Unitary tetrahedron quantum gates
Vivek Kumar Singh, Akash Sinha, Pramod Padmanabhan, Vladimir Korepin

TL;DR
This paper systematically constructs and classifies unitary tetrahedron (3-simplex) quantum gates using Clifford algebras and Yang-Baxter operator lifting, enabling new multi-qubit gates for quantum computing.
Contribution
It provides the first comprehensive classification of unitary tetrahedron operators for qubits, expanding the toolkit for quantum circuit design.
Findings
13 inequivalent families of unitary tetrahedron operators identified
12 families derived from known Yang-Baxter operators and one from Clifford algebra
Universal sets of 1-, 2-, and 3-qubit gates constructed from these operators
Abstract
Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with -qubit generalisations of Yang-Baxter gates called -simplex operators. Such multi-qubit gates potentially lead to shallower and more efficient quantum circuits as well. Finding them amounts to identifying unitary solutions of the -simplex equations, the building blocks of higher dimensional integrable systems. These are a set of highly non-linear and over determined system of equations making it notoriously hard to solve even when the local Hilbert spaces are spanned by qubits. We systematically overcome this for higher simplex operators constructed using two methods: from Clifford algebras and by lifting Yang-Baxter operators. The or the tetrahedron case is analyzed in detail. For the qubit case our…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Gold and Silver Nanoparticles Synthesis and Applications
