Related papers: Quantum Equivalence of the DLP and CDHP for Group …
It is well known that the graph isomorphism problem is polynomial-time reducible to the graph automorphism problem (in fact these two problems are polynomial-time equivalent). We show that, analogously, the group isomorphism problem is…
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…
In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the…
This paper proposes a parallel approach for the Vector Quantization (VQ) problem in image processing. VQ deals with codebook generation from the input training data set and replacement of any arbitrary data with the nearest codevector. Most…
Previous work has shown that there are two major complexity barriers in the synthesis of fault-tolerant distributed programs: (1) generation of fault-span, the set of states reachable in the presence of faults, and (2) resolving deadlock…
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…
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 consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset…
Parallel Quantum Annealing is a technique to solve multiple optimization problems simultaneously. Parallel quantum annealing aims to optimize the utilization of available qubits on a quantum topology by addressing multiple independent…
An approach to the equivalence problem of vector valued maps is offered which, in particular, covers the equivalence problem of paths and patches of differential geometry with respect to different motion groups. In the last case, in…
Motivated by the problem of effectively executing clustering algorithms on very large data sets, we address a model for large scale distributed clustering methods. To this end, we briefly recall some standards on the quantization problem…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
We present the first explicit connection between quantum computation and lattice problems. Namely, we show a solution to the Unique Shortest Vector Problem (SVP) under the assumption that there exists an algorithm that solves the hidden…
We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
We present a polynomial time reduction from the multi-graph isomorphism problem to the problem of code equivalence of additive codes over finite extensions of ${\mathbb F}_2$.
The polynomial-time hierarchy ($\mathrm{PH}$) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as $\mathrm{PH}$ does not collapse). Here, we study whether two…
Quantum algorithms that can speed up certain tasks, such as factorisation and unstructured search, have driven a decades-long development of quantum computers and quantum technologies. Yet, outside specialized applications, quantum…
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…