Universal MBQC with generalised parity-phase interactions and Pauli measurements

• Published in: Quantum (Vienna, Austria) Vol. 3; p. 134
• Main Authors: Kissinger, Aleks, van de Wetering, John
• Format: Journal Article
• Language: English
• Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 26-04-2019
• ISSN: 2521-327X; 2521-327X
• DOI: 10.22331/q-2019-04-26-134

We introduce a new family of models for measurement-based quantum computation which are deterministic and approximately universal. The resource states which play the role of graph states are prepared via 2-qubit gates of the form
exp
⁡
(
−
i
π
2
n
Z
⊗
Z
)
. When
n
=
2
, these are equivalent, up to local Clifford unitaries, to graph states. However, when
n
>
2
, their behaviour diverges in two important ways. First, multiple applications of the entangling gate to a single pair of qubits produces non-trivial entanglement, and hence multiple parallel edges between nodes play an important role in these generalised graph states. Second, such a state can be used to realise deterministic, approximately universal computation using only Pauli
Z
and
X
measurements and feed-forward. Even though, for
n
>
2
, the relevant resource states are no longer stabiliser states, they admit a straightforward, graphical representation using the ZX-calculus. Using this representation, we are able to provide a simple, graphical proof of universality. We furthermore show that for every
n
>
2
this family is capable of producing all Clifford gates and all diagonal gates in the
n
-th level of the Clifford hierarchy.