arXiv subjects

Brian Swingle

Publications and source records attributed to Brian Swingle.

At least 19 recordsLinked to original sources

arXiv2026

Twirled Perfect Tensor Networks: Computationally covariant holographic tensor networks

We define a novel class of tensor networks motivated by the Python's Lunch Conjecture (PLC) in local tensor network models of the black hole interior. We start from the observation that, for extended black brane states with short-range correlations, the PLC predicts a complexity that is smaller than the upper bound for generic short-range correlated states. We argue that the PLC makes implicit assumptions about the fine structure of the relevant tensor networks modeling gravity that render them non-generic. We demonstrate this explicitly in random tensor network models of the python's lunch, where the exponential complexity is not generally controlled by the PLC exponent. We trace the difference with the PLC to a lack of "computational covariance" in random tensor networks: while the PLC is motivated by an ability to arbitrarily decompose space into low-complexity units provided certain basic rules are followed, we show that random tensor networks do not generically have this property. We propose another class of tensor networks built from what we call "twirled perfect tensors" that do satisfy the computational covariance property and have a complexity bounded by the PLC value. We still find a discrete limitation from local postselection that appears to be absent in gravity. Moreover, we show that this class of tensor networks combines desirable holographic features of perfect tensor networks and random tensor networks, for example, it obeys a lattice Ryu-Takayanagi formula for arbitrary boundary subregions. Though motivated by holography, these tensor networks provide a flexible framework with potential applications beyond quantum gravity.

hep-th↗

arXiv2026

Preparing High-Fidelity Thermofield Double States

A major promise of quantum computers is the controlled preparation of many-body quantum states beyond the reach of efficient classical computation. Among the most important targets are thermal mixed states and their thermofield double (TFD) purifications, which play central roles in quantum many-body physics and quantum gravity. For target systems with a bounded energy spectrum that obey the eigenstate thermalization hypothesis (ETH), we present a parent Hamiltonian built from two copies of the target Hamiltonian and ultra-local couplings between the copies, which we argue is gapped with a ground state that approximates a TFD state of the target Hamiltonian. By adiabatically evolving down from strong coupling, we can thus prepare a high-fidelity TFD state. We study two variants of the parent Hamiltonian using numerical methods in two classes of models: mixed field Ising models in one and two dimensions and non-local "spin Sachdev-Ye-Kitaev'' models. In the simpler variant, the parent Hamiltonian ground state has high overlap with a TFD for system sizes accessible to near-term quantum devices. However, the global overlap decays exponentially with the number of qubits, with a small error per degree of freedom. The second variant introduces an additional penalty term which can be tuned to reduce or remove the decay of the overlap with system size. Together with a general ETH-based analysis, these results suggest a broadly applicable method for TFD preparation that is not limited to particular temperatures or geometric locality.

quant-ph↗

arXiv2026

Scaling at Chiral Clock Criticality via Entanglement Renormalization

We employ the Multiscale Entanglement Renormalization Ansatz (MERA) tensor network to investigate a critical line of continuous quantum phase transitions of the $\mathbb{Z}_3$ chiral clock model. This critical line is believed to be described by a slow renormalization group flow from the 3-state Potts fixed point to another fixed point that features anisotropic scaling of space and time. We use the variational principle to construct a MERA representation of the model's ground state, from which we obtain the ground state energy and the set of scaling operators and their scaling dimensions. These scaling dimensions determine the critical exponents of the model, and we study these critical exponents and other scaling data as a function of the model's chiral parameter. We find a set of effective scaling data that smoothly varies starting from the Potts data as the chiral parameter is increased. Within the context of our approach, we discuss how this result may nevertheless be consistent with the two fixed point hypothesis provided the renormalization group flow is sufficiently slow. Our findings demonstrate MERA's effectiveness in capturing the complex low-energy physics of the chiral clock model and in extracting field theory data for an anisotropic continuum theory.

cond-mat.stat-mech↗

arXiv2026

Magic and Wormholes in the Sachdev-Ye-Kitaev Model

Any quantum state is fully specified by the expectation values of a complete set of Hermitian operators. For a system of Majorana fermions, such as the Sachdev-Ye-Kitaev (SYK) model, this set of observables can be taken to be all possible strings of Majorana fermion operators. The expectation values of these fermion strings in a thermal state depend erratically on the microscopic couplings that specify the SYK Hamiltonian, and we study their statistical properties directly in the thermodynamic limit using path integral techniques. When the underlying SYK Hamiltonian is chaotic, we find that these expectation values are well-modeled as real Gaussian random variables with zero mean and a variance that we compute. In contrast, for the integrable variant of SYK, we find that the expectation values are actually non-Gaussian. We then use these results to study measures of magic in the SYK thermal state, including the robustness of magic and the stabilizer R\'enyi entropy. We also show that our results can be quantitatively reproduced with a dual gravity calculation in the chaotic case at sufficiently low temperature. In this dual gravity model the variance of a given microscopic operator string is related to a wormhole geometry stabilized by a massive particle which is dual to the operator string. Our results thus provide a concrete and quantitative setting in which to study the relationship between randomness, wormholes and closed universes, as well as a holographic dual of quantum magic.

hep-th↗

arXiv2026

Building Holographic Entanglement by Measurement

We propose a framework for preparing quantum states with a holographic entanglement structure, in the sense that the entanglement entropies are governed by minimal surfaces in a chosen bulk geometry. We refer to such entropies as holographic because they obey a relation between entropies and bulk minimal surfaces, known as the Ryu-Takayanagi formula, that is a key feature of holographic models of quantum gravity. Typically in such models, the bulk geometry is determined by solving Einstein's equations. Here, we simply choose a bulk geometry, then discretize the geometry into a coupling graph comprising bulk and boundary nodes. Evolving under this graph of interactions and measuring the bulk nodes leaves behind the desired pure state on the boundary. We numerically demonstrate that the resulting entanglement properties approximately reproduce the predictions of the Ryu-Takayanagi formula in the chosen bulk geometry. We consider graphs associated with hyperbolic disk and wormhole geometries, but the approach is general. The minimal ingredients in our proposal involve only Gaussian operations and measurements and are readily implementable in photonic and cold-atom platforms.

quant-ph↗

arXiv2025

Baby Universes from Thermal Pure States in SYK

We construct a simple two-dimensional holographic model of a closed "baby" universe. The baby universe spacetime originates from the black hole interior in Jackiw-Teitelboim (JT) gravity. The holographic description is a low-temperature thermal pure state of two Sachdev-Ye-Kitaev (SYK) models. The construction of the state relies on the insertion of a heavy matter operator, which supports the baby universe, together with a first-order thermal phase transition between a black hole phase and an empty Anti de Sitter (AdS) phase. For the transition, we employ a version of the Maldacena-Qi phase transition of two coupled SYK systems. The bulk entanglement between the AdS region and the baby universe remains O(N) below the transition, owing to the large number of light bulk fields. This entanglement admits a definition through coarse-graining over SYK couplings.

hep-th↗

arXiv2025

The Baby Universe is Fine and the CFT Knows It: On Holography for Closed Universes

Big bang/big crunch closed universes can be realized in AdS/CFT, even though they lack asymptotically AdS boundaries. With enough bulk entanglement, the bulk Hilbert space of a closed universe can be holographically encoded in the CFT. We clarify the relation of this encoding to observer-clone proposals and refute recent arguments about the breakdown of semiclassical physics in such spaces. In the limit of no bulk entanglement, the holographic encoding breaks down. The oft-cited one-dimensional nature of the closed universe Hilbert space represents the limitation of the external (CFT) Hilbert space to access the quantum information in the closed universe, similar to the limitations imposed on observers outside a perfectly isolated quantum lab. We advocate that the CFT nevertheless continues to determine the physical properties of the closed universe in this regime, showing how to interpret this relationship in terms of a final state projection in the closed universe. We provide a dictionary between the final state wavefunction and CFT data. We propose a model of the emergence of an arrow of time in the universe with a given initial or final state projection. Finally, we show that the conventional EFT in the closed universe, without any projection, can be recovered as a maximally ignorant description of the final state. This conventional EFT is encoded in CFT data, and it can be probed by computing coarse-grained observables. We provide an example of one such observable. Taken together, these results amount to a clean bill of health for baby universes born of AdS/CFT.

hep-th↗

arXiv2025

Generalized Spectral Statistics in the Kicked Ising model

The kicked Ising model has been studied extensively as a model of quantum chaos. Bertini, Kos, and Prosen studied the system in the thermodynamic limit, finding an analytic expression for the spectral form factor, $K(t)$, at the self-dual point with periodic boundary conditions. The spectral form factor is the 2nd moment of the trace of the time evolution operator, and we study the higher moments of this random variable in the kicked Ising model. A previous study of these higher moments by Flack, Bertini, and Prosen showed that, surprisingly, the trace behaves like a real Gaussian random variable when the system has periodic boundary conditions at the self dual point. By contrast, we investigate the model with open boundary conditions at the self dual point and find that the trace of the time evolution operator behaves as a complex Gaussian random variable as expected from random matrix universality based on the circular orthogonal ensemble. This result highlights a surprisingly strong effect of boundary conditions on the statistics of the trace. We also study a generalization of the spectral form factor known as the Loschmidt spectral form factor and present results for different boundary conditions.

cond-mat.stat-mech↗

arXiv2025

Scrambling Dynamics with Imperfections in a Solvable Model

We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order correlator (ROTOC) in the model with $N$ qubits, and we show that the circuit-averaged ROTOC is controlled by an effective probability distribution in operator weight space which obeys a system of $N$ non-linear equations of motion. These equations can be easily solved numerically for large system sizes which are beyond the reach of exact methods. Moreover, for an operator initially concentrated on weight one $w_0=1$, we provide an exact solution to the equations in the thermodynamic limit of many qubits that is valid for all times, all non-vanishing perturbation strengths $p\gtrsim 1/\sqrt{N}$, and all decoherence strengths. We also show that a generic initial condition $w_0 >1$ leads to a metastable state that eventually collapses to the $w_0=1$ case after a lifetime $\sim \log(N/w_0)$. Our results highlight situations where it is still possible to extract the unperturbed chaos exponent even in the presence of imperfections, and we comment on the applications of our results to existing experiments with nuclear spins and to future scrambling experiments.

quant-ph↗

arXiv2025

ER for typical EPR

What do the typical entangled states of two black holes look like? Do they contain semiclassical interiors? We approach these questions constructively, providing ensembles of states which densely explore the black hole Hilbert space. The states contain very long Einstein-Rosen (ER) caterpillars: semiclassical wormholes with large numbers of matter inhomogeneities. Distinguishing these ensembles from the typical entangled states of the black holes is hard. We quantify this by deriving the correspondence between a microscopic notion of quantum randomness and the geometric length of the wormhole. This formalizes a ``complexity = geometry'' relation.

hep-th↗

arXiv2024

Random Circuits in the Black Hole Interior

In this paper, we present a quantitative holographic relation between a microscopic measure of randomness and the geometric length of the wormhole in the black hole interior. To this end, we perturb an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. We use the random circuit to prepare ensembles of states of the black hole whose semiclassical duals contain Einstein-Rosen (ER) caterpillars: long cylindrical wormholes with large numbers of matter inhomogeneities, of linearly growing length with the circuit time. In this setup, we show semiclassically that the ensemble of ER caterpillars of average length $k\ell_{\Delta}$ and matter correlation scale $\ell_{\Delta}$ forms an approximate quantum state $k$-design of the black hole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. We comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.

hep-th↗

arXiv2024

The Magnetic Maze: A System With Tunable Scale Invariance

Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical systems. Here we consider the physics of a charged quantum particle moving in a ``magnetic maze'': a high-dimensional space filled with a randomly chosen vector potential and a corresponding magnetic field. We derive a path integral description of the model by introducing appropriate collective variables and integrating out the random vector potential, and we solve for the dynamics in the limit of large dimensionality. We derive and analyze the equations of motion for Euclidean and real-time dynamics, and we calculate out-of-time-order correlators. We show that a special choice of vector potential correlations gives rise, in the low temperature limit, to a novel scale-invariant quantum theory with a tunable dynamical exponent. Moreover, we show that the theory is chaotic with a tunable chaos exponent which approaches the chaos bound at low temperature and strong coupling.

hep-th↗

arXiv2024

The Structure of the Majorana Clifford Group

In quantum information science, Clifford operators and stabilizer codes play a central role for systems of qubits (or qudits). In this paper, we study their analogues for systems composed of Majorana fermions. In this case, a crucial role is played by fermion parity symmetry, which is an unbreakable symmetry present in any system with fundamentally fermionic degrees of freedom. We prove that the subgroup of parity-preserving Majorana Cliffords can be represented by the orthogonal group over the binary field $\F$, and we show how it can be generated by braiding operators and used to construct any (even-parity) Majorana stabilizer code. We also analyze the frame potential for this so-called p-Clifford group when acting on a fixed-parity sector of the Hilbert space, proving that it is equivalent to the frame potential of the ordinary Clifford group acting on the same sector.

quant-ph↗

arXiv2024

Complexity is not Enough for Randomness

We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium thermal partition function, and provide a set of conditions that guarantee a linear time to design. We relate the trace distance to design to spectral properties of the time-evolution operator. We apply these considerations to the Brownian $p$-SYK model as a function of the degree of locality $p$. We show that the time to design is linear, with a slope proportional to $1/p$. We corroborate that when $p$ is of order the system size this reproduces the behavior of a completely non-local Brownian model of random matrices. For the random matrix model, we reinterpret these results from the point of view of classical Brownian motion in the unitary manifold. Therefore, we find that the generation of randomness typically persists for exponentially long times in the system size, even for systems governed by highly non-local time-dependent Hamiltonians. We conjecture this to be a general property: there is no efficient way to generate approximate Haar random unitaries dynamically, unless a large degree of fine-tuning is present in the ensemble of time-dependent Hamiltonians. We contrast the slow generation of randomness to the growth of quantum complexity of the time-evolution operator. Using known bounds on circuit complexity for unitary designs, we obtain a lower bound determining that complexity grows at least linearly in time for Brownian systems. We argue that these bounds on circuit complexity are far from tight and that complexity grows at a much faster rate, at least for non-local systems.

hep-th↗

arXiv2024

Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits

Monitored random circuits, consisting of alternating layers of entangling two-qubit gates and projective single-qubit measurements applied to some fraction $p$ of the qubits, have been a topic of recent interest. In particular, the resulting steady state exhibits a phase transition from highly correlated states with "volume-law" entanglement at $p p_{c}$. It is hard to access this transition experimentally, as it cannot be seen at the ensemble level. Naively, to observe it one must repeat the experiment until the set of measurement results repeats itself, with likelihood that is exponentially small in the number of measurements. To overcome this issue, we present a hybrid quantum-classical algorithm which creates a matrix product state (MPS) based "unitary mirror" of the projected circuit. Polynomial-sized tensor networks can represent quantum states with area-law entanglement, and so the unitary mirror can well-approximate the experimental state above $p_{c}$ but fails exponentially below it. The breaking of this mirror can thus pinpoint the critical point. We outline the algorithm and how such results would be obtained. We present a bound on the maximum entanglement entropy of any given state that is well-represented by an MPS, and from the bound suggest how the volume-law phase can be bounded. We consider whether the entanglement could similarly be bounded from below where the MPS fails. Finally, we present numerical results for small qubit numbers and for monitored circuits with random Clifford gates.

quant-ph↗

arXiv2023

The Glass Transition of Quantum Hard Spheres in High Dimensions

We study the equilibrium thermodynamics of quantum hard spheres in the infinite-dimensional limit, determining the boundary between liquid and glass phases in the temperature-density plane by means of the Franz-Parisi potential. We find that as the temperature decreases from high values, the effective radius of the spheres is enhanced by a multiple of the thermal de Broglie wavelength, thus increasing the effective filling fraction and decreasing the critical density for the glass phase. Numerical calculations show that the critical density continues to decrease monotonically as the temperature decreases further, suggesting that the system will form a glass at sufficiently low temperatures for any density.

cond-mat.stat-mech↗

arXiv2023

A Bosonic Model of Quantum Holography

We analyze a model of qubits which we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum $q$-spin model because it features $q$-local interactions between qubits. It was previously studied as a model of a quantum spin glass, and while we find that the model is glassy for $q=2$, $q=3$, and likely $q=4$, we also find evidence for previously unexpected SYK-like behavior for the quenched free energy down to the lowest temperatures for $q \geq 5$. This SYK-like physics includes power-law correlation functions and an extensive low temperature entropy, so we refer to the model as Spin SYK. The model is generic in that it includes all possible $q$-body couplings, lacks most symmetries, and has no spatial structure, so our results can be construed as establishing a certain ubiquity of quantum holography in systems dominated by many-body interactions. Furthermore, we discuss a generalized family of models which includes Spin SYK and which provably exhibit SYK-like physics in the solvable limit of large local Hilbert space dimension. We also comment on implications of a bosonic system with SYK-like properties for the study of holography, Hamiltonian complexity, and related topics.

hep-th↗

arXiv2023

Temperature dependence of energy transport in the $\mathbb{Z}_3$ chiral clock model

We employ matrix product state simulations to study energy transport within the non-integrable regime of the one-dimensional $\mathbb{Z}_3$ chiral clock model. To induce a non-equilibrium steady state throughout the system, we consider open system dynamics with boundary driving featuring jump operators with adjustable temperature and footprint in the system. Given a steady state, we diagnose the effective local temperature by minimizing the trace distance between the true local state and the local state of a uniform thermal ensemble. Via a scaling analysis, we extract the transport coefficients of the model at relatively high temperatures above both its gapless and gapped low-temperature phases. In the medium-to-high temperature regime we consider, diffusive transport is observed regardless of the low-temperature physics. We calculate the temperature dependence of the energy diffusion constant as a function of model parameters, including in the regime where the model is quantum critical at the low temperature. Notably, even within the gapless regime, an analysis based on power series expansion implies that intermediate-temperature transport can be accessed within a relatively confined setup. Although we are not yet able to reach temperatures where quantum critical scaling would be observed, our approach is able to access the transport properties of the model over a broad range of temperatures and parameters. We conclude by discussing the limitations of our method and potential extensions that could expand its scope, for example, to even lower temperatures.

cond-mat.str-el↗