Abstract
The cluster state, the highly entangled state that is the central resource for one-way quantum computing, can be efficiently generated in a variety of physical implementations via global nearest-neighbor interactions. In practice, a systematic phase error is expected in the entangling process, resulting in imperfect cluster states. We present a stochastic measurement technique to generate large perfect cluster states and other graph states with high probability from imperfect cluster states even when their initial entanglement is weak.
Highlights
One-way quantum computing (1WQC) [1, 2] boasts the advantage over the standard quantum circuit approach of allowing all entanglement to be prepared in a single initial step prior to any logical operations
The cluster state can be efficiently p√roduced from a physical lattice of qubits, each initialized in the state |+ = (|0 + |1 ) / 2, by applying controlled-σz (CZ) operators between all nearest-neighbor qubit pairs, where σx, σy, and σz are the standard Pauli matrices
We have presented a stochastic measurement protocol, together with a technique for selectively entangling qubits, that enables the efficient growth of perfect cluster states and other perfect graph states even though the global entangling operator is always imperfect
Summary
One-way quantum computing (1WQC) [1, 2] boasts the advantage over the standard quantum circuit approach of allowing all entanglement to be prepared in a single initial step prior to any logical operations. It has been shown that standard fault tolerance schemes can be applied to 1WQC [13, 14], a more direct approach to removing these non-separable correlated errors would allow greater efficiency This issue has been previously considered in the context of NMR [15, 16]; composite pulse sequences were proposed as a means for reducing the effects of systematic phase errors in two-qubit gates. The composite pulse approach was further generalized by Brown et al [16] to allow two-qubit gates to be performed with arbitrary accuracy, though this required arbitrarily long composite pulse sequences These investigations were framed in the context of NMR and the conventional circuit model of quantum computing, it can in principle be applied to the generation of cluster states in the various aforementioned physical implementations. The work of Tame et al [12] suggests a practical technique for complete removal, rather than reduction, of systematic phase errors is desirable
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