Related papers: Quantum computation from a quantum logical perspec…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
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…
The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…
We determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the…
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given. This algorithm is based on a combinatorial expression for a particular bijection among binary strings. The algorithm, which adheres to the…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
The classical 3SUM conjecture states that the class of 3SUM-hard problems does not admit a truly subquadratic $O(n^{2-\delta})$-time algorithm, where $\delta >0$, in classical computing. The geometric 3SUM-hard problems have widely been…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
Quantum machine learning applies principles such as superposition and entanglement to data processing and optimization. Variational quantum models operate on qubits in high-dimensional Hilbert spaces and provide an alternative approach to…
We identify a sub-class of BQP that captures certain structural commonalities among many quantum algorithms including Shor's algorithms. This class does not contain all of BQP (e.g. Grover's algorithm does not fall into this class). Our…
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
Shor's algorithm is one of the most important quantum algorithm proposed by Peter Shor [Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124--134]. Shor's algorithm can factor a large integer with…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
A causal set C can describe a discrete spacetime, but this discrete spacetime is not quantum, because C is endowed with Boolean logic, as it does not allow cycles. In a quasi-ordered set Q, cycles are allowed. In this paper, we consider a…
Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a…
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…
Theory of computer calculations strongly depends on the nature of elements the computer is made of. Quantum interference allows to formulate the Shor factorization algorithm turned out to be more effective than any one written for classical…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…