Noisy intermediate-scale quantum simulation of the one-dimensional wave equation

• URL: http://arxiv.org/abs/2402.19247v2
• Date: Wed, 20 Nov 2024 17:41:08 GMT
• Title: Noisy intermediate-scale quantum simulation of the one-dimensional wave equation
• Authors: Lewis Wright, Conor Mc Keever, Jeremy T. First, Rory Johnston, Jeremy Tillay, Skylar Chaney, Matthias Rosenkranz, Michael Lubasch,
• Abstract summary: We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. Our approach to simulating the wave equation can be used with appropriate state preparation algorithms across different quantum processors and serve as an application-oriented benchmark.
• Score: 0.0
• License:
• Abstract: We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The circuit depth of our approach scales as $O(n^{2})$ for $n$ qubits representing the solution on $2^{n}$ grid points, and leads to infidelities of $O(2^{-4n} t^{2})$ for simulation time $t$ assuming smooth initial conditions. By varying the qubit count we study the interplay between the algorithmic and physical gate errors to identify the optimal working point of minimum total error. Our approach to simulating the wave equation can be used with appropriate state preparation algorithms across different quantum processors and serve as an application-oriented benchmark.

Related papers

• A two-circuit approach to reducing quantum resources for the quantum lattice Boltzmann method [41.66129197681683]
  Current quantum algorithms for solving CFD problems use a single quantum circuit and, in some cases, lattice-based methods. We introduce the a novel multiple circuits algorithm that makes use of a quantum lattice Boltzmann method (QLBM) The problem is cast as a stream function--vorticity formulation of the 2D Navier-Stokes equations and verified and tested on a 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Two quantum algorithms for solving the one-dimensional advection-diffusion equation [0.0]
  Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other.
  arXiv  Detail & Related papers  (2023-12-30T21:23:15Z)
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach [1.237454174824584]
  We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS) Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum many-body Hamiltonians. For simulation problems on 100 qubits, we show that AQCtensor achieves at least an order of magnitude reduction in the depth of the resulting optimized circuit.
  arXiv  Detail & Related papers  (2023-01-20T14:40:29Z)
• Phenomenological Theory of Variational Quantum Ground-State Preparation [0.0]
  The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a Hamiltonian exploiting parametrized quantum circuits. We show that the algorithm's success crucially depends on other parameters such as the learning rate. We propose a symmetry-enhanced simulation protocol that should be used if the gap closes.
  arXiv  Detail & Related papers  (2022-05-12T18:00:04Z)
• Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications [10.436969366019015]
  We show that any $Theta(n)$-depth circuit can be prepared with a $Theta(log(nd)) with $O(ndlog d)$ ancillary qubits. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories.
  arXiv  Detail & Related papers  (2022-01-27T13:16:30Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
  Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. Here, we propose an adaptive approach to construct a low-depth time evolution circuit. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
  arXiv  Detail & Related papers  (2020-11-10T18:00:42Z)
• Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
  We study two different methods to prepare excited states on a quantum computer. We benchmark these techniques on emulated and real quantum devices. These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
  arXiv  Detail & Related papers  (2020-09-28T17:21:25Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

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.