sf.ops.Squeezed¶
-
class
Squeezed(r=0.0, p=0.0)[source]¶ Bases:
strawberryfields.ops.PreparationPrepare a mode in a squeezed vacuum state.
- Parameters
r (float) – squeezing magnitude
p (float) – squeezing angle \(\phi\)
Details and Conventions
Definition
The squeezed state \(\ket{z}\), \(z=re^{i\phi}\) is a squeezed vacuum state defined by
\[\ket{z} = S(z)\ket{0}\]Tip
Available in Strawberry Fields as a NumPy array by
strawberryfields.utils.squeezed_state()A squeezed state is a minimum uncertainty state with unequal quadrature variances, and satisfies the following eigenstate equation:
\[\left(\a\cosh(r)+\ad e^{i\phi}\sinh(r)\right)\ket{z} = 0\]In the Fock basis, it has the decomposition
\[|z\rangle = \frac{1}{\sqrt{\cosh(r)}}\sum_{n=0}^\infty \frac{\sqrt{(2n)!}}{2^n n!}(-e^{i\phi}\tanh(r))^n|2n\rangle\]whilst in the Gaussian formulation, \(\bar{\mathbf{r}} = (0,0)\), \(\mathbf{V} = \frac{\hbar}{2}R(\phi/2)\begin{bmatrix}e^{-2r} & 0 \\ 0 & e^{2r} \\\end{bmatrix}R(\phi/2)^T\).
We can use the squeezed vacuum state to approximate the zero position and zero momentum eigenstates;
\[\ket{0}_x \approx S(r)\ket{0}, ~~~~ \ket{0}_p \approx S(-r)\ket{0}\]where \(z=r\) is sufficiently large.
Attributes
Extra dependencies due to parameters that depend on measurements.
-
measurement_deps¶ Extra dependencies due to parameters that depend on measurements.
- Returns
dependencies
- Return type
set[RegRef]
-
ns= 1¶
Methods
apply(reg, backend, **kwargs)Ask a local 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 local backend to execute the operation on the current register state right away.
Takes care of parameter evaluations and any pending formal transformations (like dagger) and then calls
Operation._apply().- Parameters
reg (Sequence[RegRef]) – subsystem(s) the operation is acting on
backend (BaseBackend) – backend to execute the operation
- Returns
the result of self._apply
- Return type
Any
-
decompose(reg, **kwargs)¶ Decompose the operation into elementary operations supported by the backend API.
See
strawberryfields.backends.base.
-
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