Noisy intermediate-scale quantum simulation of the one-dimensional wave equation
Lewis Wright, Conor Mc Keever, Jeremy T. First, Robert H. Johnston, Jeremy Tillay, Skylar Chaney, Matthias Rosenkranz, Michael Lubasch
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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>O</a:mi><a:mo>(</a:mo><a:msup><a:mi>n</a:mi><a:mn>2</a:mn></a:msup><a:mo>)</a:mo></a:mrow></a:math> for <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>n</b:mi></b:math> qubits representing the solution on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msup><c:mn>2</c:mn><c:mi>n</c:mi></c:msup></c:math> grid points, and leads to infidelities of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>O</d:mi><d:mo>(</d:mo><d:msup><d:mn>2</d:mn><d:mrow><d:mo>−</d:mo><d:mn>4</d:mn><d:mi>n</d:mi></d:mrow></d:msup><d:msup><d:mi>t</d:mi><d:mn>2</d:mn></d:msup><d:mo>)</d:mo></d:mrow></d:math> for simulation time <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>t</e:mi></e:math> 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. Published by the American Physical Society 2024