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Julian Miller

Publications and source records attributed to Julian Miller.

6 recordsLinked to original sources
arXiv2004

Quantum Searching via Entanglement and Partial Diffusion

In this paper, we will define a quantum operator that performs the inversion about the mean only on a subspace of the system (Partial Diffusion Operator). This operator is used in a quantum search algorithm that runs in O(sqrt{N/M}) for searching an unstructured list of size N with M matches such that 1<= M<=N. We will show that the performance of the algorithm is more reliable than known {fixed operators quantum search algorithms} especially for multiple matches where we can get a solution after a single iteration with probability over 90% if the number of matches is approximately more than one-third of the search space. We will show that the algorithm will be able to handle the case where the number of matches M is unknown in advance such that 1<=M<=N in O(sqrt{N/M}). A performance comparison with Grover's algorithm will be provided.

quant-ph↗
arXiv2003

Quantum Search Algorithm with more Reliable Behaviour using Partial Diffusion

In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system ({\it Partial Diffusion Operator}) to propose a quantum search algorithm runs in $O(\sqrt N/M})$ for searching unstructured list of size $N$ with $M$ matches such that, $1\le M \le N$. We will show that the performance of the algorithm is more reliable than known quantum search algorithms especially for multiple matches within the search space. A performance comparison with Grover's algorithm will be provided.

quant-ph↗
arXiv2003

A Hybrid Quantum Search Engine: A Fast Quantum Algorithm for Multiple Matches

In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid quantum search engine that integrates Grover's algorithm and the proposed algorithm here to have general performance better that any pure classical or quantum search algorithm.

quant-ph↗
arXiv2003

Representation of Boolean Quantum Circuits as Reed-Muller Expansions

In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their quantum equivalents. A direct result of this is that the problem of synthesis and optimization of quantum Boolean logic can be tackled within the field of Reed-Muller logic.

quant-ph↗
arXiv2003

Automated Method for Building CNOT Based Quantum Circuits for Boolean Functions

In this paper we discuss an efficient technique that can implement any given Boolean function as a quantum circuit. The method converts a truth table of a Boolean function to the corresponding quantum circuit using a minimal number of auxiliary qubits. We give examples of some circuits synthesized with this technique. A direct result that follows from the technique is a new way to convert any classical digital circuit to its classical reversible form.

quant-ph↗