seemps.analysis.integration.mps_fejer#
- seemps.analysis.integration.mps_fejer(start, stop, sites, strategy=<seemps.state.core.Strategy object>, cross_strategy=CrossStrategyDMRG(maxiter=100, maxbond=1000, tol_sampling=1e-10, norm_sampling=inf, num_samples=1000, tol_norm_2=None, rng=Generator(PCG64) at 0x7F72A29C7760, strategy=<seemps.state.core.Strategy object>, tol_maxvol_square=1.05, maxiter_maxvol_square=10))[source]#
Returns the binary MPS representation of the Fejér first quadrature rule on an interval. The integration nodes are given by the d zeros of the d-th Chebyshev polynomial. This is achieved using the formulation of Waldvogel (see waldvogel2006 formula 4.4) by means of a direct encoding of the Féjer phase, tensor-cross interpolation for the term $1/(1-4*k**2)$, and the bit-flipped inverse Quantum Fourier Transform (iQFT).
- Parameters:
- start
float The start of the interval.
- stop
float The end of the interval.
- sites
int The number of sites or qubits for the MPS.
- strategy
Strategy, default=DEFAULT_STRATEGY The strategy for MPS simplification.
- cross_strategy
CrossStrategyDMRG, default=CrossStrategyDMRG. The strategy for tensor cross-interpolation.
- start