workbench_algorithms.subroutines.lks_state_prep

Functions for Low-Kliuchnikov-Schaeffer state preparation.

LKSMultiplexor

LKSMultiplexor(qrom, gate, **kwargs)

Bases: Qubrick

Multiplexor using data-lookup oracles.

The construction is detailed in arXiv:1812.00954 . Circuit described in Appendix D.

Parameters:

Name	Type	Description	Default
`qrom`	`Qubrick`	Data-loader for loading angles to bits_of_precision-bits of precision.	required
`gate`	`op`	Rotation gate type to use in multiplexed rotations.	required
`**kwargs`	`dict[str, Any]`	Other arguments to pass to the init.	`{}`

compute

compute(
    index_reg,
    tgt,
    angles,
    bits_of_precision,
    lambda_val=None,
    **kwargs,
) -> None

Compute circuit for LKS multiplexor.

Parameters:

Name	Type	Description	Default
`index_reg`	`Qubits`	Index register.	required
`tgt`	`Qubits`	Register to apply rotations onto.	required
`angles`	`list or None`	List of angles to supply to rotations.	required
`bits_of_precision`	`int`	Bits of precision for rotations.	required
`lambda_val`	`int`	Power-of-two knob to trade off between gates and qubits. If `None` (default), then optimal lambda is calculated. If `None` (default), the clean decomposition will be used.	`None`
`**kwargs`	`dict[str, Any]`	Other arguments to pass to the compute.	`{}`

Note

We want to apply single-qubit \(\text{RY}\) rotations conditioned on different significant bits. We truncate the exact angle and obtain an integer approximation of it, and so, each angle we apply is \(\frac{2\pi a_k} {2^{k + 1}}\). However, we express \(\text{RY}\) rotations as \(\text{RY}(\theta) = e^{iY \frac{\theta}{2}}\). If you account for this factor of 2 in the denominator, and also convert from radians to degrees \((\frac{180}{\pi})\), you end up using:

\(\text{angle} = \frac{\frac{2\pi a_k}{2^{k + 1}}}{2} \times \frac{180}{\pi}\)
Simplified: \(\text{angle} = \frac{180 a_k}{2^{k + 1}}\)

LKSStatePrep

LKSStatePrep(coeffs, mplxr, **kwargs)

Bases: Qubrick

State preparation detailed in arXiv:1812.00954 .

This routine works for real, positive coefficients.

Parameters:

Name	Type	Description	Default
`coeffs`	`list or None`	List of coefficients to load into state.	required
`mplxr`	`Qubrick`	Multiplexor to use in state prep.	required
`**kwargs`	`dict[str, Any]`	Other arguments to pass to the init.	`{}`

compute

compute(qbits, **mplxr_kwargs) -> None

Compute circuit for LKS state prep.

Parameters:

Name	Type	Description	Default
`qbits`	`Qubits`	Qubits to prep state on.	required
`**mplxr_kwargs`	`dict`	Dictionary with keyword arguments to pass to the multiplexor.	`{}`

Other Parameters:

Name	Type	Description
`bits_of_precision`	`int`	Bits of precision for rotations.
`lambda_val`	`int`	Power-of-two knob to trade off between gates and qubits. If `None`, then optimal lambda is calculated. If `None`, the clean decomposition will be used.