workbench_algorithms.subroutines.uniform_state_prep

Qubricks for uniform state preparation.

USP

USP(**kwargs)

Bases: Qubrick

Qubrick for performing Uniform State Preparation.

From Fig. 12 in "Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity" (arXiv:1805.03662).

compute

compute(
    d,
    target_qreg,
    error_param=None,
    ctrl: int = 0,
    **kwargs,
) -> None

Prepare a uniformly distributed state.

Conceptually, starts by factoring \(d = 2^k L\), although this explicit calculation has been replaced by the num_trailing_zeros and highest_bit functions for better performance. Just applying Hadamard gates creates the desired equal superposition over k of the qubits. For the remaining qubits we need to also perform amplitude amplification to keep only basis states with value < d.

Parameters:

Name	Type	Description	Default
`d`	`int`	Desired number of uniform terms.	required
`target_qreg`	`Qubits`	The register to operate on.	required
`error_param`	`float`	Parameter determining the accuracy of truncated rotation angles. If `None` (default), angles are exact and no success qubit is output.	`None`
`ctrl`	`Qubits or int`	Register to control the USP on. Defaults to `None`.	`0`
`**kwargs`	`dict[str, Any]`	Other arguments to pass to the compute.	`{}`

Raises:

Type	Description
`ValueError`	If the register passed in is too small.

Note

The effect of setting various default args has not been tested. Creates desired state up to global phase.

ZeroAncillaUSP

ZeroAncillaUSP(qc=None, **kwargs)

Bases: Qubrick

Qubrick for performing Uniform State Preparation without auxiliary qubits.

Adapted from "An efficient quantum algorithm for preparation of uniform quantum superposition states" (arxiv:2306.11747).

compute

compute(d, target_qreg, ctrl: int = 0, **kwargs) -> None

Prepare a uniformly distributed state.

Utilizes binary decomposition of \(d\), controlled Ry and Hadamard gates to avoid auxiliary qubit usage.

Parameters:

Name	Type	Description	Default
`d`	`int`	Desired number of uniform terms.	required
`target_qreg`	`Qubits`	The register to operate on.	required
`ctrl`	`Qubits or int`	Register to control the USP on. Defaults to `None`.	`0`
`**kwargs`	`dict[str, Any]`	Other arguments to pass to the compute.	`{}`

Raises:

Type	Description
`RuntimeError`	If the register passed in is too small.

RealUSP

RealUSP(**kwargs)

Bases: Qubrick

Qubrick for performing Uniform State Preparation.

From "Even more efficient quantum computations of chemistry through tensor hypercontraction" (arxiv:2011.03494).

Note

This is the version based on the instructions (steps 1-7) under Eq. A15 of Appendix A.
A circuit diagram showing a similar implementation (but over two target registers) is shown in Fig. (3).

compute

compute(
    d,
    target_qreg,
    rotator=None,
    succ_reg=None,
    error_param=None,
    ctrl: int = 0,
    **kwargs,
) -> None

Prepare a uniformly distributed state.

Conceptually, starts by factoring \(d = 2^k L\), although this explicit calculation has been replaced by the num_trailing_zeros and highest_bit functions for better performance. Just applying Hadamard gates creates the desired equal superposition over k of the qubits. For the remaining qubits we need to also perform amplitude amplification to keep only basis states with value < d.

Utilizes one auxiliary qubit, the 'rotator', such that CZ gates perform the required reflections.

This routine uses RY rotations, resulting in only real amplitudes.

If no error_param is provided, the rotations are treated as ideal and the probability of success is 1.0. If an error_param is provided, the probability of success will be <=1.0 and a flag qubit will store the result via a comparator. This qubit can be optionally provided via succ_reg.

Parameters:

Name	Type	Description	Default
`d`	`int`	The number of nonzero terms required.	required
`target_qreg`	`Qubits`	The register to operate on.	required
`rotator`	`Qubits`	Register to perform rotation on. Defaults to `None`, in which case, it is allocated by the Qubrick.	`None`
`succ_reg`	`Qubits`	Qubit to herald success. Defaults to `None`, in which case, it is allocated by the Qubrick.	`None`
`error_param`	`float`	Parameter determining the accuracy of truncated rotation angles. If `None` (default), angles are exact and no success qubit is output.	`None`
`ctrl`	`Qubits or int`	Register to control the USP on. Defaults to `0`.	`0`
`**kwargs`	`dict[str, Any]`	Other arguments to pass to the compute.	`{}`

Raises:

Type	Description
`RuntimeError`	If the register passed in is too small.

Note

The effect of setting various default args has not been tested.