Can quantum computers have simple Hamiltonians?

Abstract

Recently, P. Shor (1994) has shown that quantum computers (computers which can operate simultaneously on a quantum superposition of inputs) permit efficient (i.e. polynomial-time) solutions of problems for which no efficient classical-mechanical solution is known. This has led to renewed interest in the question of whether or not quantum computers can be physically realized. One kind of quantum computer, quantum cellular automata, can be described by relatively simple Hamiltonians that resemble the Hamiltonians of spin systems. In this paper, we report a quantum cellular automaton which, though not itself computation-universal, forms an essential part of any quantum cellular automaton which is synchronized using Feynman's technique. This quantum cellular automaton has as its Hamiltonian the one-dimensional XY Hamiltonian, which is exactly solvable. Furthermore, there is experimental evidence from low-temperature measurements of the heat capacity and electric susceptibility that the Hamiltonian of the quantum cellular automaton is realized in nature by the rare-earth compound praseodymium ethyl sulfate near 1 K.<>