Efficient Algorithms for Approximating Quantum Partition Functions at
Low Temperature
- URL: http://arxiv.org/abs/2201.06533v2
- Date: Fri, 13 Oct 2023 00:17:28 GMT
- Title: Efficient Algorithms for Approximating Quantum Partition Functions at
Low Temperature
- Authors: Tyler Helmuth, Ryan L. Mann
- Abstract summary: We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature.
Our algorithm is based on combining the contour representation of quantum spin systems of this type due to Borgs, Koteck'y, and Ueltschi.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We establish an efficient approximation algorithm for the partition functions
of a class of quantum spin systems at low temperature, which can be viewed as
stable quantum perturbations of classical spin systems. Our algorithm is based
on combining the contour representation of quantum spin systems of this type
due to Borgs, Koteck\'y, and Ueltschi with the algorithmic framework developed
by Helmuth, Perkins, and Regts, and Borgs et al.
Related papers
- Non-equilibrium Quantum Monte Carlo Algorithm for Stabilizer Rényi Entropy in Spin Systems [0.552480439325792]
Quantum magic, or nonstabilizerness, provides a crucial characterization of quantum systems.
We propose a novel and efficient algorithm for computing stabilizer R'enyi entropy, one of the measures for quantum magic, in spin systems with sign-problem free Hamiltonians.
arXiv Detail & Related papers (2024-05-29T23:59:02Z) - 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) - Utilizing Quantum Processor for the Analysis of Strongly Correlated Materials [34.63047229430798]
This study introduces a systematic approach for analyzing strongly correlated systems by adapting the conventional quantum cluster method to a quantum circuit model.
We have developed a more concise formula for calculating the cluster's Green's function, requiring only real-number computations on the quantum circuit instead of complex ones.
arXiv Detail & Related papers (2024-04-03T06:53:48Z) - Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
Quantum computing sets the foundation for new ways of designing algorithms.
New challenges arise concerning which field quantum speedup can be achieved.
Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
arXiv Detail & Related papers (2024-02-26T09:32:07Z) - Algorithmic Cluster Expansions for Quantum Problems [0.0]
We establish a general framework for developing approximation algorithms for a class of counting problems.
We apply our framework to approximating probability amplitudes of a class of quantum circuits close to the identity.
We show that our algorithmic condition is almost optimal for expectation values and optimal for thermal expectation values in the sense of zero freeness.
arXiv Detail & Related papers (2023-06-15T09:11:48Z) - 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) - Optimal quantum control via genetic algorithms for quantum state
engineering in driven-resonator mediated networks [68.8204255655161]
We employ a machine learning-enabled approach to quantum state engineering based on evolutionary algorithms.
We consider a network of qubits -- encoded in the states of artificial atoms with no direct coupling -- interacting via a common single-mode driven microwave resonator.
We observe high quantum fidelities and resilience to noise, despite the algorithm being trained in the ideal noise-free setting.
arXiv Detail & Related papers (2022-06-29T14:34:00Z) - 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) - A Neural-Network Variational Quantum Algorithm for Many-Body Dynamics [15.435967947933404]
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems.
The proposed algorithm can be efficiently implemented in near-term quantum computers with low measurement cost.
arXiv Detail & Related papers (2020-08-31T02:54:09Z) - Efficient Algorithms for Approximating Quantum Partition Functions [0.0]
We establish a time approximation algorithm for partition functions of quantum spin models at high temperature.
Our main contribution is a simple and slightly sharper analysis for the case of pairwise interactions on bounded-degree graphs.
arXiv Detail & Related papers (2020-04-24T07:21:43Z) - Variational Quantum Algorithms for Steady States of Open Quantum Systems [2.740982822457262]
We propose a variational quantum algorithm to find the steady state of open quantum systems.
The fidelity between the optimal mixed state and the true steady state is over 99%.
This algorithm is derived from the natural idea of expressing mixed states with purification.
arXiv Detail & Related papers (2020-01-08T14:47:36Z)
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.