Dynamical mean field theory with quantum computing

• URL: http://arxiv.org/abs/2508.00118v1
• Date: Thu, 31 Jul 2025 19:14:06 GMT
• Title: Dynamical mean field theory with quantum computing
• Authors: Thomas Ayral,
• Abstract summary: Near-term quantum processors are limited in terms of the number of qubits and gates they can afford.<n>We introduce the tools and methods of quantum computing that could be used to overcome the limitations of classical impurity solvers.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Near-term quantum processors are limited in terms of the number of qubits and gates they can afford. They nevertheless give unprecedented access to programmable quantum systems that can efficiently, although imperfectly, simulate quantum time evolutions. Dynamical mean field theory, on the other hand, maps strongly-correlated lattice models like the Hubbard model onto simpler, yet still many-body models called impurity models. Its computational bottleneck boils down to investigating the dynamics of the impurity upon addition or removal of one particle. This task is notoriously difficult for classical algorithms, which has warranted the development of specific classical algorithms called "impurity solvers" that work well in some regimes, but still struggle to reach some parameter regimes. In these lecture notes, we introduce the tools and methods of quantum computing that could be used to overcome the limitations of these classical impurity solvers, either in the long term -- with fully quantum algorithms, or in the short term -- with hybrid quantum-classical algorithms.

Related papers

• Efficient Learning Implies Quantum Glassiness [0.0]
  We show a surprising relation between quantum learning theory and algorithmic hardness.<n>We show that finding near-ground states of certain sparse disordered quantum systems is average-case hard for "Lipschitz" quantum algorithms.
  arXiv  Detail & Related papers  (2025-04-30T18:00:29Z)
• Quantum Subroutines in Branch-Price-and-Cut for Vehicle Routing [0.0]
  We demonstrate in this work how quantums with limited resources can be integrated in large-scale exact optimization algorithms for NP-hard problems.<n>A key feature of our algorithm is it not only from the best solution returned by the quantum but from all solutions below a certain cost threshold.
  arXiv  Detail & Related papers  (2024-12-20T08:27:23Z)
• 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 algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• 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)
• Classical simulation of short-time quantum dynamics [0.0]
  We present classical algorithms for approximating the dynamics of local observables and nonlocal quantities. We establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.
  arXiv  Detail & Related papers  (2022-10-20T18:00:04Z)
• Limitations of variational quantum algorithms: a quantum optimal transport approach [11.202435939275675]
  We obtain extremely tight bounds for standard NISQ proposals in both the noisy and noiseless regimes. The bounds limit the performance of both circuit model algorithms, such as QAOA, and also continuous-time algorithms, such as quantum annealing.
  arXiv  Detail & Related papers  (2022-04-07T13:58:44Z)
• 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)
• 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)
• Long-Time Error-Mitigating Simulation of Open Quantum Systems on Near Term Quantum Computers [38.860468003121404]
  We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates. We simulate two systems of electrons coupled to an infinite thermal bath: 1) a system of dissipative free electrons in a driving electric field; and 2) the thermalization of two interacting electrons in a single orbital in a magnetic field -- the Hubbard atom. Our results demonstrate that algorithms for simulating open quantum systems are able to far outperform similarly complex non-dissipative algorithms on noisy hardware.
  arXiv  Detail & Related papers  (2021-08-02T21:36:37Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Limitations of optimization algorithms on noisy quantum devices [0.0]
  We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices. Our approach is based on the combination of entropic inequalities that determine how fast the quantum state converges to the fixed point of the noise model.
  arXiv  Detail & Related papers  (2020-09-11T17:07:26Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)

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.