# Quantum arithmetic and numerical analysis using Repeat-Until-Success circuits

- Published: 08 Jun 2014

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doi: 10.26421/qic16.1-2-9

- Microsoft Research United States

[10] Thomas G Draper, Samuel A Kutin, Eric M Rains, and Krysta M Svore. A logarithmic-depth quantum carry-lookahead adder. Quantum Information & Computation, 6(4):351{369, 2006.

[11] Steven A Cuccaro, Thomas G Draper, Samuel A Kutin, and Moulton David P. A new quantum ripple-carry addition circuit. 2004. arXiv preprint quant-ph/0410184.

[12] Yasuhiro Takahashi and Noboru Kunihiro. A linear-size quantum circuit for addition with no ancillary qubits. Quantum Information & Computation, 5(6):440{448, 2005.

[13] Stephane Beauregard. Circuit for Shor's algorithm using 2n + 3 qubits. arXiv preprint quant-ph/0205095, 2002.

[14] Rodney van Meter and Kohei M Itoh. Fast quantum modular exponentiation. Phys. Rev. A, 71(5):052320, 2005.

[15] Yudong Cao, Anargyros Papageorgiou, Iasonas Petras, Joseph Traub, and Sabre Kais. Quantum algorithm and circuit design solving the Poisson equation. New Journal of Physics, 15(1):013021, 2013.

[16] Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Fast and e cient exact synthesis of single-qubit unitaries generated by cli ord and t gates. Quantum Information & Computation, 13(7-8):607{630, 2013.

[17] Nathan Wiebe and Vadym Kliuchnikov. Floating point representations in quantum circuit synthesis. New Journal of Physics, 15(9):093041, 2013.

[18] Adam Paetznick and Krysta M Svore. Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries. arXiv preprint arXiv:1311.1074, 2013. [OpenAIRE]

[19] Alex Bocharov, Martin Roetteler, and Krysta M Svore. E cient synthesis of universal Repeat-Until-Success circuits. arXiv preprint arXiv:1404.5320, 2014.

[20] Neil J Ross and Peter Selinger. Optimal ancilla-free cli ord+ t approximation of z-rotations. arXiv preprint arXiv:1403.2975, 2014.

[21] Nathan Wiebe, Daniel Braun, and Seth Lloyd. Quantum algorithm for data tting. Phys. Rev. Lett., 109:050505, Aug 2012.

[22] Guoming Wang. Quantum algorithms for curve tting. arXiv preprint arXiv:1402.0660, 2014.

[23] Gilles Brassard, Peter H yer, Michele Mosca, and Alain Tapp. Quantum amplitude ampli cation and estimation. arXiv preprint quant-ph/0005055, 2000.

[24] Emanuel Knill, Raymond La amme, and Gerald J Milburn. A scheme for e cient quantum computation with linear optics. nature, 409(6816):46{52, 2001.

doi: 10.26421/qic16.1-2-9

- Microsoft Research United States

[10] Thomas G Draper, Samuel A Kutin, Eric M Rains, and Krysta M Svore. A logarithmic-depth quantum carry-lookahead adder. Quantum Information & Computation, 6(4):351{369, 2006.

[11] Steven A Cuccaro, Thomas G Draper, Samuel A Kutin, and Moulton David P. A new quantum ripple-carry addition circuit. 2004. arXiv preprint quant-ph/0410184.

[12] Yasuhiro Takahashi and Noboru Kunihiro. A linear-size quantum circuit for addition with no ancillary qubits. Quantum Information & Computation, 5(6):440{448, 2005.

[13] Stephane Beauregard. Circuit for Shor's algorithm using 2n + 3 qubits. arXiv preprint quant-ph/0205095, 2002.

[14] Rodney van Meter and Kohei M Itoh. Fast quantum modular exponentiation. Phys. Rev. A, 71(5):052320, 2005.

[15] Yudong Cao, Anargyros Papageorgiou, Iasonas Petras, Joseph Traub, and Sabre Kais. Quantum algorithm and circuit design solving the Poisson equation. New Journal of Physics, 15(1):013021, 2013.

[16] Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Fast and e cient exact synthesis of single-qubit unitaries generated by cli ord and t gates. Quantum Information & Computation, 13(7-8):607{630, 2013.

[17] Nathan Wiebe and Vadym Kliuchnikov. Floating point representations in quantum circuit synthesis. New Journal of Physics, 15(9):093041, 2013.

[18] Adam Paetznick and Krysta M Svore. Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries. arXiv preprint arXiv:1311.1074, 2013. [OpenAIRE]

[19] Alex Bocharov, Martin Roetteler, and Krysta M Svore. E cient synthesis of universal Repeat-Until-Success circuits. arXiv preprint arXiv:1404.5320, 2014.

[20] Neil J Ross and Peter Selinger. Optimal ancilla-free cli ord+ t approximation of z-rotations. arXiv preprint arXiv:1403.2975, 2014.

[21] Nathan Wiebe, Daniel Braun, and Seth Lloyd. Quantum algorithm for data tting. Phys. Rev. Lett., 109:050505, Aug 2012.

[22] Guoming Wang. Quantum algorithms for curve tting. arXiv preprint arXiv:1402.0660, 2014.

[23] Gilles Brassard, Peter H yer, Michele Mosca, and Alain Tapp. Quantum amplitude ampli cation and estimation. arXiv preprint quant-ph/0005055, 2000.

[24] Emanuel Knill, Raymond La amme, and Gerald J Milburn. A scheme for e cient quantum computation with linear optics. nature, 409(6816):46{52, 2001.