Efficient Decomposition of Unitary Matrices in Quantum Circuit Compilers
Source abstract
Abstract
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for the translation of bigger unitary gates into elementary quantum operations, which is key to executing these algorithms on existing quantum computers. The decomposition can be used as an aggressive optimization method for the whole circuit, as well as to test part of an algorithm on a quantum accelerator. For the selection and implementation of the decomposition algorithm, perfect qubits are assumed. We base our decomposition technique on Quantum Shannon Decomposition, which generates O(344n) controlled-not gates for an n-qubit input gate. In addition, we implement optimizations to take advantage of the potential underlying structure in the input or intermediate matrices, as well as to minimize the execution time of the decomposition. Comparing our implementation to Qubiter and the UniversalQCompiler (UQC), we show that our implementation generates circuits that are much shorter than those of Qubiter and not much longer than the UQC. At the same time, it is also up to 10 times as fast as Qubiter and about 500 times as fast as the UQC.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Quantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum-Dot Cellular Automata
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Quantum & Computer Engineering Department, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Computer Engineering Department, HITEC University, Taxila 47080, Pakistan
Department of Electrical Engineering, University of Leuven, Oude Markt 13, 3000 Leuven, Belgium
Department of Informatics Engineering, Faculty of Engineering, University of Porto, Praça de Gomes Teixeira, 4099-002 Porto, Portugal
References (30)
Show source-provided references
1. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer10.1137/S0097539795293172 ↗
2. Quantum mechanics helps in searching for a needle in a haystack10.1103/PhysRevLett.79.325 ↗
3. Almudever, C.G., Lao, L., Wille, R., and Guerreschi, G.G. (2020, January 9–13). Realizing Quantum Algorithms on Real Quantum Computing Devices. Proceedings of the 2020 Design, Automation Test in Europe Conference Exhibition (DATE), Grenoble, France.10.23919/DATE48585.2020.9116240 ↗
4. Tannu, S.S., and Qureshi, M.K. (2019, January 13–17). Not All Qubits Are Created Equal: A Case for Variability-Aware Policies for NISQ-Era Quantum Computers. Proceedings of the ASPLOS ’19: Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, Providence, RI, USA.10.1145/3297858.3304007 ↗
5. OpenQL: A Portable Quantum Programming Framework for Quantum Accelerators10.1145/3474222 ↗
6. Allen, G.D. (2003). Unitary Matrices. Lectures on Linear Algebra and Matrices, Texas A&M University. Chapter 4.
7. Hardware acceleration of BWA-MEM genomic short read mapping for longer read lengths10.1016/j.compbiolchem.2018.03.024 ↗
8. Sarkar, A., Al-Ars, Z., Almudever, C.G., and Bertels, K.L.M. (2021). QiBAM: Approximate Sub-String Index Search on Quantum Accelerators Applied to DNA Read Alignment. Electronics, 10.10.3390/electronics10192433 ↗
9. Quantum associative memory10.1016/S0020-0255(99)00101-2 ↗
10. Quantum computational networks10.1098/rspa.1989.0099 ↗
11. Savage, A. (2015). Introduction to Lie Groups. Course Notes of MAT 1411/MAT 5158, University of Ottawa.
12. Arbitrary two-qubit computation in 23 elementary gates10.1103/PhysRevA.68.012318 ↗
13. Quantum Circuits for General Multiqubit Gates10.1103/PhysRevLett.93.130502 ↗
14. Entanglement in a 20-Qubit Superconducting Quantum Computer10.1038/s41598-019-49805-7 ↗
15. Minimal universal two-qubit controlled-NOT-based circuits10.1103/PhysRevA.69.062321 ↗
16. Efficient Decomposition of Quantum Gates10.1103/PhysRevLett.92.177902 ↗
17. Elementary gates for quantum computation10.1103/PhysRevA.52.3457 ↗
18. Tucci, R.R. (1999). A Rudimentary Quantum Compiler. arXiv.
19. History and generality of the CS decomposition10.1016/0024-3795(94)90446-4 ↗
20. Dekant, H., Tregillus, H., Tucci, R., and Yin, T. (2022, January 06). Qubiter at GitHub. Available online: github.com/artiste-qb-net/qubiter.
21. Möttönen, M., and Vartiainen, J. (2006). Trends in Quantum Computing Research, Nova Science Publishers, Inc.. Decompositions of General Quantum Gates.
22. Synthesis of Quantum Logic Circuits10.1109/TCAD.2005.855930 ↗
23. Guennebaud, G., and Jacob, B. (2020, July 20). The Eigen Documentation v3. Available online: http://eigen.tuxfamily.org.
24. Computing the complete CS decomposition10.1007/s11075-008-9215-6 ↗
25. Blackford, S., Moore, R., and Drakos, N. (2020, October 23). LAPACK Users’ Guide. Available online: https://www.netlib.org/lapack/lug/.
26. Iten, R., Reardon-Smith, O., Malvetti, E., Mondada, L., Pauvert, G., Redmond, E., Kohli, R.S., and Colbeck, R. (2021). Introduction to UniversalQCompiler. arXiv.
27. Quantum circuits for isometries10.1103/PhysRevA.93.032318 ↗
28. A comparison of programming languages in macroeconomics10.1016/j.jedc.2015.05.009 ↗
29. Simple factorization of unitary transformations10.1103/PhysRevA.97.022328 ↗
30. Vatan, F., and Williams, C.P. (2004). Realization of a General Three-Qubit Quantum Gate. arXiv.