Identifying Critical Qubits for Gate Implementations in Measurement-Based Quantum Computing

EasyChair Preprint no. 10165

Abstract

Measurement-based quantum computing (MBQC)
is a powerful approach that relies on multi-qubit entangled
cluster states. To perform the universal set of quantum gates and,
thus, any quantum algorithm, we need to measure the cluster
state qubits in suitable measurement bases and proper order,
then use feed-forward measurement outcomes for final correction. Among photonic qubit architectures, the Gottesman-KitaevPreskill (GKP) bosonic continuous-variable (CV) qubit encoding
is a great candidate for MBQC. GKP qubits allow us to easily
apply the entangling CZ gates using beam splitters to generate the
resource cluster states. However, preparing high-quality, realistic,
finite-squeezed GKP qubits can be experimentally challenging.
It is thus reasonable to expect near-future implementations of
GKP-based MBQC on cluster states containing only a handful
of “good” quality GKP qubits, while the other qubits are either
weakly squeezed GKP qubits or just squeezed vacuum states.
In this paper, we analyze the performance of a universal set
of CV gates when a mix of different qualities (good and bad)
GKP qubits and squeezed vacuum states create the cluster
state. By comparing the performance, for the variety of quality
across all the nodes, we identify the critical qubits for each gate.
Our approach involves gate tomography, where we compare the
the output of the gates with the corresponding expected outcomes. We
present the logical error rates for the different gate realizations
as a function of the GKP squeezing for the combinations of
good and bad qubits, simulated and determined using Xanadu’s
Strawberry Fields python library.

Keyphrases: GKP, MBQC, quantum computing, tomography

@Booklet{EasyChair:10165,
  author = {Mohadeseh Azari and Kaushik Seshadreesan},
  title = {Identifying Critical Qubits for Gate Implementations in Measurement-Based Quantum Computing},
  howpublished = {EasyChair Preprint no. 10165},

  year = {EasyChair, 2023}}