Quantum Information Processing via Hamiltonian Inverse Quantum Engineering

TL;DR

This paper presents a method to design Hamiltonians for quantum algorithms, enabling implementation without auxiliary qubits and achieving high-probability Grover search with a single evolution.

Contribution

It introduces Hamiltonian inverse quantum engineering to realize quantum algorithms efficiently without extra resources or auxiliary qubits.

Findings

Feasible, time-independent Hamiltonians for Deutsch and Grover algorithms

Implementation of Deutsch algorithm without auxiliary qubits

High-probability Grover search with a single quantum evolution

Abstract

In this paper we discuss how we can design Hamiltonians to implement quantum algorithms, in particular we focus in Deutsch and Grover algorithms. As main result of this paper, we show how Hamiltonian inverse quantum engineering method allow us to obtain feasible and time-independent Hamiltonians for implementing such algorithms. From our approach for the Deutsch algorithm, different from others techniques, we can provide an alternative approach for implementing such algorithm where no auxiliary qubit and additional resources are required. In addition, by using a single quantum evolution, the Grover algorithm can be achieved with high probability $1-\epsilon^2$, where $\epsilon$ is a very small arbitrary parameter.