Near-term $n$ to $k$ distillation protocols using graph codes
- URL: http://arxiv.org/abs/2303.11465v2
- Date: Thu, 11 May 2023 15:49:59 GMT
- Title: Near-term $n$ to $k$ distillation protocols using graph codes
- Authors: Kenneth Goodenough, S\'ebastian de Bone, Vaishnavi L. Addala, Stefan
Krastanov, Sarah Jansen, Dion Gijswijt, David Elkouss
- Abstract summary: Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet.
We consider here an experimentally relevant class of distillation protocols, which distill $n$ to $k$ end-to-end entangled pairs.
We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Noisy hardware forms one of the main hurdles to the realization of a
near-term quantum internet. Distillation protocols allows one to overcome this
noise at the cost of an increased overhead. We consider here an experimentally
relevant class of distillation protocols, which distill $n$ to $k$ end-to-end
entangled pairs using bilocal Clifford operations, a single round of
communication and a possible final local operation depending on the observed
measurement outcomes. In the case of permutationally invariant depolarizing
noise on the input states, we find a correspondence between these distillation
protocols and graph codes. We leverage this correspondence to find provably
optimal distillation protocols in this class for several tasks important for
the quantum internet. This correspondence allows us to investigate use cases
for so-called non-trivial measurement syndromes. Furthermore, we detail a
recipe to construct the circuit used for the distillation protocol given a
graph code. We use this to find circuits of short depth and small number of
two-qubit gates. Additionally, we develop a black-box circuit optimization
algorithm, and find that both approaches yield comparable circuits. Finally, we
investigate the teleportation of encoded states and find protocols which
jointly improve the rate and fidelities with respect to prior art.
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