Fault-tolerant measurement-based quantum computing
Measurement-based quantum computing
“The existence of a non-zero threshold was first proven by reduction to the circuit model.” Measurement-based quantum computing can simulate an arbitrary quantum circuit.
“Subsequent developments evolved along two lines.” One assumes we are constrained to nearest-neighbor interactions between qubits; The other doesn’t.
“First, it was realized that the one-way quantum computer may be advantageously combined with the KLM scheme of optical quantum computation. Fault-tolerant schemes using photons were developed. The constraint of short-range interaction and arrangement of qubits in a 2D lattice — a characteristic feature of the initial one-way quantum computer — is not relevant for photons.”
“A second line of research kept the geometric constraint of nearest-neighbor interaction, which is a realistic scenario for stationary qubits. To achieve fault-tolerance we increase the lattice dimension from two to three.” Any 2D CSS code evolving in time can be mapped to a 3D graph state. Topological error-correction is directly built into the cluster lattice.” An example scheme that relies on this idea: Topologically fault-tolerant MBQC with non Clifford gates using local measurements in a Reed-Muller code.
- More general way of thinking: Measurement-based fault-tolerance beyond foliation;