sf.ops.CZgate¶
-
class
CZgate(s=1)[source]¶ Bases:
strawberryfields.ops.GateControlled phase gate in the position basis.
\[\text{CZ}(s) = \iint dx dy \: e^{i sxy/\hbar} \ket{x,y}\bra{x,y} = e^{i s \: \hat{x} \otimes \hat{x}/\hbar}\]In the position basis it maps \(\ket{x_1, x_2} \mapsto e^{i s x_1 x_2/\hbar} \ket{x_1, x_2}\).
- Parameters
s (float) – phase shift multiplier
Details and Conventions
Definition
\[\text{CZ}(s) = \iint dx dy \: e^{i s x_1 x_2/\hbar } \xket{x_1,x_2}\xbra{x_1,x_2} = \exp\left({i s \: \hat{x_1} \otimes \hat{x_2} /\hbar}\right).\]It is related to the addition gate by a phase space rotation in the second mode:
\[\text{CZ}(s) = R_{(2)}(\pi/2) \: \text{CX}(s) \: R_{(2)}^\dagger(\pi/2).\]In the position basis \(\text{CZ}(s) \xket{x_1, x_2} = e^{i s x_1 x_2/\hbar} \xket{x_1, x_2}\).
We can also write the action of the controlled-phase gate on the canonical operators:
\[\begin{split}\text{CZ}(s)^\dagger \x_1 \text{CZ}(s) &= \x_1\\ \text{CZ}(s)^\dagger \p_1 \text{CZ}(s) &= \p_1+ s \ \x_2\\ \text{CZ}(s)^\dagger \x_2 \text{CZ}(s) &= \x_2\\ \text{CZ}(s)^\dagger \p_2 \text{CZ}(s) &= \p_2+ s \ \x_1 \\ \text{CZ}(s)^\dagger \hat{a}_1 \text{CZ}(s) &= \a_1+ i\frac{s}{2} (\ad_2 + \a_2)\\ \text{CZ}(s)^\dagger \hat{a}_2 \text{CZ}(s) &= \a_2+ i\frac{s}{2} (\ad_1 + \a_1)\\\end{split}\]Attributes
Returns a copy of the gate with the self.dagger flag flipped.
Extra dependencies due to parameters that depend on measurements.
-
H¶ Returns a copy of the gate with the self.dagger flag flipped.
H stands for hermitian conjugate.
- Returns
formal inverse of this gate
- Return type
Gate
-
measurement_deps¶ Extra dependencies due to parameters that depend on measurements.
- Returns
dependencies
- Return type
set[RegRef]
-
ns= 2¶
Methods
apply(reg, backend, **kwargs)Ask a backend to execute the operation on the current register state right away.
decompose(reg, **kwargs)Decompose the operation into elementary operations supported by the backend API.
merge(other)Merge the operation with another (acting on the exact same set of subsystems).
-
apply(reg, backend, **kwargs)¶ Ask a backend to execute the operation on the current register state right away.
Like
Operation.apply(), but takes into account the special nature of p[0] and applies self.dagger.- Returns
Gates do not return anything, return value is None
- Return type
None
-
decompose(reg, **kwargs)¶ Decompose the operation into elementary operations supported by the backend API.
Like
Operation.decompose(), but applies self.dagger.
-
merge(other)¶ Merge the operation with another (acting on the exact same set of subsystems).
Note
For subclass overrides: merge may return a newly created object, or self, or other, but it must never modify self or other because the same Operation objects may be also used elsewhere.
- Parameters
other (Operation) – operation to merge this one with
- Returns
other * self. The return value None represents the identity gate (doing nothing).
- Return type
Operation, None
- Raises
MergeFailure – if the two operations cannot be merged