Quantum Information

Fault-tolerant logical entangling gates are essential for scalable quantum computing but are limited by the error rates and overheads of physical two-qubit gates and stabilizer measurements. We introduce phantom codes, a class of codes that attain the minimal possible cost: all in-block logical entangling operations reduce to qubit permutations that can be absorbed at the compilation stage, yielding zero physical-gate overhead and perfect logical fidelity. Our first main result is the discovery of such codes via four mechanisms. By exhaustively enumerating all 2.71x1010inequivalent CSS codes up to n=14 we find all codes to this scale and then identify additional instances up to n=21 using SAT methods. We then use quantum Reed-Muller constructions to find higher k instances and a "binzarization-and-concatenation" scheme to achieve higher d. Second, through end-to-end noisy simulations, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. This includes a ~207x improvement in logical fidelity for Trotterized many-body quantum simulation at current physical error rates, with comparable qubit counts and a 22% preselection rate; the advantage persists from 8 to $64$ logical qubits. These results establish phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure.

Chirality is a fundamental feature of many-body physics, typically manifesting through the breaking of time-reversal symmetry. Yet a precise quantum information-theoretic characterization of chirality has remained elusive. A recent proposal defines a state as chiral if transforming it into its complex conjugate requires a circuit of large depth. Here, we rigorously establish many-body chirality for a broad family of two-dimensional stabilizer pure and mixed states. We also prove that these states are 4-partite chiral, but not 3-partite chiral.

The AdS/CFT duality has been extremely useful in understanding quantum gravity. Tensor networks are a toy model of holography that have provided valuable lessons that have been imported to AdS/CFT. In particular, random tensor networks have a quantitative connection with fixed-area states in the gravitational path integral. This has allowed for a translation of various tensor network results to gravity that I will discuss, including an understanding of the Renyi entropy, entanglement negativity, entanglement wedges for bulk regions and resolving entropic paradoxes using wormholes.

Assuming the polynomial hierarchy is infinite, we prove a sufficient condition for determining if uniform and polynomial size quantum circuits over a non-universal gate set are not efficiently classically simulable in the weak multiplicative sense. Our criterion exploits the fact that subgroups of SL(2; C) are essentially either discrete or dense in SL(2; C). Using our criterion, we give a new proof that both instantaneous quantum polynomial (IQP) circuits and conjugated Clifford circuits (CCCs) afford a quantum advantage. We also prove that both commuting CCCs and CCCs over various fragments of the Clifford group afford a quantum advantage, which settles two questions of Bouland, Fitzsimons, and Koh. Our results imply that circuits made of just U \otimes U-conjugated CZ gates afford a quantum advantage for almost all single-qubit unitaries U.