Rotation and State Preparation

Rotation and state preparation operators provide arbitrary-dimensional unitary rotations and the ability to prepare a target quantum state from |0⟩.

Overview

Rotation and state preparation operators overview

Operator	Operation	Unitarity class
Rot_GeneralUnitary	Apply an arbitrary-dimensional unitary matrix	BaseOperator
Rot_GeneralStatePrep	Prepare a target quantum state from |0⟩	BaseOperator

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Rot_GeneralUnitary (general unitary rotation)

Operation: Applies an arbitrary \(2^n \times 2^n\) unitary matrix to a register.

Parameters:

• reg — target register (name or ID)

• matrix — unitary matrix (DenseMatrix_complex or a NumPy array)

Dagger: Applies the conjugate transpose of the matrix.

Purpose: When the standard gate library cannot directly express the desired transformation, you can specify it directly in matrix form.

Note

The matrix dimension must match the Hilbert-space dimension \(2^n\) of the register, where \(n\) is the number of bits in the register.

import numpy as np
import pysparq as ps

ps.System.clear()
ps.System.add_register("q", ps.UnsignedInteger, 2)

state = ps.SparseState()

# Define a 4x4 unitary matrix
matrix = np.eye(4, dtype=complex)
matrix[0, 0] = 0
matrix[0, 3] = 1
matrix[3, 3] = 0
matrix[3, 0] = 1

op = ps.Rot_GeneralUnitary("q", matrix)
op(state)

# Undo
op.dag(state)

—

Rot_GeneralStatePrep (quantum state preparation)

Operation: Prepares a register from the |0⟩ state into a target quantum state.

Parameters:

• reg — target register (name or ID)

• state_vector — the target state vector (list of complex numbers or a NumPy array)

Dagger: Maps the target state back to |0⟩.

Mathematical representation: Given a target state \(|\psi\rangle = \sum_i \alpha_i |i\rangle\), construct a unitary \(U\) such that \(U|0\rangle = |\psi\rangle\).

Warning

This operator requires the register to currently be in the |0⟩ state. If the register already holds a nonzero value, the behavior is undefined.

import numpy as np
import pysparq as ps

ps.System.clear()
ps.System.add_register("q", ps.UnsignedInteger, 2)

state = ps.SparseState()

# Prepare a simplified Bell state: a uniform superposition
target = np.array([0.5, 0.5, 0.5, 0.5], dtype=complex)

op = ps.Rot_GeneralStatePrep("q", target)
op(state)

ps.pprint(state)
# |q=0⟩ : (0.5+0j)
# |q=1⟩ : (0.5+0j)
# |q=2⟩ : (0.5+0j)
# |q=3⟩ : (0.5+0j)

Helper Functions

stateprep_unitary_build_schmidt

Operation: Constructs the unitary matrix needed for state preparation using a Schmidt decomposition.

Purpose: Use it when you need to manually build or inspect the internal matrix of Rot_GeneralStatePrep.