paper / petershor / Apr 3
Three variants of quantum interactive proof systems restrict message lengths to logarithmic size: verifier-first short-to-long, logarithmic total multi-round, and verifier-polynomial-random-to-prover-short-quantum. Short messages can be eliminated in all cases without loss of expressive power, reducing to QMA for the first variant and BQP for the others. Proofs leverage quantum state tomography and the finite quantum de Finetti theorem.
quantum-interactive-proofsshort-messagesquantum-state-tomographyquantum-de-finettiqma-bqpquantum-complexity
“Verifier sends short message, prover responds with polynomial-length message: equivalent to QMA”
paper / petershor / Feb 26
The paper examines auto-equivalences of the modular tensor category of representations of a finite group's quantum double that permute simple objects via charge conjugation followed by transposing a chargeon-fluxion pair. It proves such auto-equivalences exist precisely when the group is a semidirect product of the additive and multiplicative groups of a finite field, as exemplified by S_3. Conversely, these transpositions form modular invariants if and only if the group is isomorphic to that of a finite near-field.
quantum-doublemodular-tensor-categorieschargeon-fluxionfinite-groupsquantum-physicsquantum-algebraarxiv-paper
“For the quantum double of S_3, there exists a chargeon and a fluxion that are indistinguishable.”
paper / petershor / Jan 6
The paper derives conditions under which chains of d-dimensional qudits with generic, translationally non-invariant nearest-neighbor interactions are unfrustrated, meaning ground states coincide with common ground states of all local Hamiltonian terms. These states are represented using the Matrix Product States (MPS) framework. Numerical imaginary time evolution in MPS reveals parameter ranges where ground states exhibit high entanglement, challenging MPS approximations.
quantum-physicsqudit-chainsground-statesmatrix-product-statesfrustration-freestatistical-mechanicsarxiv-paper
“Chains of d-dimensional qudits with generic nearest-neighbor interactions lack translational invariance.”