相关论文: Efficient Quantum Algorithm for Hidden Quadratic a…
The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…
Many quantum algorithms, including Shor's celebrated factoring and discrete log algorithms, proceed by reduction to a Hidden Subgroup problem, in which an unknown subgroup H of a group G must be determined from a uniform superposition on a…
Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden…
We consider a recently proposed generalisation of the abelian hidden subgroup problem: the shifted subset problem. The problem is to determine a subset S of some abelian group, given access to quantum states of the form |S+x>, for some…
We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…
We give an exposition of the hidden subgroup problem for dihedral groups from the point of view of the standard hidden subgroup quantum algorithm for finite groups. In particular, we recall the obstructions for strong Fourier sampling to…
We study the computational complexity of quantum state isomorphism problems under group actions: given two quantum circuits that prepare pure or mixed states, decide whether the two states are related by a group action. This can be seen as…
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in…
It has recently been shown that quantum computers can efficiently solve the Heisenberg hidden subgroup problem, a problem whose classical query complexity is exponential. This quantum algorithm was discovered within the framework of using…
We introduce the Shifted Legendre Symbol Problem and some variants along with efficient quantum algorithms to solve them. The problems and their algorithms are different from previous work on quantum computation in that they do not appear…
Most quantum algorithms that give an exponential speedup over classical algorithms exploit the Fourier transform in some way. In Shor's algorithm, sampling from the quantum Fourier spectrum is used to discover periodicity of the modular…
We study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to…
Daniel Simon's 1994 discovery of an efficient quantum algorithm for solving the hidden subgroup problem (HSP) over Z_2^n provided one of the first algebraic problems for which quantum computers are exponentially faster than their classical…
Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden…
In this paper we discuss the Hidden Subgroup Problem (HSP) in relation to post-quantum group-based cryptography. We review the relationship between HSP and other computational problems discuss an optimal solution method, and review the…
The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…