Sentence examples for star operator from inspiring English sources

for, and define the Hodge star operator (1.6).

The Hodge star operator : is defined by the rule (1.6).

We define the Hodge star operator by (2.1).

We denote the exterior derivative by d and the Hodge star operator by *.

We define the Hodge star operator by the rule and for all.

As usual, we still use to denote the Hodge star operator.

Products of data qubits around dark (light) squares correspond to plaquette (star) operators.

The green squares are ancillary qubits necessary to measure plaquette and star operators in a non-demolition fashion.

Note that plaquette and star operators at the boundaries are products of three qubit operators and not four as is the case in the bulk.

As was the case for the Fibonacci code, we need to introduce ancillary qubits to measure plaquette and star operators non-destructively.

We define the star operators (A_{s}) and plaquette operators (B_{p}) of the surface code as begin{aligned}& A_{s} = sigma_{s,1}^{x}sigma_{s,2}^{x} sigma_{s,3}^{x}sigma _{s,4}^{x}, end{aligned} (16) begin{aligned}& B_{p} = sigma_{p,1}^{x}sigma_{p,2}^{x} sigma_{p,3}^{x}sigma _{p,4}^{x}, end{aligned} (17) where s and p label respectively light and dark squares of the lattice, see Figure 9.