Testing shift-equivalence of polynomials by deterministic, probabilistic and quantum machines
Theoretical Computer Science
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Conjugated Operators in Quantum Algorithms
Conjugated Operators in Quantum Algorithms
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
On the power of quantum computation
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Using Fewer Qubits in Shor's Factorization Algorithm Via Simultaneous Diophantine Approximation
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Mathematical Methods in Computer Science
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Decomposing finite Abelian groups
Quantum Information & Computation
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 measurements for hidden subgroup problems with optimal sample complexity
Quantum Information & Computation
Quantum noisy rational function reconstruction
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Exponential quantum speed-ups are generic
Quantum Information & Computation
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A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and hidden or unknown subgroups of Abelian groups. It is already known how to phrase the first four problems as the estimation of eigenvalues of certain unitary operators. Here we show how the solution to the more general Abelian hidden subgroup problem can also be described and analysed as such. We then point out how certain instances of these problems can be solved with only one control qubit, or flying qubits, instead of entire registers of control qubits.