workbench_algorithms.subroutines.qubitization

Main functions to construct circuits for Qubitization.

Qubitization

Qubitization(
    block_encoding: Qubrick, **kwargs: dict[str, Any]
)

Bases: Qubrick

Canonical qubitization iterate.

This Qubrick follows the canonical form of Qubitization introduced in "Hamiltonian Simulation by Qubitization" (arXiv:1610.06546) and used extensively in Lin Lin's lecture notes). This convention starts with a block encoding followed by an all-zero reflection.

Parameters:

Name	Type	Description	Default
block_encoding	Qubrick	Qubrick to apply the block encoding circuit.	required
**kwargs	dict[str, Any]	Other arguments to pass to the init.	{}

compute

compute(
    psi: Qubits,
    be_ancilla_reg: Qubits,
    data: PauliSum | list[int],
    ctrl: Qubits | int = 0,
    **kwargs: dict[str, Any],
)

Compute the qubitization.

Parameters:

Name	Type	Description	Default
psi	Qubits	Target state register.	required
be_ancilla_reg	Qubits	Block encoding auxiliary register.	required
data	PauliSum | list[int]	Hamiltonian or bitstring values to be qubitized.	required
ctrl	Qubits | int	Register to control the qubitization on. Defaults to 0.	0
**kwargs	dict[str, Any]	Other arguments to pass to the compute.	{}

QubitizedWalkOperator

QubitizedWalkOperator(
    state_prep: Qubrick,
    select: Qubrick,
    **kwargs: dict[str, Any],
)

Bases: Qubrick

Qubitization iterate.

This Qubrick uses the form introduced in "Quantum Algorithm for Spectral Measurement with Lower Gate Count" (arxiv:1711.11025).

This form is also used by the Google group for their QPE-Qubitization papers. This form differs from the canonical Qubitization iterate (see Fig. 1 of "Even more efficient quantum computations of chemistry through tensor hypercontraction" (arXiv:2011.03494)), and effectively performs a qubitization of a quantum walk, hence the name QubitizedWalkOperator.

Note

Despite being a Qubitization iterate, this Qubrick has a different signature than the canonical Qubitization Qubrick, in that it is defined in terms of \(\text{PREP}\) and \(\text{SELECT}\) rather than arbitrary block encodings. Furthermore, when plugging it in to QPE, one must be careful with what initial state is passed to QPE. When using this Qubrick, one must first call \(\text{PREP}\)'s compute before calling QPE's compute, as this \(\text{PREP}\) effectively prepares a portion of an eigenstate of the QubitizedWalkOperator (or at least a state which has meaningful support on it).

Parameters:

Name	Type	Description	Default
state_prep	Qubrick	Qubrick to apply the state prep.	required
select	Qubrick	Qubrick to select the Hamiltonian terms from.	required
**kwargs	dict[str, Any]	Other arguments to pass to the init.	{}

compute

compute(
    psi: Qubits,
    be_ancilla_reg: Qubits,
    data: PauliSum | list[int],
    ctrl: Qubits | int = 0,
    **kwargs: dict[str, Any],
)

Compute the qubitization.

Parameters:

Name	Type	Description	Default
psi	Qubits	Target state register.	required
be_ancilla_reg	Qubits	Block encoding auxiliary register.	required
data	PauliSum | list[int]	Hamiltonian or bitstring values to be qubitized.	required
ctrl	Qubits | int	Register to control the qubitization on. Defaults to 0.	0
**kwargs	dict[str, Any]	Other arguments to pass to the compute.	{}