1Institute for Theoretical Physics, Heinrich Heine University Düsseldorf, Germany
2Institute for Quantum Inspired and Quantum Optimization, Hamburg University of Technology, Germany
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abstract
Multi-qubit entangling interactions arise naturally in several quantum computing platforms and promise advantages over traditional two-qubit gates. In particular, a fixed multi-qubit Ising-type interaction together with single-qubit X-gates can be used to synthesize global ZZ-gates (GZZ gates). In this work, we first show that the synthesis of such quantum gates that are time-optimal is NP-hard. Second, we provide explicit constructions of special time-optimal multi-qubit gates. They have constant gate times and can be implemented with linearly many X-gate layers. Third, we develop a heuristic algorithm with polynomial runtime for synthesizing fast multi-qubit gates. Fourth, we derive lower and upper bounds on the optimal GZZ gate-time. Based on explicit constructions of GZZ gates and numerical studies, we conjecture that any GZZ gate can be executed in a time O($n$) for $n$ qubits. Our heuristic synthesis algorithm leads to GZZ gate-times with a similar scaling, which is optimal in this sense. We expect that our efficient synthesis of fast multi-qubit gates allows for faster and, hence, also more error-robust execution of quantum algorithms.
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[1] X. Wang, A. Sørensen, kanye no-K. Mølmer, amasango e-Multibit ekhompuyutha ye-quantum, i-Phys. Umfundisi Lett. 86, 3907 (2001), arXiv:quant-ph/0012055.
https://doi.org/10.1103/PhysRevLett.86.3907
arXiv:quant-ph/0012055
[2] T. Monz, P. Schindler, JT Barreiro, M. Chwalla, D. Nigg, WA Coish, M. Harlander, W. Hänsel, M. Hennrich, kanye no-R. Blatt, 14-qubit entanglement: Indalo nokuhambisana, i-Phys. Umfundisi Lett. 106, 130506 (2011), arXiv:1009.6126.
https://doi.org/10.1103/PhysRevLett.106.130506
i-arXiv: 1009.6126
[3] M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annual Review of Condensed Matter Physics 11, 369 (2020), arXiv:1905.13641.
https://doi.org/10.1146/annurev-conmatphys-031119-050605
i-arXiv: 1905.13641
[4] C. Figgatt, A. Ostrander, NM Linkke, KA Landsman, D. Zhu, D. Maslov, kanye no-C. Monroe, imisebenzi ebambekayo e-Parallel kukhompyutha ye-universal ion-trap quantum, Nature 572, 368 (2019), arXiv:1810.11948 .
https://doi.org/10.1038/s41586-019-1427-5
i-arXiv: 1810.11948
[5] Y. Lu, S. Zhang, K. Zhang, W. Chen, Y. Shen, J. Zhang, J.-N. Zhang, and K. Kim, Scalable global entangling gates on arbitrary ion qubits, Nature 572, 363 (2019), arXiv:1901.03508.
https://doi.org/10.1038/s41586-019-1428-4
i-arXiv: 1901.03508
[6] P. Baßler, M. Zipper, C. Cedzich, M. Heinrich, P. H. Huber, M. Johanning, and M. Kliesch, Synthesis of and compilation with time-optimal multi-qubit gates, Quantum 7, 984 (2023), arXiv:2206.06387.
https://doi.org/10.22331/q-2023-04-20-984
i-arXiv: 2206.06387
[7] F. Barahona and A. R. Mahjoub, On the cut polytope, Mathematical Programming 36, 157 (1986).
https://doi.org/10.1007/BF02592023
[8] M. R. Garey and D. S. Johnson, Computers and intractability, Vol. 29 (W. H. Freeman and Company, New York, 2002).
[9] M. J. Bremner, A. Montanaro, and D. J. Shepherd, Average-case complexity versus approximate simulation of commuting quantum computations, Phys. Rev. Lett. 117, 080501 (2016), arXiv:1504.07999.
https://doi.org/10.1103/PhysRevLett.117.080501
i-arXiv: 1504.07999
[10] J. Allcock, J. Bao, J. F. Doriguello, A. Luongo, and M. Santha, Constant-depth circuits for Uniformly Controlled Gates and Boolean functions with application to quantum memory circuits, arXiv:2308.08539 (2023).
i-arXiv: 2308.08539
[11] U-S. Bravyi, D. Maslov, kanye no-Y. Nam, Ukuqaliswa kwezindleko eziqhubekayo zokusebenza kwe-Clifford namasango alawulwayo aphindaphindekayo kusetshenziswa ukusebenzisana komhlaba wonke, i-Phys. Umfundisi Lett. 129, 230501 (2022), arXiv:2207.08691.
https://doi.org/10.1103/PhysRevLett.129.230501
i-arXiv: 2207.08691
[12] S. Bravyi kanye no-D. Maslov, amasekethe angenawo ka-Hadamard adalula ukwakheka kweqembu le-Clifford, i-IEEE Trans. Inf. Ithiyori 67, 4546 (2021), arXiv:2003.09412.
https://doi.org/10.1109/TIT.2021.3081415
i-arXiv: 2003.09412
[13] D. Maslov and B. Zindorf, Depth optimization of CZ, CNOT, and Clifford circuits, IEEE Transactions on Quantum Engineering 3, 1 (2022), arxiv:2201.05215.
https://doi.org/10.1109/TQE.2022.3180900
i-arXiv: 2201.05215
[14] S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, 2009).
[15] E. Rich, The problem classes FP and FNP, in Automata, Computability and Complexity: Theory and Applications (Pearson Education, 2007) pp. 510–511.
https://www.cs.utexas.edu/~ear/cs341/automatabook/AutomataTheoryBook.pdf
[16] M. Johanning, Isospaced linear ion strings, Appl. Phys. B 122, 71 (2016).
https://doi.org/10.1007/s00340-016-6340-0
[17] M. Laurent and S. Poljak, On a positive semidefinite relaxation of the cut polytope, Linear Algebra and its Applications 223-224, 439 (1995).
https://doi.org/10.1016/0024-3795(95)00271-R
[18] M. M. Deza and M. Laurent, Geometry of Cuts and Metrics, 1st ed., Algorithms and Combinatorics (Springer Berlin Heidelberg, 2009).
https://doi.org/10.1007/978-3-642-04295-9
[19] M. E.-Nagy, M. Laurent, and A. Varvitsiotis, Complexity of the positive semidefinite matrix completion problem with a rank constraint, Springer International Publishing , 105 (2013), arXiv:1203.6602.
https://doi.org/10.1007/978-3-319-00200-2_7
i-arXiv: 1203.6602
[20] R. E. A. C. Paley, On orthogonal matrices, Journal of Mathematics and Physics 12, 311 (1933).
https://doi.org/10.1002/sapm1933121311
[21] A. Hedayat and W. D. Wallis, Hadamard matrices and their applications, The Annals of Statistics 6, 1184 (1978).
https://doi.org/10.1214/aos/1176344370
[22] H. Kharaghani and B. Tayfeh-Rezaie, A Hadamard matrix of order 428, Journal of Combinatorial Designs 13, 435 (2005).
https://doi.org/10.1002/jcd.20043
[23] D. Ž. Đoković, O. Golubitsky, and I. S. Kotsireas, Some new orders of Hadamard and Skew-Hadamard matrices, Journal of Combinatorial Designs 22, 270 (2014), arXiv:1301.3671.
https://doi.org/10.1002/jcd.21358
i-arXiv: 1301.3671
[24] J. Cohn, M. Motta, kanye no-RM Parrish, i-Quantum filter diagonalization nge-compressed double-factorized Hamiltonians, PRX Quantum 2, 040352 (2021), arXiv:2104.08957.
https://doi.org/10.1103/PRXQuantum.2.040352
i-arXiv: 2104.08957
[25] U-DA Spielman no-S.-H. I-Teng, Ukuhlaziywa okubushelelezi kwama-algorithms: Kungani i-algorithm ye-simplex ivamise ukuthatha isikhathi se-polynomial, Ijenali ye-ACM 51, 385 (2004), arXiv:cs/0111050.
https://doi.org/10.1145/990308.990310
arXiv:cs/0111050
[26] S. Diamond and S. Boyd, CVXPY: A Python-embedded modeling language for convex optimization, J. Mach. Learn. Res. 17, 1 (2016), arXiv:1603.00943.
i-arXiv: 1603.00943
http://jmlr.org/papers/v17/15-408.html
[27] A. Agrawal, R. Verschueren, S. Diamond, kanye no-S. Boyd, Isistimu yokubhala kabusha yezinkinga ze-convex optimization, J. Control Decis. 5, 42 (2018), arXiv:1709.04494.
https://doi.org/10.1080/23307706.2017.1397554
i-arXiv: 1709.04494
[28] Isisekelo Sesofthiwe Yamahhala, i-GLPK (I-GNU Linear Programming Kit) (2012), inguqulo: 0.4.6.
https://www.gnu.org/software/glpk/
[29] A. T. Phillips and J. B. Rosen, A parallel algorithm for constrained concave quadratic global minimization, Mathematical Programming 42, 421 (1988).
https://doi.org/10.1007/BF01589415
[30] M. Dür, R. Horst, and M. Locatelli, Necessary and sufficient global optimality conditions for convex maximization revisited, Journal of Mathematical Analysis and Applications 217, 637 (1998).
https://doi.org/10.1006/jmaa.1997.5745
[31] M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear programming: theory and algorithms, 3rd edition (John wiley & sons, 2013).
https://doi.org/10.1002/0471787779
[32] M. A. Hanson, Invexity and the Kuhn–Tucker Theorem, Journal of Mathematical Analysis and Applications 236, 594 (1999).
https://doi.org/10.1006/jmaa.1999.6484
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