Geometric representations of braid and Yang-Baxter gates
arXiv:2406.08320 · doi:10.1088/1751-8121/ad85b2
Abstract
Brick-wall circuits composed of the Yang-Baxter gates are integrable. It becomes an important tool to study the quantum many-body system out of equilibrium. To put the Yang-Baxter gate on quantum computers, it has to be decomposed into the native gates of quantum computers. It is favorable to apply the least number of native two-qubit gates to construct the Yang-Baxter gate. We study the geometric representations of all X-type braid gates and their corresponding Yang-Baxter gates via the Yang-Baxterization. We find that the braid and Yang-Baxter gates can only exist on certain edges and faces of the two-qubit tetrahedron. We identify the parameters by which the braid and Yang-Baxter gates are the Clifford gate, the matchgate, and the dual-unitary gate. The geometric representations provide the optimal decompositions of the braid and Yang-Baxter gates in terms of other two-qubit gates. We also find that the entangling powers of the Yang-Baxter gates are determined by the spectral parameters. Our results provide the necessary conditions to construct the braid and Yang-Baxter gates on quantum computers.
Published version, 27 pages, 7 figures, 2 tables
References in corpus (37)
- Quantum Computing in the NISQ era and beyond
- Optimal Quantum Circuits for General Two-Qubit Gates
- A geometric theory of non-local two-qubit operations
- Classical simulation of noninteracting-fermion quantum circuits
- Minimal Universal Two-qubit Quantum Circuits
- A practical scheme for quantum computation with any two-qubit entangling gate
- A universal quantum circuit for two-qubit transformations with three CNOT gates
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Matchgates and classical simulation of quantum circuits
- Braiding Operators are Universal Quantum Gates
- Comparing Quantum Entanglement and Topological Entanglement
- Integrable Trotterization: Local Conservation Laws and Boundary Driving
- Ballistic spin transport in a periodically driven integrable quantum system
- Formation of robust bound states of interacting microwave photons
- Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
- Braiding transformation, entanglement swapping and Berry phase in entanglement space
- Efficient quantum circuits for one-way quantum computing
- Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
- Optimal quantum circuit synthesis from Controlled-U gates
- Correlations and commuting transfer matrices in integrable unitary circuits
- Entangling power and local invariants of two-qubit gates
- Conditions for optimal construction of two-qubit non-local gates
- A Yang-Baxter integrable cellular automaton with a four site update rule
- Extending matchgates into universal quantum computation
- Teleportation, Braid Group and Temperley--Lieb Algebra
- Conserved charges in the quantum simulation of integrable spin chains
- Yang-Baxter operators need quantum entanglement to distinguish knots
- Introduction to Quantum Integrability
- Classifying Quantum Entanglement through Topological Links
- Integrable deformations of superintegrable quantum circuits
- The Floquet Baxterisation
- Braiding quantum gates from partition algebras
- Optimal realization of Yang-Baxter gate on quantum computers
- Quantum Computing via The Bethe Ansatz
- Local invariants of braiding quantum gates -- associated link polynomials and entangling power
- Localization and integrability breaking in weakly interacting Floquet circuits
- Quantum Gates Between Distant Qubits via Spin-Independent Scattering