相关论文: On the Impossibility of a Quantum Sieve 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…

It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many…

Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…

The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…

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…

We present a quantum algorithm for the dihedral hidden subgroup problem with time and query complexity $O(\exp(C\sqrt{\log N}))$. In this problem an oracle computes a function $f$ on the dihedral group $D_N$ which is invariant under a…

Quantum algorithm is a key tool for cryptanalysis. At present, people are committed to building powerful quantum algorithms and tapping the potential of quantum algorithms, so as to further analyze the security of cryptographic algorithms…

The Hidden Subgroup Problem (HSP) is a computational problem which includes as special cases integer factorization, the discrete logarithm problem, graph isomorphism, and the shortest vector problem. The celebrated polynomial-time quantum…

Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…

The hidden subgroup problem (HSP) provides a unified framework to study problems of group-theoretical nature in quantum computing such as order finding and the discrete logarithm problem. While it is known that Fourier sampling provides an…

The computational cost of simulating quantum many-body systems can often be reduced by taking advantage of physical symmetries. While methods exist for specific symmetry classes, a general algorithm to find the full permutation symmetry…

We consider the isomorphism problem for groups specified by their multiplication tables. Until recently, the best published bound for the worst-case was achieved by the n^(log_p n + O(1)) generator-enumeration algorithm. In previous work…

The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…

We present efficient quantum algorithms for the hidden subgroup problem (HSP) on the semidirect product of cyclic groups $\Z_{p^r}\rtimes_{\phi}\Z_{p^2}$, where $p$ is any odd prime number and $r$ is any integer such that $r>4$. We also…

The problem of Subgraph Isomorphism is defined as follows: Given a pattern H and a host graph G on n vertices, does G contain a subgraph that is isomorphic to H? Eppstein [SODA 95, J'GAA 99] gives the first linear time algorithm for…

The arguments given in this paper suggest that Grover's and Shor's algorithms are more closely related than one might at first expect. Specifically, we show that Grover's algorithm can be viewed as a quantum algorithm which solves a…

The first quantum algorithm to offer an exponential speedup (in the query complexity setting) over classical algorithms was Simon's algorithm for identifying a hidden exclusive-or mask. Here we observe how part of Simon's algorithm can be…

We consider the problem of learning $N$ identical copies of an unknown $n$-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly $d$ neighboring vertices. Here, we…

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the…