arXiv subjects

Andrew Lucas

Publications and source records attributed to Andrew Lucas.

At least 19 recordsLinked to original sources

arXiv2026

Interaction corrections to topological density three-point functions in two-dimensional Fermi liquids: a coadjoint orbit perspective

Density three-point correlations are known to probe the topology of the Fermi sea in two-dimensional noninteracting systems. Here, we study how these correlations are modified by interactions using the coadjoint-orbit effective field theory. A key advantage of the coadjoint-orbit formulation is that it provides a systematic way to incorporate generalized Landau interactions in terms of bosonized degrees of freedom, mapping fermionic loop contributions onto simpler tree-level diagrams. We show that, for a general isotropic dispersion $\epsilon(p)$, even at linear order in the generalized Landau interaction, $\mathcal{O}(\mathcal{F}^{(2,0)})$, there exists a contribution proportional to the band curvature $\epsilon''(p_F)$ that changes the nonanalytic structure of the free density three-point correlation function. This contribution introduces a distinct nonanalytic structure beyond that found in either the noninteracting case or an interacting Galilean-invariant system, showing that interaction effects can modify the topology-detecting density three-point correlation.

cond-mat.str-el↗

arXiv2026

Preparing approximate $N$-fold cat states with the phase space instruction set

The phase space instruction set is a continuous-variable universal gate set involving single-qubit rotations and qubit-dependent displacements on a single boson. Using these gates, we prove that a circuit depth $\mathrm{\Omega}(\varphi(N))$ is necessary to approximately prepare a large $N$-fold rotationally invariant Schr\"odinger cat state; here $\varphi(N) \gtrsim N/\log\log N$ is the Euler totient function. A protocol saturating this asymptotic bound on circuit depth is obtained for every prime number $N$. This protocol has an asymptotically optimal runtime, when the gates are generated by Hamiltonian evolution. Our results provide a sharp example where a universal gate set is surprisingly inefficient at preparing a simple family of states, and further imply that converting bosonic circuits between different universal gate sets can be extremely inefficient.

quant-ph↗

arXiv2026

Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity

We study the dynamics of Krylov state complexity in finite-dimensional quantum systems. Orthogonal polynomials built on a discrete energy spectrum crowd away from regions where the density of states is low at large Krylov index. The physical implication of this result is that, even using a minimalist Krylov state complexity which is defined over the entire spectrum, the Krylov complexity provably stops growing a little past the Heisenberg length in every low-energy state. This has interesting implications for the proposal that Krylov complexity is related to the wormhole length in 2D quantum gravity.

hep-th↗

arXiv2026

Characterizing electronic scattering rates with transport in multiterminal devices

Strongly interacting electrons in clean two-dimensional devices are theorized to exhibit many distinct transport regimes, such as ballistic, hydrodynamic, or diffusive. Realistic samples often lie in crossover regimes between these idealized limits. We show how a single experiment on a multiterminal device can distinguish these regimes and constrain the relevant scattering rates without space-resolved imaging. Using a linearized Boltzmann model in a five-terminal geometry, we find that current partition among the drain contacts diagnoses the ballistic-hydrodynamic-Ohmic crossover and allows extraction of momentum-relaxing and momentum-conserving scattering rates in the crossover regime. The same geometry also exhibits clear signatures of the tomographic regime, potentially allowing for a quantitative discrimination between viscous and tomographic flow in experiments. Our results demonstrate that multiterminal devices are a simpler experimental route to characterize transport regimes in electron liquids, relative to space-resolved imaging experiments.

cond-mat.mes-hall↗

arXiv2026

The Impact of Approximation on Algorithmic Progress

In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of size 1 million. A natural response to such limits is to try to find new algorithms or to parallelize existing ones, but many algorithms are already at their theoretically-optimal level and parallelization is often impossible or prohibitively expensive. Starting in the 1960's, computer scientists pursued another solution: allowing solutions to have a small amount of error (i.e. approximating them). In this paper, we survey 118 of the most important algorithm problems in computer science, quantifying the gains and tradeoffs from approximation that have been discovered over the history of the field. Overall, only $\approx$20\% of problems have benefited from approximation. However, those with good approximate algorithms can be dramatically faster to compute with little cost to accuracy. For example, a quarter of computationally intractable problems (e.g. those that take exponential time to compute) have polynomial time approximate algorithms. Approximation also increases the number of algorithms that can run in linear time by 23\%, opening up new computational opportunities for those working in the big data regime. This work also sheds light on what should be expected from progress in AI, where approximation is at the heart of how deep learning works.

cs.DS↗

arXiv2026

Cryogenic shock exfoliation for ultrahigh mobility rhombohedral graphite nanoelectronics

Rhombohedral multilayer graphene (RMG) offers a highly tunable platform for correlated electron physics, featuring field-effect control of magnetic, superconducting, and topological phases[1-24]. The promise of these materials has been held back by the limited abundance of rhombohedral stacking in natural graphite, which constrains both sample yield and useful area. Here we introduce 'cryogenic shock exfoliation' to produce large area rhombohedral graphene flakes which, combined with a low-pressure van der Waals assembly technique that preserves stacking order, enable highly uniform devices exceeding 1300 $\mu m^2$ with fabrication yields of 90%. Using scanning nanoSQUID-on-tip imaging, we demonstrate uniform spin magnetism over the full central 10 times 10 $\mu m^2$ area of our devices. Transverse magnetic focusing reveals a disorder mean free path exceeding 200 $\mu m$ at low temperatures. Within the flat surface bands of RMG[20], we observe a size-driven crossover from Poiseuille to porous electron flow in the intermediate-temperature regime of strong electron-electron hydrodynamics[16, 25], providing a further signature of ultrahigh device quality. Our approach overcomes a key materials bottleneck in the fabrication of mesoscopic rhombohedral graphene devices, paving the way for incorporating strongly correlated phases into two-dimensional nanoelectronics.

cond-mat.mes-hall↗

arXiv2026

Floquet circuits inspired by holographic matrix models

We argue that near-term experiments with neutral atoms in movable optical tweezers can simulate circuits that mimic the Trotterized time-evolution of simple matrix models in quantum mechanics. As a cartoon of this proposal, we study Floquet Clifford circuits which exhibit a number of signatures of fast scrambling. One such illustration is a simplified Hayden-Preskill recovery protocol, in which stabilizer quantum error correction replaces postselection.

quant-ph↗

arXiv2026

Robust symmetry breaking in gapless quantum magnets

We prove the existence of spontaneous symmetry breaking in suitably low-energy eigenstates of certain gapless and frustrated many-body quantum systems, namely symmetric quantum perturbations to classical models which exhibit spontaneous symmetry breaking of a finite group at some positive temperature. Additionally, the classical model need not be local in space, as long as it satisfies a quantum analogue of the Peierls condition. As an example of our technique, we establish robust ferromagnetism in random-bond Ising models in $d= 2$ dimensions with sufficiently biased random couplings, with weak transverse field. Our mathematical technique is based on establishing quantum bottlenecks, similar to a "many-body WKB" method for evaluating tunneling rates. Using these same methods, we provide new proofs of metastability and the slow decay of the false vacuum, applicable to gapless metastable states. Our work represents a first step towards a rigorous classification of stable gapless quantum phases.

math-ph↗

arXiv2026

Imaging flat band electron hydrodynamics in biased bilayer graphene

Hydrodynamic electron transport arises when carrier kinetics are dominated by interelectron collisions rather than the relaxation of momentum out of the electron system. In recent years, signatures of electron hydrodynamics have been reported in graphene devices owing to the low disorder and weak electron-phonon coupling. However, these experiments have been performed in regimes where the carrier mass is light, and the electron-electron collision length--though smaller than corresponding lengths for phonon or impurity scattering--remains large in absolute terms, typically several hundred nanometers. This restricts hydrodynamic transport phenomena to large length scales, limiting miniaturization of devices based on hydrodynamic flow. The advent of dual-gated rhombohedral graphene multilayers introduces a new route toward enhanced hydrodynamic behavior via their large--and tunable--effective mass. Here, we employ a scanning superconducting magnetic sensor to image local current flow in dual-gated bilayer graphene. Exploiting a sample geometry sensitive to both laminar and vortical flow, we identify three distinct transport regimes--ballistic, hydrodynamic, and diffusive--across the full phase space spanned by carrier density and displacement field. The strongest hydrodynamic transport is observed in the flat band regime, where fitting our results to a unified Boltzmann transport model reveals the electron-electron scattering length to be comparable to the Fermi wavelength of ~50 nm. High-current measurements, meanwhile, reveal striking nonlinearities in the flow pattern. Our results pave the way for miniaturized electronic devices based on linear and nonlinear electron hydrodynamics.

cond-mat.mes-hall↗

arXiv2026

Calderbank-Shor-Steane codes on group-valued qudits

Calderbank-Shor-Steane (CSS) codes are a versatile quantum error-correcting family built out of commuting $X$- and $Z$-type checks. We introduce CSS-like codes on $G$-valued qudits for any finite group $G$ that reduce to qubit CSS codes for $G = \mathbb{Z}_2$ yet generalize the Kitaev quantum double model for general groups. The $X$-checks of our group-CSS codes correspond to left and/or right multiplication by group elements, while $Z$-checks project onto solutions to group word equations. We describe quantum-double models on oriented two-dimensional CW complexes (which need not cellulate a manifold) and prove that, when $G$ is non-Abelian and simple, every $G$-covariant group-CSS code with suitably upper-bounded $Z$-check weight and lower-bounded $Z$-distance reduces to a CW quantum double. We describe the codespace and logical operators of CW quantum doubles via the same intuition used to obtain logical structure of surface codes. We obtain distance bounds for codes on non-Abelian simple groups from the graph underlying the CW complex, and construct intrinsically non-Abelian code families with asymptotically optimal rate and distances. Adding "ghost vertices" to the CW complex generalizes quantum double models with defects and rough boundary conditions whose logical structure can be understood without reference to non-Abelian anyons or defects. Several non-invertible symmetry-protected topological states, both with ordinary and higher-form symmetries, are the unique codewords of simply-connected CW quantum doubles with a single ghost vertex.

quant-ph↗

arXiv2026

Bidirectional teleportation using scrambling dynamics: a practical protocol

We show that quantum information scrambling can enable a generic SWAP gate between collective degrees of freedom in systems without universal local control. Our protocol combines the Hayden-Preskill recovery scheme, associated with the black hole information paradox, with quantum teleportation and runs them in parallel and in opposite directions, enabling bidirectional exchange of quantum states through global interactions alone. This approach cleanly distinguishes the roles of information spreading, entanglement, and chaos for enabling both coherent state transfer and recovery. We propose an experimental realization using the Dicke model, which can be realized in cavity-QED and trapped-ion platforms, highlighting the utility of holography in designing practical quantum gates.

quant-ph↗

arXiv2025

Minimal Models of Entropic Order

Due to entropic effects, it is possible that generic high-energy states of a quantum or classical system are ordered. This leads to spontaneous symmetry breaking at arbitrarily high temperatures. We present minimal models of entropic order that arise from very simple interactions. Our main examples are the Arithmetic Ising Model (AIM) and its quantum analogue, where usual Ising spins are replaced by non-negative integers. Using a large-flavor expansion together with numerical simulations, we find that the high-temperature phase is ordered in the classical and quantum models. We also introduce classical gas models whose interactions drive the system to a crystal at high temperatures.

cond-mat.stat-mech↗

arXiv2025

Non-perturbatively slow spread of quantum correlations in non-resonant systems

Strong disorder often has drastic consequences for quantum dynamics. This is best illustrated by the phenomenon of Anderson localization in non-interacting systems, where destructive quantum wave interference leads to the complete absence of particle and information transport over macroscopic distances. In this work, we investigate the extent to which strong disorder leads to provably slow dynamics in many-body quantum lattice models. We show that in any spatial dimension, strong disorder leads to a non-perturbatively small velocity for ballistic information transport under unitary quantum dynamics, almost surely in the thermodynamic limit, in every many-body state. In these models, we also prove the existence of a "prethermal many-body localized regime", where entanglement spreads logarithmically slowly, up to non-perturbatively long time scales. More generally, these conclusions hold for all models corresponding to quantum perturbations to a classical Hamiltonian obeying a simple non-resonant condition. Deterministic non-resonant models are found, including spin systems in strong incommensurate lattice potentials. Consequently, quantum dynamics in non-resonant potentials is asymptotically easier to simulate on both classical or quantum computers, compared to a generic many-body system.

cond-mat.dis-nn↗

arXiv2025

Supersonic flow and hydraulic jump in an electronic de Laval nozzle

In very clean solid-state systems, where carrier-carrier interactions dominate over any other scattering mechanisms, the flow of electrons can be described within a hydrodynamic framework. In these cases, analogues of viscous fluid phenomena have been experimentally observed. However, experimental studies of electron hydrodynamics have so far been limited to the low velocity, linear response regime. At velocities approaching the speed of sound, the electronic fluid is expected to exhibit compressible behaviour where nonlinear effects and discontinuities such as shocks and choked flow have long been predicted. This compressible regime remains unexplored in electronic systems, despite its promise of strongly nonlinear flow phenomena. Here, we demonstrate compressible electron flow in bilayer graphene through an electronic de Laval nozzle, a structure that accelerates charge carriers past the electronic speed of sound, until they slow down suddenly in a shock. Discontinuities in transport measurements and local flattening of potential in Kelvin probe measurements are consistent with a viscous electron shock front and the presence of supersonic electron flow, and are not consistent with Ohmic or ballistic flow. Breaking the sound barrier in electron liquids opens the door for novel, intrinsically nonlinear electronic devices beyond the paradigm of incompressible flow.

cond-mat.mes-hall↗

arXiv2025

Introducing the Quantum Economic Advantage Online Calculator

Developing a systematic view of where quantum computers will outperform classical ones is important for researchers, policy makers and business leaders. But developing such a view is challenging because quantum advantage analyses depend not only on algorithm properties, but also on a host of technical characteristics (error correction, gate speeds, etc.). Because various analyses make different assumptions about these technical characteristics, it can be challenging to make comparisons across them. In this paper, we introduce an open-access web-tool designed to make such comparisons easy. Built on the framework introduced by Choi, Moses, and Thompson (2023), it calculates when quantum systems will outperform classical computers for a given algorithmic problem. These estimates can be easily updated based on various assumptions for error correction, overhead, and connectivity. Different hardware roadmaps can also be used and algorithm running times can be customized to particular applications. It can currently be accessed at https://futuretech.mit.edu/quantum-economic-advantage-calculator. This integrated prediction tool also allows us to explore which technical factors are most important for quantum ``economic" advantage (outperforming on a cost-equivalent basis). Overall, we find that for some algorithms (e.g. Shor's) the timing of advantage is quite robust, whereas for others (e.g. Grover's) it is contingent, with numerous technical characteristics substantially impacting these dates. In the paper, we discuss both why this occurs and what we can learn from it.

quant-ph↗

arXiv2025

Quadrupole-conserving dynamics in the non-commutative plane

Inspired by ``fracton hydrodynamic" universality classes of dynamics with unusual conservation laws, we present a new dynamical universality class that arises out of local area-preserving dynamics in the non-commutative plane. On this symplectic manifold, the area-preserving spatial symmetry group $\mathrm{SL}(2,\mathbb{R})\rtimes \mathbb{R}^2$ is a symmetry group compatible with non-trivial many-body dynamics. The conservation laws associated to this symmetry group correspond to the dipole and quadrupole moments of the particles. We study the unusual dynamics of a crystal lattice subject to such symmetries, and argue that the hydrodynamic description of lattice dynamics breaks down due to relevant nonlinearities. Numerical simulations of classical Hamiltonian dynamical systems with this symmetry are largely consistent with a tree-level effective field theory estimate for the endpoint of this instability.

cond-mat.stat-mech↗

arXiv2025

Towards self-correcting quantum codes for neutral atom arrays

Discovering low-overhead quantum error-correcting codes is of significant interest for fault-tolerant quantum computation. For hardware capable of long-range connectivity, the bivariate bicycle codes offer significant overhead reduction compared to surface codes with similar performance. In this work, we present "ZSZ codes", a simple non-abelian generalization of the bivariate bicycle codes based on the group $\mathbb{Z}_\ell \rtimes \mathbb{Z}_m$. We numerically demonstrate that certain instances of this code family achieve competitive performance with the bivariate bicycle codes under circuit-level depolarizing noise using a belief-propagation and ordered-statistics decoder, with an observed threshold around $0.5\%$. We also benchmark the performance of this code family under local "self-correcting" decoders, where we observe significant improvements over the bivariate bicycle codes, including evidence of a sustainable threshold around $0.095\%$, which is higher than the $0.06\%$ that we estimate for the four-dimensional toric code under the same noise model. These results suggest that ZSZ codes are promising candidates for scalable self-correcting quantum memories. Finally, we describe how ZSZ codes can be realized with neutral atoms trapped in movable tweezer arrays, where a complete round of syndrome extraction can be achieved using simple global motions of the atomic arrays.

quant-ph↗

arXiv2025

On the reconstruction map in JT gravity

An open question in AdS/CFT is how to reconstruct semiclassical bulk operators precisely enough that non-perturbative quantum effects can be computed. We propose a set of physically-motivated requirements for such a reconstruction map, and explicitly construct a map satisfying these requirements in Jackiw-Teitelboim (JT) gravity. Our map is found by canonically quantizing "action-angle" variables for JT gravity, which are chosen to ensure that the spectrum of the fundamental quantum theory matches known results from the gravitational path integral. We then study unitary quantum dynamics in this theory, and obtain analytical predictions for the dynamics of the wormhole length, including its quantum fluctuations, leveraging techniques from quantum ergodicity theory. Level repulsion in the non-perturbative JT spectrum implies that the average wormhole length is non-monotonic in time, that fluctuations in wormhole length are non-perturbatively suppressed until nearly the Heisenberg time, and that the late-time-evolved Hartle-Hawking state has a heavy-tailed distribution of lengths. We discuss the implications of our results for the "complexity = volume" conjecture.

hep-th↗