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| Main Authors: | , , , , , |
|---|---|
| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17190634 |
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Table of Contents:
- <p>Realizing the promised advantage of quantum computers over classical computers requires both physical devices and corresponding methods for the design, verification and analysis of quantum circuits. In this regard, decision diagrams have proven themselves to be an indispensable tool due to their capability to represent both quantum states and unitaries (circuits) compactly. Nonetheless, recent results show that decision diagrams can grow to exponential size even for the ubiquitous stabilizer states, which are generated by Clifford circuits. Since Clifford circuits can be efficiently simulated classically, this is surprising. Moreover, since Clifford circuits play a crucial role in many quantum computing applications, from networking, to error correction, this limitation forms a major obstacle for using decision diagrams for the design, verification and analysis of quantum circuits. The recently proposed Local Invertible Map Decision Diagram (LIMDD) solves this problem by combining the strengths of decision diagrams and the stabilizer formalism that enables efficient simulation of Clifford circuits. However, LIMDDs have only been introduced on paper thus far and have not been implemented yet - preventing an investigation of their practical capabilities through experiments.<br> <br>In this work, we present the first implementation of LIMDDs for quantum circuit simulation and verification, and test this implementation in two settings. The first is a case study in which we investigate a quantum circuit which applies a Quantum Fourier Transform (QFT) to a random stabilizer state. The second is a purely artificial circuit, constructed specifically to favor the strengths of LIMDDs. We simulate these circuits using five methods: LIMDDs, existing DDs (QMDDs), matrix product states, the extended stabilizer formalism and the state vector method. On the artifical circuits we unsurprisingly find that LIMDDs beat all other simulation methods. However, on the QFT case study we find that LIMDDs perform better than three alternative simulation methods: existing DDs, matrix product state simulations and the extended stabilizer formalism, while all four methods perform worse than the "naive" state vector-based simulation method. On the other hand, we note that, although the latter state vector-based method performed better on these benchmarks, it is effectively limited to 30 qubits no matter the circuit since it always allocates the same amount of memory, whereas the other simulation methods do not suffer from this limitation. We find that while LIMDDs fill a theoretical gap, they do not yet fill a practical gap. More work is required to understand for which real-world circuits LIMDDs offer an advantage.</p> <p>This repository contains the files necessary to reproduce the benchmark results.</p>