Efficient Quantum Computation with Probabilistic Quantum Gates

With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The required computational overhead scales efficiently both with $1/p$ and $n$, where $n$ is the number of qubits in the computation. This approach provides an efficient way to combat noise in a class of quantum computation implementation schemes, where the dominant noise leads to probabilistic signaled errors with an error probability $1-p$ far beyond any threshold requirement.

Figure 1

Illustration of the three properties of the cluster states which are important for our construction of such states with the probabilistic entangling gates: (a) extend cluster states with CPF gates; (b) recover cluster states by removing bad qubits; (c) shrink cluster states for more complicated links.

Figure 2

Illustration of the steps for construction of the 2D square lattice cluster states from a set of cluster chains. (a) Construction of the basic $+$-shape states from cluster chains by applying first a Hardmard gate H on the middle qubit of one chain, and then a CPF gate to connect the two middle qubits, and finally a $X$ measurement on one middle qubit to remove it. (b),(c) Construction of the square lattice cluster state from the $+$-shape states through probabilistic CPF gates along the legs and $X$ measurements to remove the remaining redundant qubits.