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Optimal ancilla-free Clifford+T approximation of z-rotations · Around

2014

Optimal ancilla-free Clifford+T approximation of z-rotations

Ross, Neil J., Selinger, Peter

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We consider the problem of approximating arbitrary single-qubit z-rotations by ancilla-free Clifford+T circuits, up to given epsilon.

We present a fast new probabilistic algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance.
The algorithm requires a factoring oracle (such as a quantum computer).
Even in the absence of a factoring oracle, the algorithm is still near-optimal under a mild number-theoretic hypothesis.

Built on

Distillation of nonstabilizer states for universal quantum computation
Original
G. Duclos-Cianci and K. M. Svore · 1980
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Probabilistic algorithms in finite fields
M. O. Rabin · 1980
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Algorithms for quantum computation: discrete logarithms and factoring
P. W. Shor · 1994
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Constructing arbitrary Steane code single logical qubit fault-tolerant gates
A. G. Fowler · 2011
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Efficient decomposition of single-qubit gates into V V basis circuits
Original
A. Bocharov, Y. Gurevich, and K. M. Svore · 2013
Earlier work this paper cites.
Exact synthesis of multiqubit Clifford+ T T circuits
Original
B. Giles and P. Selinger · 2013
Earlier work this paper cites.

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