Related papers: Quantum Computation and Quadratically Signed Weigh…
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
We outline an algorithm for the Quantum Counting problem using Adiabatic Quantum Computation (AQC). We show that using local adiabatic evolution, a process in which the adiabatic procedure is performed at a variable rate, the problem is…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
This note is a stripped down version of a published paper on the Potts partition function, where we concentrate solely on the linear coding aspect of our approach. It is meant as a resource for people interested in coding theory but who do…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
We present authorized quantum computation, where only a user with a non-cloneable quantum authorization key can perform a unitary operation created by an authenticated programmer. The security of our authorized quantum computation is based…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…
Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in…
Quantum computing is expected to have transformative influences on many domains, but its practical deployments on industry problems are underexplored. We focus on applying quantum computing to operations management problems in industry, and…