Title:
EFFICIENT SYNTHESIS OF REPEAT-UNTIL-SUCCESS CIRCUITS IN CLIFFORD + T BASIS
Document Type and Number:
WIPO Patent Application WO/2015/157049
Kind Code:
A3
Abstract:
Repeat-Until-Success (RUS) circuits are compiled in a Clifford+T basis by selecting a suitable cyclotomic integer approximation of a target rotation so that the rotation is approximated within a predetermined precision. The cyclotomic integer approximation is randomly modified until a modified value can be expanded into a single- qubit unitary matrix by solving one or more norm equations. The matrix is then expanded into a two-qubit unitary matrix of special form, which is then decomposed into an optimal two-qubit Clifford+T circuit. A two-qubit RUS circuit using a primary qubit and an ancillary qubit is then obtained based on the latter decomposition. An alternate embodiment is disclosed that keeps the total T-depth of the derived circuit small using at most 3 additional ancilla qubits. Arbitrary unitary matrices defined over the cyclotomic field of 8th roots of unity are implemented with RUS circuits.
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Inventors:
BOCHAROV ALEXEI (US)
SVORE KRYSTA M (US)
ROETTELER MARTIN (US)
SVORE KRYSTA M (US)
ROETTELER MARTIN (US)
Application Number:
PCT/US2015/023757
Publication Date:
December 23, 2015
Filing Date:
April 01, 2015
Export Citation:
Assignee:
MICROSOFT TECHNOLOGY LICENSING LLC (US)
International Classes:
G06N99/00; B82Y10/00
Other References:
NEIL ROSS: "Optimal ancilla-free Clifford+T approximation of z-rotations", 12 March 2014 (2014-03-12), pages 1 - 36, XP002748649, Retrieved from the Internet [retrieved on 20151026]
WIEBE N ET AL: "Floating point representations in quantum circuit synthesis", NEW JOURNAL OF PHYSICS IOP PUBLISHING LTD. UK, vol. 15, no. 9, September 2013 (2013-09-01), pages 093041/1 - 24, XP020250127, ISSN: 1367-2630
BRETT GILES: "Exact synthesis of multiqubit Clifford+T circuits", 2 April 2013 (2013-04-02), pages 1 - 7, XP002749958, Retrieved from the Internet [retrieved on 20151030]
VADYM KLIUCHNIKOV: "Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits", 13 March 2014 (2014-03-13), pages 1 - 11, XP002748651, Retrieved from the Internet [retrieved on 20151026]
PETER SELINGER: "Efficient Clifford+T approximation of single-qubit operators", 26 December 2012 (2012-12-26), pages 1 - 16, XP002748652, Retrieved from the Internet [retrieved on 20151026]
WIEBE N ET AL: "Floating point representations in quantum circuit synthesis", NEW JOURNAL OF PHYSICS IOP PUBLISHING LTD. UK, vol. 15, no. 9, September 2013 (2013-09-01), pages 093041/1 - 24, XP020250127, ISSN: 1367-2630
BRETT GILES: "Exact synthesis of multiqubit Clifford+T circuits", 2 April 2013 (2013-04-02), pages 1 - 7, XP002749958, Retrieved from the Internet
VADYM KLIUCHNIKOV: "Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits", 13 March 2014 (2014-03-13), pages 1 - 11, XP002748651, Retrieved from the Internet
PETER SELINGER: "Efficient Clifford+T approximation of single-qubit operators", 26 December 2012 (2012-12-26), pages 1 - 16, XP002748652, Retrieved from the Internet
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