Efficient simulations of quantum many body systems is an important topic within physics. We are exploiting the fact that certain quantum circuits, so-called match gate circuits can be compressed into an exponentially smaller systems. That is, the computation can be carried out using just log(n) instead of n qubits. Interesting phenomena such as quantum phase transitions of e.g. the 1D Ising model can hence be observed with current technology. One of the aims here is to generalize the notion of compressed quantum computation and simulation to other models within condensed matter physics and quantum information.
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