Abstract
We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities than what is currently available in the literature. We provide a software tool for analytical and numerical study of the generated purification circuits, under customizable error models. These new purification protocols pave the way to practical implementations of modular quantum computers and quantum repeaters. Our approach is particularly attentive to the effects of finite resources and imperfect local operations - phenomena neglected in the usual asymptotic approach to the problem. The choice of the building blocks permitted in the construction of the circuits is based on a thorough enumeration of the local Clifford operations that act as permutations on the basis of Bell states.
Highlights
The eventual construction of a scalable quantum computer is bound to revolutionize both how we solve practical problems like quantum simulation, and how we approach foundational questions ranging from topics in computational complexity to quantum gravity
While great many high performing errorcorrecting codes have been constructed by theorists, only recently did experiments start approaching hardware-level error rates that are sufficiently close to the threshold at which codes start to help [1, 2]
The infidelity of created Bell pairs is on the order of 10%, while noise due to local gates and measurements can be much lower than 1%
Summary
We consider each two-qubit gate Uto be performed correctly with a chance p2 and to completely depolarize the two qubits i and j it is acting upon with chance 1 − p2. As discussed throughout the main text, a useful way to represent the operations performed in the circuit is as permutations of the Bell basis. For this example we will use perfect operations (i.e. only initialization errors). The following table describes how “mirrored” CNOT operation acts on the basis states (“AD” stands for “the sacrificial pair is in state D and the pair to be purified is in state A”): initial state. With this mapping we can trace how the state of the system evolves. Bellow we describe how the errors propagate: After the CNOT gate we have the following redistribution of errors: on preserved
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