Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers

• URL: http://arxiv.org/abs/2103.03207v1
• Date: Thu, 4 Mar 2021 18:21:00 GMT
• Title: Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers
• Authors: Mekena Metcalf, Emma Stone, Katherine Klymko, Alexander F. Kemper, Mohan Sarovar, and Wibe A. de Jong
• Abstract summary: We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
• Score: 52.77024349608834
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo (QMCMC) process that allows sampling of the Gibbs distribution of a multivariate model. To demonstrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

Related papers

• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution [0.0]
  Quantum computers are expected to enable us to simulate large systems at finite temperatures. We propose a method suitable for quantum devices in this early stage to calculate the thermal-equilibrium expectation value of an observable at finite temperatures.
  arXiv  Detail & Related papers  (2024-09-11T07:38:46Z)
• Accelerated quantum circuit Monte-Carlo simulation for heavy quark thermalization [0.0]
  We introduce and formalize an accelerated quantum circuit Monte-Carlo framework to simulate heavy quark thermalization. With simplified drag and diffusion coefficients connected by Einstein's relation, we simulate the thermalization of a heavy quark in isotropic and anisotropic mediums.
  arXiv  Detail & Related papers  (2023-12-26T19:01:19Z)
• Programmable Simulations of Molecules and Materials with Reconfigurable Quantum Processors [0.3320294284424914]
  We introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics. We show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials.
  arXiv  Detail & Related papers  (2023-12-04T19:00:01Z)
• Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations [0.0]
  We describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits.
  arXiv  Detail & Related papers  (2023-01-06T16:40:06Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials [0.0]
  We propose the use of the Time Evolving Density operator with Orthogonal Polynomials Algorithm (TEDOPA) on a quantum computer. We show that exponential scalings of computational resources can potentially be avoided for time-evolution simulations of the systems considered in this work.
  arXiv  Detail & Related papers  (2022-03-28T11:16:33Z)
• Implementation of a two-stroke quantum heat engine with a collisional model [50.591267188664666]
  We put forth a quantum simulation of a stroboscopic two-stroke thermal engine in the IBMQ processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm.
  arXiv  Detail & Related papers  (2022-03-25T16:55:08Z)
• 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)
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics [51.15339237964982]
  "hierarchical equations of motion" (HEOM) is a powerful exact numerical approach to solve the dynamics. It has been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics. We present a numerical library in Python, integrated with the powerful QuTiP platform, which implements the HEOM for both bosonic and fermionic environments.
  arXiv  Detail & Related papers  (2020-10-21T07:54:56Z)

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.