workbench_algorithms.subroutines.phase_gradient_adder

Qubrick for phase gradient adder.

PhaseGradientAdder

PhaseGradientAdder(**kwargs)

Bases: Qubrick

Optimized adder for use in phase gradient addition.

Parameters:

Name	Type	Description	Default
`**kwargs`	`dict[str, Any]`	Keyword arguments	`{}`

compute(lhs: QUInt, rhs: QUInt, ctrl: Qubits | None = None)

Circuit for optimized phase gradient adder.

This construction comes from Fig. 13 in arXiv:2007.07391.

Parameters:

Name	Type	Description	Default
`lhs`	`QUInt \| None`	The register with the phase gradient catalyst state. May be `None` when `rhs` is a single qubit and the implicit one-qubit catalyst is dropped.	required
`rhs`	`QUInt`	The register we are adding into the phase gradient register.	required
`ctrl`	`(Optional, int \| Qubits)`	Control register. Defaults to `0` (i.e. no control).	`None`

Note

The phase gradient register is usually one qubit smaller than the rhs.
However, there exists at least one known case where they are equal in size (ex. when using GivensRotationTwoAdders).
When they are the same size, we can actually drop a CZ, and so, we distinguish these cases.
For rhs two qubits and lhs one qubit shorter than rhs, the Fig.~13 chain collapses to three bilinear gates (no temporary elbow). With no adder control, those are lhs.z(rhs[0]), lhs.x(rhs[0]), rhs[1].z(). With a control register ctrl (e.g. bidirectional rotation tests), merge ctrl into each gate as lhs[0].z(rhs[0] | ctrl), lhs[0].x(rhs[0] | ctrl), rhs[1].z(cond=ctrl).
For lhs and rhs both a single qubit, only the closing segment remains (matching GidneyAdd on one-qubit lhs).