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Efficient Clifford+T approximation of singlequbit operators
, 1212
"... We give an efficient randomized algorithm for approximating an arbitrary element of SU(2) by a product of Clifford+T operators, up to any given error threshold ǫ> 0. Under a mild hypothesis on the distribution of primes, the algorithm’s expected runtime is polynomial in log(1/ǫ). If the operator ..."
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Cited by 12 (1 self)
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We give an efficient randomized algorithm for approximating an arbitrary element of SU(2) by a product of Clifford+T operators, up to any given error threshold ǫ> 0. Under a mild hypothesis on the distribution of primes, the algorithm’s expected runtime is polynomial in log(1/ǫ). If the operator
The singlequbit T gate
"... Abstract. We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive to implement faulttolerantly. We therefore view ..."
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Abstract. We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive to implement faulttolerantly. We therefore view
Svore, “RepeatUntilSuccess: Nondeterministic decomposition of singlequbit unitaries,” p
, 2013
"... We present a decomposition technique that uses nondeterministic circuits to approximate an arbitrary singlequbit unitary to within distance and requires significantly fewer nonClifford gates than existing techniques. We develop “RepeatUntilSuccess ” (RUS) circuits and characterize unitaries th ..."
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Cited by 4 (1 self)
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We present a decomposition technique that uses nondeterministic circuits to approximate an arbitrary singlequbit unitary to within distance and requires significantly fewer nonClifford gates than existing techniques. We develop “RepeatUntilSuccess ” (RUS) circuits and characterize unitaries
A ResourceOptimal Canonical Form for Singlequbit Quantum Circuits
"... Abstract. Determining the optimal implementation of a quantum gate is critical for designing a quantum computer. We consider the crucial task of efficiently decomposing a general singlequbit quantum gate into a sequence of faulttolerant quantum operations. For a given singlequbit circuit, we cons ..."
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Abstract. Determining the optimal implementation of a quantum gate is critical for designing a quantum computer. We consider the crucial task of efficiently decomposing a general singlequbit quantum gate into a sequence of faulttolerant quantum operations. For a given singlequbit circuit, we
Representation of Quantum Circuits with Clifford and π/8 Gates
, 806
"... Abstract. In this paper, we introduce the notion of a normal form of one qubit quantum circuits over the basis {H, P, T}, where H, P and T denote the Hadamard, Phase and π/8 gates, respectively. This basis is known as the standard set and its universality has been shown by Boykin et al. [FOCS ’99]. ..."
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Cited by 6 (0 self)
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Abstract. In this paper, we introduce the notion of a normal form of one qubit quantum circuits over the basis {H, P, T}, where H, P and T denote the Hadamard, Phase and π/8 gates, respectively. This basis is known as the standard set and its universality has been shown by Boykin et al. [FOCS ’99
Quantum universality by state distillation
, 2009
"... Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This “magic states distillation ” question is closely related to quantum fault tolerance. Lower bounds on the noi ..."
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Cited by 5 (1 self)
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on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for faulttolerant computation. Upper bounds show the limits of threshold upperbound arguments based on the GottesmanKnill theorem. We extend the range of singlequbit mixed states that are known to give
Generalised Clifford groups and simulation of associated quantum circuits
, 2007
"... Quantum computations that involve only Clifford operations are classically simulable despite the fact that they generate highly entangled states; this is the content of the GottesmanKnill theorem. Here we isolate the ingredients of the theorem and provide generalisations of some of them with the ai ..."
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Cited by 7 (3 self)
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seek G such that G ⊗ G has an entangling normaliser. Via a generalisation of the GottesmanKnill theorem the resulting normalisers lead to classes of quantum circuits that can be classically efficiently simulated. For the qubit case d = 2 we exhaustively treat all finite subgroups of U(2) and find
Classical simulation complexity of extended Clifford circuits. Quantum Information and Computation
, 2014
"... Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The GottesmanKnill theorem asserts that Clifford computations can be classically efficiently simulated but this is true only in a suitably restricted setting. Here we consider Cliffo ..."
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Cited by 3 (0 self)
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Clifford computations with a variety of additional ingredients: (a) strong vs. weak simulation, (b) inputs being computational basis states vs. general product states, (c) adaptive vs. nonadaptive choices of gates for circuits involving intermediate measurements, (d) single line outputs vs. multi
Five Lectures on Optical Quantum Computing
, 705
"... Photons as qubits, phase shifters, beam splitters, polarization rotations, polarizing beam splitters, interferometers. 2 Twoqubit gates and the KLM scheme 6 Twophoton entanglement, the KLM approach, Clifford operations, twophoton interference, HongOuMandel effect, fusion gates. 3 Cluster states ..."
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13 From circuits to clusters, singlequbit gates, twoqubit gates, universal cluster states, making clusters with fusion gates. 4 Quantum computing with matter qubits and photons 18 Quantum memories, doubleheralding entangling procedure, making clusters with double heralding, quantum computer
Distillation of NonStabilizer States for Universal Quantum Computation
"... Magic state distillation is a fundamental technique for realizing faulttolerant universal quantum computing, and produces highfidelity Clifford eigenstates, called magic states, which can be used to implement the nonClifford π/8 gate. We propose an efficient protocol for distilling other nonstab ..."
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Cited by 4 (0 self)
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stabilizer states that requires only Clifford operations, measurement, and magic states. One critical application of our protocol is efficiently and fault tolerantly implementing arbitrary, nonClifford, singlequbit rotations in average constant online circuit depth and polylogarithmic (in precision) offline
Results 1  10
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