Chronological feed of everything captured from Barbara Terhal.
Fermionic k-SAT decides if a fermionic state exists in the null-space of parity-conserving projectors on n modes, each involving at most k modes. Fermionic 2-SAT is solvable efficiently classically, including variants with fixed particle number parity. However, particle-number-conserving Fermionic 2-SAT for a given particle number is NP-complete, and Fermionic 9-SAT is QMA_1-hard.
Morphing circuits enable direct optimization of quantum error correction syndrome extraction circuits by incorporating hardware constraints like qubit connectivity, choice of two-qubit gates (ISWAP vs. CNOT), and total physical qubits. Applied to Abelian two-block group algebra (2BGA) codes, they handle 2D boundaries, single-shot properties, and improve stability against measurement/reset errors. Alternating time-reversed syndrome rounds simplify fault-tolerance analysis compared to non-alternating circuits. The approach yields new codes and circuits with superior parameters and connectivity.
This paper investigates the optimization problem for fermionic Hamiltonians with classical interactions, which is QMA-hard due to its connection to Coulomb electron-electron interaction. The authors demonstrate that fermionic Gaussian states achieve an approximation ratio of at least 1/3 for these Hamiltonians, irrespective of sparsity. This finding indicates that classical interactions successfully prevent the vanishing Gaussian approximation ratio observed in SYK-type models. The work also presents efficient semi-definite programming algorithms for Gaussian approximations.
Transversal logical gates in the surface code enable fast, low-noise quantum logic, but interspersing them with parity check measurements creates complex, cross-gate decoding challenges. This work presents a "logical observable" minimum-weight-perfect-matching (MWPM) decoder capable of handling arbitrary sequences of transversal gates on the unrotated surface code under circuit-level noise. Two windowed decoder variants are introduced: a computationally efficient basic decoder suited for slow (quiescent) resets, and an advanced two-step decoder supporting fast resets at the cost of computational efficiency. Both decoders expose sublinear-in-d error structures that can cause logical failures, and the authors propose targeted adaptations to eliminate them.