Mixed-Dimensional Quantum Circuit Simulation with Decision Diagrams

TL;DR

This paper introduces a decision diagram-based simulator for mixed-dimensional quantum circuits involving qudits, demonstrating efficient simulation of large systems with over 100 qudits, thus advancing quantum software tools.

Contribution

It presents a novel qudit simulator using decision diagrams that efficiently handles mixed-dimensional systems, supporting more than 100 qudits in a single circuit.

Findings

Capable of simulating large mixed-dimensional quantum circuits

Efficient handling of over 100 qudits in one circuit

Open-source implementation available on GitHub

Abstract

Quantum computers promise to solve several categories of problems faster than classical computers ever could. Current research mostly focuses on qubits, i.e., systems where the unit of information can assume only two levels. However, the underlying physics of most (if not all) of the technological platforms supports more than two levels, commonly referred to as qudits. Performing computations with qudits increases the overall complexity while, at the same time, reducing the number of operations and providing a lower error rate. Furthermore, qudits with different number of levels can be mixed in one system to ease the experimental control and keep representations as compact as possible. Exploiting these capabilities requires dedicated software support to tackle the increased complexity in an automated and efficient fashion. In this paper, we present a qudit simulator that handles mixed-dimensional systems based on Decision Diagrams (DDs). More precisely, we discuss the type of decision diagram introduced as underlying data structure as well as the resulting implementation. Experimental evaluations demonstrate that the proposed solution is capable of efficiently simulating mixed-dimensional quantum circuits, with specific use cases including more than 100 qudits in one circuit. The source code of the simulator is available via github.com/cda-tum/MiSiM under the MIT~license.