mps

Call MPSAlgorithm().run() with your target vector Psi, target_qubits, and optionally mps_max_bond_dim to cap bond dimensions. The algorithm builds a right-canonical MPS via SVD, synthesizes a circuit with QR-completed unitaries, and returns the prepared state, total error, and work leakage.

Bond dimension truncation caps the retained singular values at each SVD cut to a power-of-two limit set by mps_max_bond_dim. This reduces circuit cost for low-entanglement states but discards state weight, which appears as increased total error and must be checked against target_error.

Yes, pass a list of NumPy tensors via the mps parameter. They must follow the shape contract: first tensor (2, chi), interior tensors (chi_left, 2, chi_right), last tensor (chi, 2), with matching power-of-two bonds. Set right_canonicalize=True if they are not already right-canonical.

Work leakage measures probability outside the all-zero auxiliary subspace, computed as 1 minus the squared norm of the zero-work projection. High leakage usually indicates bond truncation removed significant state weight or the work-wire count is insufficient for the largest bond dimension.

The approach only reduces cost for low-entanglement states; highly entangled states need bond dimensions growing exponentially with qubits. The implementation uses dense NumPy evolution for validation, so large qubit counts become memory-bound, and all explicit bonds must be powers of two.