New paper published in PRL

Measurement based quantum computation is an alternative to standard ``circuit based" based computation. Rather than performing a sequence of unitary gates on an initially unentangled state, the computation flows by measurement only. In one scheme known as cluster state computing, you start with an easily prepared entangled resource state on a 2D lattice of spin-1/2 particles and the computation proceeds by single qubit measurements. Logical information is encoded into rows of qubits and the time flows when measuring along columns. A difficulty is making the cluster fault tolerant to errors while waiting for the qubits to be measured. We have found a way to prepare a computational resource in the ground state of a gapped two body Hamiltonian. (G.K. Brennen and Akimasa Miyake, http://arxiv.org/abs/0803.1478 and published version) that makes errors much less likely. Any local error costs a finite amount of energy and the logical information is stored in non local string operators. In the figure, each logical wire consist of N spin-1 particles with spin-1/2 particles on the boundaries. The initial state of each wire is a unique ground state of a 1D Hamiltonian. One starts by measuring the rightmost spin-1/2 particle which initializes the logical wire to 0 or 1. Afterward each wire has a two-fold degenerate (qubit) ground state space and single qubit computation flows to the right [just as in reading Japanese comics --though PRL wouldn't let us describe it that way] by measurement on the spin-1 particles. Two qubit operations involve two spin measurements on pairs of spin-1 particles on adjacent wires. At the end the information is read out on the left most spin-1/2 particles. The gates are probabilistic (2/3) but heralded (you know when it fails) and can retry with exponentially small failure rate with only a small linear size increase.
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