Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum Circuits with Unbounded Fan-out
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
General-Purpose Parallel Simulator for Quantum Computing
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Improved bounds for the approximate QFT
WISICT '04 Proceedings of the winter international synposium on Information and communication technologies
Architectural implications of quantum computing technologies
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Scaling and Better Approximating Quantum Fourier Transform by Higher Radices
IEEE Transactions on Computers
Uniformity of quantum circuit families for error-free algorithms
Theoretical Computer Science
ACM SIGACT News
Arithmetic on a distributed-memory quantum multicomputer
ACM Journal on Emerging Technologies in Computing Systems (JETC)
On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography
Theory of Quantum Computation, Communication, and Cryptography
Parallelizing quantum circuits
Theoretical Computer Science
The computational complexity of linear optics
Proceedings of the forty-third annual ACM symposium on Theory of computing
A lower bound method for quantum circuits
Information Processing Letters
On the Effect of Quantum Interaction Distance on Quantum Addition Circuits
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Circuit for Shor's algorithm using 2n+3 qubits
Quantum Information & Computation
A quantum circuit for shor's factoring algorithm using 2n + 2 qubits
Quantum Information & Computation
Quantum lower bounds for fanout
Quantum Information & Computation
A geometric approach to quantum circuit lower bounds
Quantum Information & Computation
The quantum fourier transform on a linear nearest neighbor architecture
Quantum Information & Computation
Efficient quantum circuits for approximating the Jones polynomial
Quantum Information & Computation
An O(m2)-depth quantum algorithm for the elliptic curve discrete logarithm problem over GF(2m)a
Quantum Information & Computation
Quantum universality by state distillation
Quantum Information & Computation
Bounds on the power of constant-depth quantum circuits
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Quantum fourier transform over symmetric groups
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
A 2D nearest-neighbor quantum architecture for factoring in polylogarithmic depth
Quantum Information & Computation
Quantum Information & Computation
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We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n+log log(1//spl epsiv/)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2/sup n/ with error bounded by /spl epsiv/. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log(n//spl epsiv/)). As an application of this depth bound, we show that P. Shor's (1997) factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial size, in combination with classical polynomial-time pre- and postprocessing. Next, we prove an /spl Omega/(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically tight (for a reasonable range of values of /spl epsiv/). We also give an upper bound of O(n(log n)/sup 2/ log log n) on the circuit size of the exact QFT modulo 2/sup n/, for which the best previous bound was O(n/sup 2/). Finally, based on our circuits for the QFT with power-of-2 moduli, we show that the QFT with respect to an arbitrary modulus m can be approximated with accuracy /spl epsiv/ with circuits of depth O((log log m)(log log 1//spl epsiv/)) and size polynomial in log m+log(1//spl epsiv/).