mps_product.py

import opt_einsum as oe
import numpy as np


# generates inner product of two mps states, phys_dim can vary
# code adapted from: https://optimized-einsum.readthedocs.io/en/stable/ex_large_expr_with_greedy.html
# License at the bottom of this file
def matrix_product_state(
    n=100, phys_dim_min=10, phys_dim_max=200, bond_dim=20, seed=None
):
    """Generates a matrix product state (MPS) for a quantum computing simulation.

    Args:
        n (int): The number of sites in the MPS. Default is 100.
        phys_dim_min (int): The minimum physical dimension of each site. Default is 10.
        phys_dim_max (int): The maximum physical dimension of each site. Default is 200.
        bond_dim (int): The bond dimension between neighboring sites. Default is 20.
        seed (int): The seed for the random number generator. Default is None.

    Returns:
        tuple: A tuple containing the einsum string and the shapes of the tensors in the MPS.

    Example:
        >>> format_string, shapes = matrix_product_state(n=100, phys_dim_min=10, phys_dim_max=200, bond_dim=20, seed=0)

    """
    # start with the first site
    einsum_str = "ab,ac,"
    shapes = [(phys_dim_min, bond_dim), (phys_dim_min, bond_dim)]

    if seed is not None:
        np.random.seed(seed)

    # generate the einsum string for the middle tensors
    for i in range(1, n - 1):
        j = 3 * i
        ul, ur, m, ll, lr = (oe.get_symbol(i) for i in (j - 1, j + 2, j, j - 2, j + 1))
        einsum_str += "{}{}{},{}{}{},".format(m, ul, ur, m, ll, lr)

        phys_d = np.random.randint(phys_dim_min, phys_dim_max + 1)
        shapes.extend([(phys_d, bond_dim, bond_dim), (phys_d, bond_dim, bond_dim)])

    # finish with the last site
    i = n - 1
    j = 3 * i
    ul, m, ll = (oe.get_symbol(i) for i in (j - 1, j, j - 2))
    einsum_str += "{}{},{}{}".format(m, ul, m, ll)
    shapes.extend([(phys_dim_min, bond_dim), (phys_dim_min, bond_dim)])

    einsum_str += "->"
    return einsum_str, shapes


# The MIT License (MIT)

# Copyright (c) 2014 Daniel Smith

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# copies of the Software, and to permit persons to whom the Software is
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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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