A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of 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
Regular Article: On Quantum Algorithms for Noncommutative Hidden Subgroups
Advances in Applied Mathematics
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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)
The power of basis selection in fourier sampling: hidden subgroup problems in affine groups
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Fast quantum algorithms for computing the unit group and class group of a number field
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Polynomial time quantum algorithm for the computation of the unit group of a number field
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The Symmetric Group Defies Strong Fourier Sampling
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Random Measurement Bases, Quantum State Distinction and Applications to the Hidden Subgroup Problem
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
On the power of random bases in fourier sampling: hidden subgroup problem in the heisenberg group
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the impossibility of a quantum sieve algorithm for graph isomorphism
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum algorithms for Simon's problem over general groups
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Mathematical Methods in Computer Science
Quantum algorithms for Simon's problem over nonabelian groups
ACM Transactions on Algorithms (TALG)
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Algebraic methods in quantum informatics
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
On the complexity of the hidden subgroup problem
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Quantum algorithms for highly non-linear Boolean functions
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the Impossibility of a Quantum Sieve Algorithm for Graph Isomorphism
SIAM Journal on Computing
Finding conjugate stabilizer subgroups in PSL(2; q) and related groups
Quantum Information & Computation
For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets
Quantum Information & Computation
Quantum measurements for hidden subgroup problems with optimal sample complexity
Quantum Information & Computation
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
Quantum Information & Computation
Efficient quantum algorithm for identifying hidden polynomials
Quantum Information & Computation
Quantum algorithms for shifted subset problems
Quantum Information & Computation
Efficient quantum algorithms for the hidden subgroup problem over semi-direct product groups
Quantum Information & Computation
McEliece and niederreiter cryptosystems that resist quantum fourier sampling attacks
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Solutions to the hidden subgroup problem on some metacyclic groups
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
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It has been known for some time that graph isomorphism reduces to the hidden subgroup problem (HSP). What is more, most exponential speedups in quantum computation are obtained by solving instances of the HSP. A common feature of the resulting algorithms is the use of quantum coset states, which encode the hidden subgroup. An open question has been how hard it is to use these states to solve graph isomorphism. It was recently shown by Moore, Russell, and Schulman [30] that only an exponentially small amount of information is available from one, or a pair of coset states. A potential source of power to exploit are entangled quantum measurements that act jointly on many states at once. We show that entangled quantum measurements on at least Ω(n log n) coset states are necessary to get useful information for the case of graph isomorphism, matching an information theoretic upper bound. This may be viewed as a negative result because highly entangled measurements seem hard to implement in general. Our main theorem is very general and also rules out using joint measurements on few coset states for some other groups, such as GL(n,Fpm) and Gn where G is finite and satisfies a suitable property.