Random generation of combinatorial structures from a uniform
Theoretical Computer Science
Notes on the history of reversible computation
IBM Journal of Research and Development
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Randomized algorithms
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
A framework for fast quantum mechanical algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Handbook of Applied Cryptography
Handbook of Applied Cryptography
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Quantum searching amidst uncertainty
UC'05 Proceedings of the 4th international conference on Unconventional Computation
| Hi-index | 5.23 |
For every "computation" there corresponds the physical task of manipulating a starting state into an output state with a desired property. As the classical theory of physics has been replaced by quantum physics, it is interesting to consider the capabilities of a computer that can exploit the distinctive quantum features of nature. The extra capabilities seem enormous. For example, with only an expected O(square rootN) evaluations of a function f : {0; 1; : : : ; N - 1} → {0; 1}, we can find a solution to f(x) = 1 provided one exists. Another example is the ability to 1nd efficiently the order of an element g in a group by using a quantum computer to estimate a random eigenvalue of the unitary operator that multiplies by g in the group. By using this eigenvalue estimation algorithm to estimate an eigenvalue of the unitary operator used in quantum searching we can approximately count the number of solutions to f(x) = 1. This paper describes this eigenvector approach to quantum counting and related algorithms.