A non-anyonic qudit ZW-calculus
- URL: http://arxiv.org/abs/2109.11285v2
- Date: Tue, 12 Oct 2021 12:12:11 GMT
- Title: A non-anyonic qudit ZW-calculus
- Authors: Quanlong Wang
- Abstract summary: ZW-calculus is a useful graphical language for pure qubit quantum computing.
In this paper, we give a new type of qudit ZW-calculus which has generators and rewriting rules similar to that of the qubit ZW-calculus.
- Score: 0.3655021726150367
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: ZW-calculus is a useful graphical language for pure qubit quantum computing.
It is via the translation of the completeness of ZW-calculus that the first
proof of completeness of ZX-calculus was obtained. A d-level generalisation of
qubit ZW-calculus (anyonic qudit ZW-calculus) has been given in [Hadzihasanovic
2017] which is universal for pure qudit quantum computing. However, the
interpretation of the W spider in this type of ZW-calculus has so-called
q-binomial coefficients involved, thus makes computation quite complicated. In
this paper, we give a new type of qudit ZW-calculus which has generators and
rewriting rules similar to that of the qubit ZW-calculus. Especially, the Z
spider is exactly the same as that of the qudit ZX-calculus as given in [Wang
2021], and the new W spider has much simpler interpretation as a linear map.
Furthermore, we establish a translation between this qudit ZW-calculus and the
qudit ZX-calculus which is universal as shown in [Wang 2021], therefore this
qudit ZW-calculus is also universal for pure qudit quantum computing.
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