Solver Module

The solver module provides the main functionality for solving Quantum Signal Processing (QSP) problems.

qsppack.solver.solve(coef, parity, opts)

Given coefficients of a polynomial P, yield corresponding phase factors.

The reference chose the first half of the phase factors as the optimization variables, while in the code we used the second half of the phase factors. These two formulations are equivalent.

To simplify the representation, a constant pi/4 is added to both sides of the phase factors when evaluating the objective and the gradient. In the output, the FULL phase factors with pi/4 are given.

Parameters:

• coef (array_like) – Coefficients of polynomial P under Chebyshev basis. P should be even/odd, only provide non-zero coefficients. Coefficients should be ranked from low order term to high order term.

• parity (int) – Parity of polynomial P (0 – even, 1 – odd)

• opts (dict, optional) –

  Options dictionary with fields:

  • criteriafloat

    Stop criteria

  • useRealbool

    Use only real arithmetics if true

  • targetPrebool

    Want Pre to be target function if true

  • method{‘LBFGS’, ‘FPI’, ‘Newton’}

    Optimization method to use

  • typePhi{‘full’, ‘reduced’}

    Type of phase factors to return

Returns:

• phi_proc (ndarray) – Solution of optimization problem, FULL phase factors

• out (dict) – Information of solving process containing:

  • iterint

    Number of iterations

  • timefloat

    Runtime in seconds

  • valuefloat

    Final error value

  • parityint

    Input parity value

  • targetPrebool

    Whether Pre was target function

  • typePhistr

    Type of phase factors returned

The solve function is the main entry point for QSP optimization. It takes a target polynomial and returns the optimized phase factors.

Example usage:

import numpy as np
from qsppack.solver import solve

# Define a target polynomial (e.g., P(x) = x)
target_poly = np.array([0, 1])

# Solve for phase factors
result = solve(target_poly, method='lbfgs')