.

Related papers

• Synthesis of discrete-continuous quantum circuits with multimodal diffusion models [0.5277756703318045]
  Efficiently compiling quantum operations remains a major bottleneck in scaling quantum computing.<n>We introduce a multimodal denoising diffusion model that simultaneously generates a circuit's structure and its continuous parameters for compiling a target unitary.<n>We benchmark the model over different experiments, analyzing the method's accuracy across varying qubit counts, circuit depths, and proportions of parameterized gates.
  arXiv  Detail & Related papers  (2025-06-02T13:35:33Z)
• Quantum error mitigation in optimized circuits for particle-density correlations in real-time dynamics of the Schwinger model [0.0]
  In principle, it is possible to calculate non-equal-time correlation functions, from which one can detect interesting phenomena.<n>In practice, these calculations are strongly affected by noise, due to the complexity of the required quantum circuits.<n>We derive a digital circuit implementation of the time-evolution of particle-density correlation operators and their correlation, comparing results from exact evolution, bare noisy simulations and simulations with different error mitigation techniques.
  arXiv  Detail & Related papers  (2025-01-18T17:32:59Z)
• 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)
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities [0.0]
  We present and benchmark quantum computing approaches for calculating real-time single-particle Green's functions and nonlinear susceptibilities of Hamiltonian systems. The approaches leverage adaptive variational quantum algorithms for state preparation and propagation.
  arXiv  Detail & Related papers  (2024-07-01T14:19:38Z)
• Perturbative variational quantum algorithms for material simulations [9.656656772874062]
  We propose a variational quantum eigensolver based perturbation theory algorithm to accurately simulate electron correlation of periodic materials. New algorithms are able to accurately describe electron correlation of the LiH crystal with only one circuit parameter.
  arXiv  Detail & Related papers  (2024-01-13T05:45:44Z)
• Efficient estimation of trainability for variational quantum circuits [43.028111013960206]
  We find an efficient method to compute the cost function and its variance for a wide class of variational quantum circuits. This method can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem.
  arXiv  Detail & Related papers  (2023-02-09T14:05:18Z)
• 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)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Accurate methods for the analysis of strong-drive effects in parametric gates [94.70553167084388]
  We show how to efficiently extract gate parameters using exact numerics and a perturbative analytical approach. We identify optimal regimes of operation for different types of gates including $i$SWAP, controlled-Z, and CNOT.
  arXiv  Detail & Related papers  (2021-07-06T02:02:54Z)
• A variational quantum eigensolver for dynamic correlation functions [0.9176056742068814]
  We show how the calculation of zero-temperature dynamic correlation functions can be recast into a modified VQE algorithm. This allows for important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis. We believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors.
  arXiv  Detail & Related papers  (2021-05-04T18:52:45Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)

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.