Qiskit MPS Initializer

State preparation with layers of one- and two-qubit gates from matrix product states (MPS), for circuits much shallower than exact state preparation at the cost of an approximation. Its releases up to 0.2.4 are on PyPI as qiskit-mps-initializer.

Installation

pip install qiu-mps-initializer

Layers of MPS gates

mps builds the layers (Ran, Phys. Rev. A 101, 032310, 2020):

• bond2_mps_approximation(state) truncates a state of 2 qubits or more to an MPS of bond dimension at most 2.
• disentangler_matrices(mps) completes the tensors of such an MPS to unitaries, a two-qubit one per site but the last and a single-qubit one for the last.
• mps_layer(mps) places them into the circuit U with U|0...0> the state of the MPS: the two-qubit gates on neighboring qubits from the most significant one down, then the single-qubit gate on qubit 0.

State preparation

state_preparation.mps_state_preparation(state, max_layers, tolerance=None) prepares a state with at most max_layers layers. Each layer prepares the bond-2 approximation of what the layers before it leave, the residual U_k^dagger ... U_1^dagger |state>, until the residual reaches |0...0>: by default when it equals it as a Qiskit Statevector, up to Qiskit's tolerances, or within the distance tolerance. The result holds the circuit, its layers, the error of the prepared state, i.e. its distance to the target including the global phase, and whether it converged.

States of up to 3 qubits and product states are prepared exactly by one layer. For more qubits, the error decreases with the number of layers, though not always monotonically, and slowly for highly entangled states.

Usage

import numpy as np
from qiskit.quantum_info import Statevector
from qiu_mps_initializer.state_preparation import mps_state_preparation

rng = np.random.default_rng(0)
state = rng.normal(size=32) + 1j * rng.normal(size=32)
state /= np.linalg.norm(state)

preparation = mps_state_preparation(state, max_layers=20)
fidelity = abs(np.vdot(Statevector(preparation.circuit).data, state)) ** 2
assert fidelity > 0.99 and preparation.num_layers == 20

The state of an intensity signal f = alpha |psi|**2, e.g. of a qiu-signals signal, follows from qiu_quantum_computing.phase_propagator.sample_based.sample_based_decomposition(signal).

Changes from version 0.2

The functionality of version 0.2 is carried over onto the packages of this monorepo:

Besides:

• max_layers is required and bounds the number of layers; formerly, one layer more than asked for could be added, and without a maximum the construction could run forever.
• Single-qubit states are supported.
• The package no longer depends on pydantic, pydantic-numpy and qiskit-aer.

Documentation

The documentation, with the API reference from the docstrings, is built from docs/ with MkDocs and published at https://blackwild.github.io/qiu/qiu-mps-initializer/. To serve it locally, from the repository root:

uv run mkdocs serve -f packages/qiu-mps-initializer/mkdocs.yml

Tests

From the repository root:

uv run pytest packages/qiu-mps-initializer