Speaker
Description
Quantum machine-learning and simulation algorithms often assume data encoded directly in quantum amplitudes or q-sample states, where probability distributions are represented coherently. Yet changing the resolution of such data is nontrivial: since the cost of refining a grid from (2^n) to (2^{n+m}) is exponential. We introduce a multiscale upsampling framework that refines quantum-state and tensor-train representations while remaining in compressed form. Starting from an (n)-qubit state, or equivalently an (n)-core tensor train, the method produces an ((n+m))-qubit state or ((n+m))-core tensor train on a finer grid.
Our main quantum contribution is a circuit construction for quasi-interpolating positive functions and probability distributions encoded in q-sample states. The refined state is prepared by a (\mathrm{poly}(n,m,p))-size circuit using only (\lceil \log_2(p+1)\rceil) ancillas, where (p) controls the smoothness of the kernel. For fixed kernel order, the ancilla cost is constant, and the approximation error scales quadratically with the initial grid spacing. Thus, quantum-encoded distributions can be refined coherently without explicitly materializing the fine grid.
The tensor-train formulation provides the classical tensor-network counterpart and supports interpolation, quasi-interpolation, augmentation, and synthesis by low-rank contractions. The added refinement cores have constant rank, the interpolation error is independent of the number of added grid points, and the cost is logarithmic in the final grid size at fixed accuracy. We validate the approach on functions, derivatives, airfoil masks, and three-dimensional random fields, including turbulence. These results connect interpolation theory, tensor networks, and quantum-state representations, enabling resolution-aware quantum data loading, multiscale q-sample preparation, and tensor-network-assisted quantum machine learning.
| Topic | Encoding and processing of data in quantum systems |
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| Additional Topic | Quantum state reconstruction from data |