相关论文: Is Grover's Algorithm a Quantum Hidden Subgroup Al…
It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across \Omega(n \log n) coset states. One of the only known models…
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 ($\mathsf{HSP}$) has been attracting much attention in quantum computing, since several well-known quantum algorithms including Shor algorithm can be described in a uniform framework as quantum methods to address…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
Grover's algorithm is one of the most important quantum algorithms, which performs the task of searching an unsorted database without a priori probability. Recently the adiabatic evolution has been used to design and reproduce quantum…
In this paper, we study the nature of entanglement in quantum Grover's and Shor's algorithms. So far, the authors who have been interested in this problem have approached the question quantitatively by introducing entanglement measures…
It has been shown in recent years that quantum information has a topological nature (\cite{AC}, \cite{Co}, \cite{Co2}). In \cite{V}, Vicary undergoes the study of quantum algorithms using this new topological approach. The advantage of this…
Many exponential speedups that have been achieved in quantum computing are obtained via hidden subgroup problems (HSPs). We show that the HSP over Weyl-Heisenberg groups can be solved efficiently on a quantum computer. These groups are…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model,…
The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to…
The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are…
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…
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…
This work presents a precise connection between Clifford circuits, Shor's factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all…
Search is one of the most commonly used primitives in quantum algorithm design. It is known that quadratic speedups provided by Grover's algorithm are optimal, and no faster quantum algorithms for Search exist. While it is known that at…
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…