Related papers: Polynomial-Time Solution to the Hidden Subgroup Pr…
This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum…
We show that every countable group H with solvable word problem (=computable group) can be subnormally embedded into a 2-generated group G which also has solvable word problem. Moreover, the membership problem for H < G is also solvable. We…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
We present a series of examples of precompact, noncompact, reflexive topological Abelian groups. Some of them are pseudocompact or even countably compact, but we show that there exist precompact non-pseudocompact reflexive groups as well.…
The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm…
In this paper, we give a quantum algorithm which solves collision problem in an expected polynomial time. Especially, when the function is two-to-one, we present a quantum algorithm which can find a collision with certainty in a worst-case…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…
Unit group computations are a cryptographic primitive for which one has a fast quantum algorithm, but the required number of qubits is $\tilde O(m^5)$. In this work we propose a modification of the algorithm for which the number of qubits…
A family of nonhermitian quantum graphs (exhibiting, presumably, a hidden form of hermiticity) is proposed and studied via their discretization.
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
Quantum information processing requires a high degree of isolation from the detrimental effects of the environment as well as an extremely precise level of control on the way quantum dynamics unfolds in the information-processing system. In…
We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup.
We give an algorithm for the hidden subgroup problem for the dihedral group $D_N$, or equivalently the cyclic hidden shift problem, that supersedes our first algorithm and is suggested by Regev's algorithm. It runs in $\exp(O(\sqrt{\log…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle…
We suggest that quantum computers can solve quantum many-body problems that are impracticable to solve on a classical computer.