Magic state parity-checker with pre-distilled components

Earl T. Campbell; Mark Howard

doi:10.22331/q-2018-03-14-56

Magic state parity-checker with pre-distilled components

Earl T. Campbell and Mark Howard

Department of Physics & Astronomy, University of Sheffield, Sheffield, S3 7RH, United Kingdom.

Published:	2018-03-14, volume 2, page 56
Eprint:	arXiv:1709.02214v3
Doi:	https://doi.org/10.22331/q-2018-03-14-56
Citation:	Quantum 2, 56 (2018).

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Abstract

Magic states are eigenstates of non-Pauli operators. One way of suppressing errors present in magic states is to perform parity measurements in their non-Pauli eigenbasis and postselect on even parity. Here we develop new protocols based on non-Pauli parity checking, where the measurements are implemented with the aid of pre-distilled multiqubit resource states. This leads to a two step process: pre-distillation of multiqubit resource states, followed by implementation of the parity check. These protocols can prepare single-qubit magic states that enable direct injection of single-qubit axial rotations without subsequent gate-synthesis and its associated overhead. We show our protocols are more efficient than all previous comparable protocols with quadratic error reduction, including the protocols of Bravyi and Haah.

► BibTeX data

@article{Campbell2018magicstateparity,
  doi = {10.22331/q-2018-03-14-56},
  url = {https://doi.org/10.22331/q-2018-03-14-56},
  title = {Magic state parity-checker with pre-distilled components},
  author = {Campbell, Earl T. and Howard, Mark},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {56},
  month = mar,
  year = {2018}
}

► References

[1] Earl T Campbell, Barbara M Terhal, and Christophe Vuillot. Roads towards fault-tolerant universal quantum computation. Nature, 549 (7671): 172, 2017. 10.1038/nature23460.
https://doi.org/10.1038/nature23460

[2] Sergey Bravyi and Alexei Kitaev. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A, 71: 022316, 2005. 10.1103/PhysRevA.71.022316.
https://doi.org/10.1103/PhysRevA.71.022316

[3] Adam M. Meier, Bryan Eastin, and Emanuel Knill. Magic-state distillation with the four-qubit code. Quant. Inf. and Comp., 13: 195, 2013.

[4] Sergey Bravyi and Jeongwan Haah. Magic-state distillation with low overhead. Phys. Rev. A, 86: 052329, Nov 2012. 10.1103/PhysRevA.86.052329.
https://doi.org/10.1103/PhysRevA.86.052329

[5] Cody Jones. Multilevel distillation of magic states for quantum computing. Phys. Rev. A, 87: 042305, Apr 2013a. 10.1103/PhysRevA.87.042305.
https://doi.org/10.1103/PhysRevA.87.042305

[6] Jeongwan Haah, Matthew B. Hastings, D. Poulin, and D. Wecker. Magic state distillation with low space overhead and optimal asymptotic input count. Quantum, 1: 31, October 2017. ISSN 2521-327X. 10.22331/q-2017-10-03-31.
https://doi.org/10.22331/q-2017-10-03-31

[7] Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Asymptotically optimal approximation of single qubit unitaries by clifford and $t$ circuits using a constant number of ancillary qubits. Phys. Rev. Lett., 110: 190502, May 2013. 10.1103/PhysRevLett.110.190502.
https://doi.org/10.1103/PhysRevLett.110.190502

[8] David Gosset, Vadym Kliuchnikov, Michele Mosca, and Vincent Russo. An algorithm for the t-count. Quant. Inf. & Comp., 14 (15-16): 1261–1276, 2014.

[9] Neil J Ross and Peter Selinger. Optimal ancilla-free clifford+ t approximation of z-rotations. Quant. Inf. and Comp., 16: 901, 2016.

[10] Adam Paetznick and Krysta M Svore. Repeat-until-success: Non-deterministic decomposition of single-qubit unitaries. Quant. Inf. & Comp., 14 (15-16): 1277–1301, 2014.

[11] Alex Bocharov, Martin Roetteler, and Krysta M. Svore. Efficient synthesis of probabilistic quantum circuits with fallback. Phys. Rev. A, 91: 052317, May 2015. 10.1103/PhysRevA.91.052317.
https://doi.org/10.1103/PhysRevA.91.052317

[12] Andrew J Landahl and Chris Cesare. Complex instruction set computing architecture for performing accurate quantum $ z $ rotations with less magic. arXiv preprint arXiv:1302.3240, 2013. URL https://arxiv.org/pdf/1302.3240.pdf.
arXiv:1302.3240

[13] Cody Jones. Distillation protocols for fourier states in quantum computing. arXiv preprint arXiv:1303.3066, 2013b. URL https://arxiv.org/pdf/1303.3066.pdf.
arXiv:1303.3066

[14] Guillaume Duclos-Cianci and David Poulin. Reducing the quantum-computing overhead with complex gate distillation. Phys. Rev. A, 91: 042315, Apr 2015. 10.1103/PhysRevA.91.042315.
https://doi.org/10.1103/PhysRevA.91.042315

[15] Earl T Campbell and Joe O'Gorman. An efficient magic state approach to small angle rotations. Quantum Science and Technology, 1 (1): 015007, 2016. doi:10.1088/2058-9565/1/1/015007.

[16] Jeongwan Haah. Towers of generalized divisible quantum codes. arXiv preprint arXiv:1709.08658, 2017. URL https://arxiv.org/pdf/1709.08658.pdf.
arXiv:1709.08658

[17] Cody Jones. Low-overhead constructions for the fault-tolerant toffoli gate. Phys. Rev. A, 87: 022328, Feb 2013c. 10.1103/PhysRevA.87.022328.
https://doi.org/10.1103/PhysRevA.87.022328

[18] Bryan Eastin. Distilling one-qubit magic states into toffoli states. Phys. Rev. A, 87: 032321, Mar 2013. 10.1103/PhysRevA.87.032321.
https://doi.org/10.1103/PhysRevA.87.032321

[19] Earl T. Campbell and Mark Howard. Unifying gate synthesis and magic state distillation. Phys. Rev. Lett., 118: 060501, Feb 2017a. 10.1103/PhysRevLett.118.060501.
https://doi.org/10.1103/PhysRevLett.118.060501

[20] Earl T. Campbell and Mark Howard. Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost. Phys. Rev. A, 95: 022316, Feb 2017b. 10.1103/PhysRevA.95.022316.
https://doi.org/10.1103/PhysRevA.95.022316

[21] Jeongwan Haah, Matthew B Hastings, D Poulin, and D Wecker. Magic state distillation at intermediate size. Quant. Inf. and Comp., 18: 0114, 2018.

[22] Matthew B. Hastings and Jeongwan Haah. Distillation with sublogarithmic overhead. Phys. Rev. Lett., 120: 050504, Jan 2018. 10.1103/PhysRevLett.120.050504.
https://doi.org/10.1103/PhysRevLett.120.050504

[23] Daniel Gottesman and Isaac L. Chuang. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 402: 390, 1999. 10.1038/46503.
https://doi.org/10.1038/46503

[24] Earl T. Campbell and Dan E. Browne. On the structure of protocols for magic state distillation. Lecture Notes in Computer Science, 5906: 20, 2009. 10.1007/978-3-642-10698-9_3. arXiv:0908.0838.
https://doi.org/10.1007/978-3-642-10698-9_3
arXiv:0908.0838

[25] R. Raussendorf, J. Harrington, and K. Goyal. A fault-tolerant one-way quantum computer. Annals of Physics, 321 (9): 2242 – 2270, 2006. ISSN 0003-4916. 10.1016/j.aop.2006.01.012.
https://doi.org/10.1016/j.aop.2006.01.012

[26] Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A, 86: 032324, Sep 2012. 10.1103/PhysRevA.86.032324.
https://doi.org/10.1103/PhysRevA.86.032324

[27] Joe O'Gorman and Earl T. Campbell. Quantum computation with realistic magic-state factories. Phys. Rev. A, 95: 032338, Mar 2017. 10.1103/PhysRevA.95.032338.
https://doi.org/10.1103/PhysRevA.95.032338

[28] Jeongwan Haah and Matthew B Hastings. Codes and protocols for distilling $ t $, controlled-$ s $, and toffoli gates. arXiv preprint arXiv:1709.02832, 2017. URL https://arxiv.org/pdf/1709.02832.pdf.
arXiv:1709.02832

Cited by

[1] Ryuji Takagi and Hiroyasu Tajima, "Universal limitations on implementing resourceful unitary evolutions", Physical Review A 101 2, 022315 (2020).

[2] Michael Beverland, Earl Campbell, Mark Howard, and Vadym Kliuchnikov, "Lower bounds on the non-Clifford resources for quantum computations", Quantum Science and Technology 5 3, 035009 (2020).

[3] Akalank Jain and Shiroman Prakash, "Qutrit and ququint magic states", Physical Review A 102 4, 042409 (2020).

[4] Daniel Litinski, "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", Quantum 3, 128 (2019).

[5] Earl Campbell, Ankur Khurana, and Ashley Montanaro, "Applying quantum algorithms to constraint satisfaction problems", Quantum 3, 167 (2019).

[6] Earl Campbell, "Random Compiler for Fast Hamiltonian Simulation", Physical Review Letters 123 7, 070503 (2019).

[7] Lingling Lao and Ben Criger, Proceedings of the 19th ACM International Conference on Computing Frontiers 113 (2022) ISBN:9781450393386.

[8] Xin Wang, Mark M Wilde, and Yuan Su, "Quantifying the magic of quantum channels", New Journal of Physics 21 10, 103002 (2019).

[9] Christopher Chamberland, Kyungjoo Noh, Patricio Arrangoiz-Arriola, Earl T. Campbell, Connor T. Hann, Joseph Iverson, Harald Putterman, Thomas C. Bohdanowicz, Steven T. Flammia, Andrew Keller, Gil Refael, John Preskill, Liang Jiang, Amir H. Safavi-Naeini, Oskar Painter, and Fernando G.S.L. Brandão, "Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes", PRX Quantum 3 1, 010329 (2022).

[10] Daniel Litinski, "Magic State Distillation: Not as Costly as You Think", Quantum 3, 205 (2019).

[11] Gary J. Mooney, Charles D. Hill, and Lloyd C. L. Hollenberg, "Cost-optimal single-qubit gate synthesis in the Clifford hierarchy", Quantum 5, 396 (2021).

[12] Xin Wang, Mark M. Wilde, and Yuan Su, "Efficiently Computable Bounds for Magic State Distillation", Physical Review Letters 124 9, 090505 (2020).

[13] Christopher Chamberland and Earl T. Campbell, "Universal Quantum Computing with Twist-Free and Temporally Encoded Lattice Surgery", PRX Quantum 3 1, 010331 (2022).

[14] Shraddha Singh, Andrew S. Darmawan, Benjamin J. Brown, and Shruti Puri, "High-fidelity magic-state preparation with a biased-noise architecture", Physical Review A 105 5, 052410 (2022).

[15] James R. Seddon and Earl T. Campbell, "Quantifying magic for multi-qubit operations", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475 2227, 20190251 (2019).

[16] Craig Gidney and Austin G. Fowler, "Efficient magic state factories with a catalyzed|CCZ⟩to2|T⟩transformation", Quantum 3, 135 (2019).

[17] Xin Wang, Mark M. Wilde, and Yuan Su, "Quantifying the magic of quantum channels", arXiv:1903.04483, (2019).

[18] Xin Wang, Mark M. Wilde, and Yuan Su, "Efficiently computable bounds for magic state distillation", arXiv:1812.10145, (2018).

[19] Jeongwan Haah, "Towers of generalized divisible quantum codes", Physical Review A 97 4, 042327 (2018).

The above citations are from Crossref's cited-by service (last updated successfully 2023-03-31 13:15:08) and SAO/NASA ADS (last updated successfully 2023-03-31 13:15:09). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.