Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach

• URL: http://arxiv.org/abs/2407.15357v1
• Date: Mon, 22 Jul 2024 03:57:41 GMT
• Title: Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach
• Authors: Zhiyan Ding, Marius Junge, Philipp Schleich, Peixue Wu,
• Abstract summary: We present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Our framework can be applied to both unital and non-unital quantum dynamics.
• Score: 5.193557673127421
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulating quantum dynamics is one of the most promising applications of quantum computers. While the upper bound of the simulation cost has been extensively studied through various quantum algorithms, much less work has focused on establishing the lower bound, particularly for the simulation of open quantum system dynamics. In this work, we present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Given a fixed accessible unitary set, we introduce the concept of convexified circuit depth to quantify the quantum simulation cost and analyze the necessary circuit depth to construct a quantum simulation scheme that achieves a specific order. Our framework can be applied to both unital and non-unital quantum dynamics, and the tightness of our lower bound technique is illustrated by showing that the upper and lower bounds coincide in several examples.

Related papers

• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Benchmarking digital quantum simulations above hundreds of qubits using quantum critical dynamics [42.29248343585333]
  We benchmark quantum hardware and error mitigation techniques on up to 133 qubits. We show reliable control up to a two-qubit gate depth of 28, featuring a maximum of 1396 two-qubit gates. Results are transferable to applications such as Hamiltonian simulation, variational algorithms, optimization, or quantum machine learning.
  arXiv  Detail & Related papers  (2024-04-11T18:00:05Z)
• Quantum Tunneling: From Theory to Error-Mitigated Quantum Simulation [49.1574468325115]
  This study presents the theoretical background and the hardware aware circuit implementation of a quantum tunneling simulation. We use error mitigation techniques (ZNE and REM) and multiprogramming of the quantum chip for solving the hardware under-utilization problem.
  arXiv  Detail & Related papers  (2024-04-10T14:27:07Z)
• Quantum improvement in Spatial Discretization [0.0]
  We introduce a quantum algorithm that improves spatial discretization within constraints. Our algorithm bridges the gap from theoretical models to tangible quantum circuitry.
  arXiv  Detail & Related papers  (2023-12-14T15:36:10Z)
• 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)
• On-the-fly Tailoring towards a Rational Ansatz Design for Digital Quantum Simulations [0.0]
  It is imperative to develop low depth quantum circuits that are physically realizable in quantum devices. We develop a disentangled ansatz construction protocol that can dynamically tailor an optimal ansatz. The construction of the ansatz may potentially be performed in parallel quantum architecture through energy sorting and operator commutativity prescreening.
  arXiv  Detail & Related papers  (2023-02-07T11:22:01Z)
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer [0.11744028458220425]
  We simulate the groundstate of the quantum Ising model through its quantum critical point on a superconducting quantum device. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states.
  arXiv  Detail & Related papers  (2022-05-25T18:05:53Z)
• Simulating quantum circuits using the multi-scale entanglement renormalization ansatz [0.0]
  We propose a scalable technique for approximate simulations of intermediate-size quantum circuits. We benchmark the proposed technique for checkerboard-type intermediate-size quantum circuits of 27 qubits with various depths.
  arXiv  Detail & Related papers  (2021-12-28T09:05:01Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale [57.84751206630535]
  We present a modernized version of the Quantum Virtual Machine (TNQVM) which serves as a quantum circuit simulation backend in the e-scale ACCelerator (XACC) framework. The new version is based on the general purpose, scalable network processing library, ExaTN, and provides multiple quantum circuit simulators. By combining the portable XACC quantum processors and the scalable ExaTN backend we introduce an end-to-end virtual development environment which can scale from laptops to future exascale platforms.
  arXiv  Detail & Related papers  (2021-04-21T13:26:42Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)

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.