Two-qubit stabilizer circuits and recovery procedures

Presenting Author: Raymond Wong, University of California Santa Barbara
Contributing Author(s): Wim van Dam

Stabilizer operations play an integral part in several techniques that are fundamental to building a universal fault-tolerant quantum computer. Understanding the boundaries of their utility on general input is important to realizing a cost-effective strategy to running a quantum computation. We consider the problem of categorizing the different ways we may use stabilizer operations to reduce a two-qubit state down to one. We reveal two new findings from our investigation. First, we prove that for any postselected two-qubit stabilizer circuit, there exists an alternate that achieves the same output but uses at most one CNOT or SWAP gate surrounded by single qubit Clifford gates. In the process we identify three circuit forms characterizing all such alternative circuits. Second, we show that some postselected circuits have the capacity to “recycle” qubits. In particular, when one circuit fails to obtain a desired qubit, a second circuit may reuse the output to try recover one the input qubits that was used in the first. We design a recovery procedure involving multiple such circuits, thereby lowering demand to prepare another copy of that qubit. Under certain imputs, we can even cut down our qubit usage by as much as half.

(Session 5 : Thursday from 5:00pm - 7:00 pm)


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