aqc

Import AQCAlgorithm from unitarylab_algorithms and call run with parameters like n=2, T=0 for automatic step selection, p=1.4, and a backend such as torch. The result dictionary includes the quantum solution, classical solution, residual norm, and post-selection amplitude.

AQC solves Ax=b by preparing |b> with a Householder transform, block-encoding a normalized matrix A via SVD, and evolving under a discretized adiabatic schedule. Post-selecting the ancilla register yields a state proportional to the solution direction, which is then rescaled classically.

The solver targets 1 to 6 system qubits, meaning dense matrices up to dimension 64. It is an educational statevector solver, not a scalable fault-tolerant QLSP, so practical examples should start with n=1 or n=2.

A near-zero post-selection amplitude usually means the adiabatic step count T is too small for the problem's condition number. Increase T or reduce n; with T=0 the source automatically selects ceil(10*kappa) rounded up to an even number.

A good direction with a large residual indicates a scaling problem rather than an evolution failure. Check the normalization factors a_scale and b_scale and the internal least-squares scale factor used to reconstruct the original-system solution.