Compressed Quantum Simulation of the Ising Model

Jozsa et al. [Proc. R. Soc. A 466, 809 2009)] have shown that a match gate circuit running on n qubits can be compressed to a universal quantum computation on log(n) + 3 qubits. Here, we show how this compression can be employed to simulate the Ising interaction of a 1D chain consisting of n qubits using a universal quantum computer running on log(n) qubits. We demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which displays a quantum phase transition, can be measured. This shows that the quantum phase transition of very large systems can be observed experimentally with current technology.