Quantum Information

Entanglement is usually discussed in the context of two subsystems at a fixed time. A natural question is whether this notion can be meaningfully extended to subsystems at different time slices. In this talk, I will present a family of entanglement measures defined for time-separated subsystems. A key property of these quantities is that they bound time-separated correlation functions, in close analogy with bounds on spatial correlators in terms of mutual information. For relativistic quantum field theories, our definition agrees with the analytic continuation from spacelike to timelike separated regions. I will discuss measurement protocols, computations for the Ising chain and holographic theories, and the relation of these constructions to the recently introduced timelike pseudoentropy. Based on https://arxiv.org/abs/2502.12240 .

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.

The Fibonacci topological order is the prime candidate for the realization of universal topological quantum computation, and when simulated on qubit arrays, has the potential to be an effective quantum error correcting code. Here, we devise quantum circuits to demonstrate the non-Abelian nature of the doubled Fibonacci topological order, as realized in the Levin-Wen string net model. Our circuits effectively initialize the ground state, create excitations, twist and braid them, all in the smallest lattices possible. We further design methods to determine the fusion amplitudes and braiding phases of multiple excitations by carrying out a single qubit measurement. We show that, at the minimal level, the fusion channels of the doubled Fibonacci model can be detected using only three qubits, twisting phases can be measured using five, and braiding can be demonstrated using nine qubits. We then describe how these designs can be generalized for large scale implementations. These designs provide the simplest possible settings for demonstrating the properties of Fibonacci anyons and can be used as realistic blueprints for implementation on many modern quantum architectures. Work is based on arXiv:2407.21761 plus some new results.

Surface codes are a basic ingredient in topological quantum computation, but do not admit a universal set of topologically protected gates. In this talk I introduce group surface codes, which generalize the usual Z2 surface code to non-Abelian finite groups G. By identifying a simple labelling of the logical states, I will show that these codes admit transversal non-Clifford gates for suitable choices of G. I then discuss how to switch between Z2 and non-Abelian group surface codes to complete a universal gate set. This talk is based on work in preparation with Vieri Mattei, Apoorv Tiwari, and Tyler Ellison.

Recent advancements in near-term quantum devices have opened new avenues for exploring quantum phenomena in controllable settings. These developments, in turn, motivate new theoretical perspectives on the dynamics of many-body systems. In the first part of the talk, I will discuss our recent progress on quantum state preparation. I will show that two primary classes of low-overhead circuits for preparing long-range entangled states—sequential unitary circuits and measurement-feedback circuits—can be unified through a simple spacetime rotation, revealing an unexpected connection between the two seemingly distinct protocols. In the second part, motivated by the inevitability of decoherence in realistic quantum systems, I will turn to many-body mixed states and discuss a novel phenomenon: strong-to-weak spontaneous symmetry breaking. I will show how these symmetry-breaking patterns naturally emerge on the spatial boundary of bulk topological orders in one higher dimension, thereby uncovering an intriguing holographic duality.

One of the oldest problems in quantum information theory is to study if there exists a state with negative partial transpose which is undistillable. In the last decades, the study of this problem was reduced to a very special family: Werner states. In this work, we present a new characterization of this problem in terms of partial trace inequalities for the Frobenius norm and general matrices. For this reason, we will study general properties and new inequalities for partial traces of general matrices. Consequently, we will extend the interval of Werner states in which they are provably 2-undistillable in any dimension d ≥ 4. Finally, we find new Schmidt-number witnesses and k-positive maps.

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.