5,923 research outputs found
Distillation protocols for Fourier states in quantum computing
Fourier states are multi-qubit registers that facilitate phase rotations in
fault-tolerant quantum computing. We propose distillation protocols for
constructing the fundamental, -qubit Fourier state with error at
a cost of Toffoli gates and Clifford gates, or any arbitrary
Fourier state using gates. We analyze these protocols with methods
from digital signal processing. These results suggest that phase kickback,
which uses Fourier states, could be the current lowest-overhead method for
generating arbitrary phase rotations.Comment: 18 pages, 4 figure
Efficient classical simulation of the approximate quantum Fourier transform
We present a method for classically simulating quantum circuits based on the
tensor contraction model of Markov and Shi (quant-ph/0511069). Using this
method we are able to classically simulate the approximate quantum Fourier
transform in polynomial time. Moreover, our approach allows us to formulate a
condition for the composability of simulable quantum circuits. We use this
condition to show that any circuit composed of a constant number of approximate
quantum Fourier transform circuits and log-depth circuits with limited
interaction range can also be efficiently simulated.Comment: 5 pages, 3 figure
Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition
We present the detailed process of converting the classical Fourier Transform
algorithm into the quantum one by using QR decomposition. This provides an
example of a technique for building quantum algorithms using classical ones.
The Quantum Fourier Transform is one of the most important quantum subroutines
known at present, used in most algorithms that have exponential speed up
compared to the classical ones. We briefly review Fast Fourier Transform and
then make explicit all the steps that led to the quantum formulation of the
algorithm, generalizing Coppersmith's work.Comment: 12 pages, 1 figure (generated within LaTeX). To appear in Journal of
Computational and Applied Mathematic
Learning DNFs under product distributions via {\mu}-biased quantum Fourier sampling
We show that DNF formulae can be quantum PAC-learned in polynomial time under
product distributions using a quantum example oracle. The best classical
algorithm (without access to membership queries) runs in superpolynomial time.
Our result extends the work by Bshouty and Jackson (1998) that proved that DNF
formulae are efficiently learnable under the uniform distribution using a
quantum example oracle. Our proof is based on a new quantum algorithm that
efficiently samples the coefficients of a {\mu}-biased Fourier transform.Comment: 17 pages; v3 based on journal version; minor corrections and
clarification
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