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Optimal joint cutting of two-qubit rotation gates (2312.09679v2)
Published 15 Dec 2023 in quant-ph and physics.comp-ph
Abstract: Circuit cutting, the partitioning of quantum circuits into smaller independent fragments, has become a promising avenue for scaling up current quantum-computing experiments. Here, we introduce a scheme for joint cutting of two-qubit rotation gates based on a virtual gate-teleportation protocol. By that, we significantly lower the previous upper bounds on the sampling overhead and prove optimality of the scheme. Furthermore, we show that no classical communication between the circuit partitions is required. For parallel two-qubit rotation gates we derive an optimal ancilla-free decomposition, which include CNOT gates as a special case.
- P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in Proceedings 35th Annual Symposium on Foundations of Computer Science (IEEE Comput. Soc. Press, 1994) p. 124.
- E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm (2014), arXiv:1411.4028 .
- M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339, 1169 (2013).
- C. Monroe and J. Kim, Scaling the ion trap quantum processor, Science 339, 1164 (2013).
- L. Brenner, C. Piveteau, and D. Sutter, Optimal wire cutting with classical communication (2023), arXiv:2302.03366 .
- H. Harada, K. Wada, and N. Yamamoto, Doubly optimal parallel wire cutting without ancilla qubits (2023), arXiv:2303.07340 .
- P. Pednault, An alternative approach to optimal wire cutting without ancilla qubits (2023), arXiv:2303.08287 .
- H. F. Hofmann, How to simulate a universal quantum computer using negative probabilities, J. Phys. A: Math. Theor. 42, 275304 (2009).
- K. Mitarai and K. Fujii, Constructing a virtual two-qubit gate by sampling single-qubit operations, New J. Phys. 23, 023021 (2021a).
- K. Mitarai and K. Fujii, Overhead for simulating a non-local channel with local channels by quasiprobability sampling, Quantum 5, 388 (2021b).
- C. Piveteau and D. Sutter, Circuit knitting with classical communication, IEEE Trans. Inf. Theory , 1 (2023).
- H. Pashayan, J. J. Wallman, and S. D. Bartlett, Estimating outcome probabilities of quantum circuits using quasiprobabilities, Phys. Rev. Lett. 115, 070501 (2015).
- C. Piveteau, D. Sutter, and S. Woerner, Quasiprobability decompositions with reduced sampling overhead, NPJ Quantum Inf. 8, 12 (2022).
- K. Temme, S. Bravyi, and J. M. Gambetta, Error mitigation for short-depth quantum circuits, Phys. Rev. Lett. 119, 180509 (2017).
- D. Collins, N. Linden, and S. Popescu, Nonlocal content of quantum operations, Phys. Rev. A 64, 032302 (2001).
- D. Gottesman and I. L. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature 402, 390 (1999).
- D. Stahlke and R. B. Griffiths, Entanglement requirements for implementing bipartite unitary operations, Phys. Rev. A 84, 032316 (2011).
- A. Soeda, P. S. Turner, and M. Murao, Entanglement cost of implementing controlled-unitary operations, Phys. Rev. Lett. 107, 180501 (2011).
- B. Groisman and B. Reznik, Implementing nonlocal gates with nonmaximally entangled states, Phys. Rev. A 71, 032322 (2005).
- G. Vidal and R. Tarrach, Robustness of entanglement, Phys. Rev. A 59, 141 (1999).
- It can be shown that all operations in the virtual teleportation protocol are elements of the extended definition of local operations used in Ref. [23, 15].
- B. Nash, V. Gheorghiu, and M. Mosca, Quantum circuit optimizations for nisq architectures, Quantum Sci. Technol. 5, 025010 (2020).
- J. Sperling and W. Vogel, Representation of entanglement by negative quasiprobabilities, Phys. Rev. A 79, 042337 (2009a).
- J. Sperling and W. Vogel, Erratum: Representation of entanglement by negative quasiprobabilities [Phys. Rev. A 79, 042337 (2009)], Phys. Rev. A 80, 029905 (2009b).
- K. Mitarai and K. Fujii, Methodology for replacing indirect measurements with direct measurements, Phys. Rev. Research 1, 013006 (2019).
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