Is CNOT gate Hermitian?
These sets are called Hermitian quantum gates. Many quantum gates such as CNOT, SWAP, Toffoli, Fredkin, Hadamard, and Pauli gates, which are used frequently in quantum circuits, are Hermitian [Pathak 2013].
What is a Z gate?
What is the Z-gate? The Z-gate is a unitary gate that acts on only one qubit. Specifically it maps 1 to -1 and leaves 0 unchanged. It does this by rotating around the Z axis of the qubit by π radians (180 degrees). By doing this it flips the phase of the qubit.
How is the ZX calculus used in lattice surgery?
The ZX-calculus is a language for lattice surgery on surface codes. It has been used to find and verify correctness of quantum error correcting codes. It has been used to optimize quantum circuits. Tools. The rewrite rules of the ZX-calculus can be implemented formally as an instance of double-pushout rewriting.
Is the ZX calculus universal to quantum circuit notation?
The ZX-calculus is universal in the sense that any linear map between qubits can be represented as a ZX-diagram, and different sets of graphical rewrite rules are complete for different families of linear maps. ZX-diagrams can be seen as a generalisation of quantum circuit notation .
What was the first completeness result for the ZX calculus?
In 2009 Duncan and Perdrix found the additional Euler decomposition rule for the Hadamard gate, which was used by Backens in 2013 to establish the first completeness result for the ZX-calculus. Namely that there exists a set of rewrite rules that suffice to prove all equalities between stabilizer ZX-diagrams, where phases are multiples of
Are there graphical rewrite rules for the ZX calculus?
In addition to the equalities between ZX-diagrams that are generated by topological deformations, the ZX-calculus also has a set of graphical rewrite rules for transforming ZX-diagrams into one another.