Speaker
Description
Pauli correlation encoding (PCE) compresses many classical variables into expectation values of Pauli strings on fewer qubits. This compression has been used as a variational representation for combinatorial optimization, but a complementary primitive is needed to make the encoding bidirectional: given classical data or a classical solution, one would like to upload it directly into the compressed Pauli-correlation register. We introduce an explicit state-preparation unitary for this task. For the family of $k$-body $Z$ correlators, we prove that the induced correlation map has full-rank Jacobian at the origin and admits a certified local inverse. In particular, for $m=\binom nk$ encoded coordinates, every target vector in an explicit image cube of radius $\rho(r)\in\Omega(1/m)$ can be prepared from a parameter cube with $r<\log(2)/m$. We then use this upload primitive in two ways. First, we warm-start PCE optimization by injecting classical bit strings into the signs of Pauli correlators before a second variational optimization round. On weighted MaxCut instances with 400 variables encoded on 15 qubits, this improves the solutions obtained after the first round and suppresses the barren-plateau behavior observed for standard random initialization. Second, we demonstrate classical data upload on Quantinuum's H2-2 trapped-ion processor by encoding and retrieving images with 494 and 1476 pixels using only two-body $ZZ$ correlations on 32 and 56 qubits, respectively.
| Topic | Hybrid quantum-classical approaches for learning and optimization |
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| Additional Topic | Encoding and processing of data in quantum systems |