Linear Combination of Unitaries

lcu

Functions:

Name	Description
`lcu`	[Qmod Classiq-library function]
`lcu_pauli`	[Qmod Classiq-library function]

lcu

lcu(
    coefficients: list[float],
    unitaries: QCallableList,
    block: QNum[
        Literal["max(ceiling(log(coefficients.len, 2)), 1)"]
    ],
) -> None

[Qmod Classiq-library function]

Implements a general linear combination of unitaries (LCU) procedure. The algorithm prepares a superposition over the unitaries according to magnitudes, and then conditionally applies each unitary controlled by the block.

The operation is of the form:

\[\sum_j \alpha_j U_j\]

where \(U_j\) is a unitary operation applied to data.

Parameters:

Name	Type	Description	Default
`coefficients`	`list[float]`	L1-normalized array of \(\{ \alpha_j \}\) of the LCU coefficients.	required
`unitaries`	`QCallableList`	A list of quantum callable functions to be applied conditionally.	required
`block`	`QNum[Literal['max(ceiling(log(coefficients.len, 2)), 1)']]`	Quantum variable that holds the superposition index used for conditional application of each unitary.	required

lcu_pauli

lcu_pauli(
    operator: SparsePauliOp,
    data: QArray[QBit, Literal["operator.num_qubits"]],
    block: QNum[
        Literal[
            "max(ceiling(log(operator.terms.len, 2)), 1)"
        ]
    ],
) -> None

[Qmod Classiq-library function]

Applies a linear combination of unitaries (LCU) where each unitary is a Pauli term, represented as a tensor product of Pauli operators. The function prepares a superposition over the unitaries according to the given magnitudes and phases, and applies the corresponding Pauli operators conditionally.

This is useful for implementing Hamiltonian terms of the form:

\[H=\sum_j \alpha_j P_j\]

where \(P_j\) is a tensor product of Pauli operators.

Parameters:

Name	Type	Description	Default
`operator`	`SparsePauliOp`	Operator consists of pauli strings with their coefficients, represented in a sparse format.	required
`data`	`QArray[QBit, Literal['operator.num_qubits']]`	Quantum Variable on which the Pauli operators act. Its size must match the number of qubits required by the Pauli operator.	required
`block`	`QNum[Literal['max(ceiling(log(operator.terms.len, 2)), 1)']]`	Quantum variable that holds the superposition index used for conditional application of each term.	required