arXiv subjects

Pranjal Nayak

Publications and source records attributed to Pranjal Nayak.

15 recordsLinked to original sources

arXiv2026

Plaquette: A hardware-aware design platform for fault-tolerant quantum computers

Hardware teams building fault-tolerant quantum computers (FTQCs) must decide which imperfections to suppress, and that decision requires the logical performance of the architecture under the device's actual noise. Hardware noise often departs from the stochastic Pauli models used by scalable stabilizer simulators: superconducting transmons leak out of the computational subspace, neutral atoms scatter through intermediate states, trapped ions heat as their motional modes absorb phonons, and miscalibrated controls over-rotate coherently. We present Plaquette, a theoretical framework and software suite that computes the logical performance of fault-tolerant architectures directly from the physics of such imperfections. In Plaquette, a hardware error model is specified once, as Kraus operators, Hamiltonian-Lindblad dynamics, or an experimentally reconstructed quantum channel, and is compiled automatically into the exact or approximate representation required by each of four sampler classes: stabilizer sampling for Pauli noise, the new XPauli sampler for leakage and environment sectors, near-Clifford samplers for coherent errors, and full-state simulation for exact reference calculations. We validate the XPauli and near-Clifford samplers against full-state simulation, which they can match within statistical uncertainty while Pauli twirling can fall short depending on the error model. We demonstrate the framework on three error models: leakage in superconducting qubits, intermediate-state scattering in neutral atoms, and heating in trapped ions. The size of the discrepancy between Plaquette and Clifford-only simulations varies with platform and noise process, so reliable thresholds, error budgets, and overhead estimates require the most accurate simulation available. Plaquette provides a direct path from the open-system physics of a device to the logical performance of the FTQC built on it.

quant-ph↗

arXiv2025

Hilbert Space Diffusion in Systems with Approximate Symmetries

Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT behaviour at intermediate time scales in systems with approximate symmetries. At early times, the symmetries allow us to organize the Hilbert space into approximately decoupled sectors, each of which contributes independently to the SFF. At late times, the SFF transitions into the final ramp of the fully mixed chaotic Hamiltonian. For approximate continuous symmetries, the transitional behaviour is governed by a universal process that we call Hilbert space diffusion. The diffusion constant corresponding to this process is related to the relaxation rate of the associated nearly conserved charge. By implementing a chaotic sigma model for Hilbert-space diffusion, we formulate an analytic theory of this process which agrees quantitatively with our numerical results for different examples.

cond-mat.stat-mech↗

arXiv2024

Approximate CFTs and Random Tensor Models

A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of `CFT data'. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of `CFT data' satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS$_3$ as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.

hep-th↗

arXiv2022

Generalized Spectral Form Factors and the Statistics of Heavy Operators

The spectral form factor is a powerful probe of quantum chaos that diagnoses the statistics of energy levels, but is blind to other features of a theory such as matrix elements of operators or OPE coefficients in conformal field theories. In this paper, we introduce generalized spectral form factors: new probes of quantum chaos sensitive to the dynamical data of a theory. These quantities can be studied using an effective theory of quantum chaos. We focus our attention on a particular combination of heavy-heavy-heavy OPE coefficients that generalizes the genus-2 partition function of two-dimensional CFTs, for which we define a spectral form factor. We probe heavy-heavy-heavy OPE coefficients and find statistical correlations that agree with the OPE Randomness Hypothesis: these coefficients have a random matrix component in the ergodic regime. The EFT of quantum chaos predicts that the genus-2 spectral form factor displays a ramp and a plateau. Our results suggest that this is a common property of generalized spectral form factors.

hep-th↗

arXiv2021

Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity

We generalize the eigenstate thermalization hypothesis to systems with global symmetries. We present two versions, one with microscopic charge conservation and one with exponentially suppressed violations. They agree for correlation functions of simple operators, but differ in the variance of charged one-point functions at finite temperature. We then apply these ideas to holography and to gravitational low-energy effective theories with a global symmetry. We show that Euclidean wormholes predict a non-zero variance for charged one-point functions, which is incompatible with microscopic charge conservation. This implies that global symmetries in quantum gravity must either be gauged or explicitly broken by non-perturbative effects.

hep-th↗

arXiv2021

From operator statistics to wormholes

For a generic quantum many-body system, the quantum ergodic regime is defined as the limit in which the spectrum of the system resembles that of a random matrix theory (RMT) in the corresponding symmetry class. In this paper we analyse the time dependence of correlation functions of operators. We study them in the ergodic limit as well as their approach to the ergodic limit which is controlled by non-universal massive modes. An effective field theory (EFT) corresponding to the causal symmetry and its breaking describes the ergodic phase. We demonstrate that the resulting Goldstone-mode theory has a topological expansion, analogous to the one described in arXiv:2008.02271 with added operator sources, whose leading non-trivial topologies give rise to the universal ramp seen in correlation functions. The ergodic behaviour of operators in our EFT is seen to result from a combination of RMT-like spectral statistics and Haar averaging over wave-functions. Furthermore we analytically capture the plateau behaviour by taking into account the contribution of a second saddle point. Our main interest are quantum many-body systems with holographic duals and we explicitly establish the validity of the EFT description in the SYK-class of models, starting from their microscopic description. By studying the tower of massive modes above the Goldstone sector we get a detailed understanding of how the ergodic EFT phase is approached and derive the relevant Thouless time scales. We point out that the topological expansion can be reinterpreted in terms of contributions of bulk wormholes and baby-universes.

hep-th↗

arXiv2019

Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory

In this paper we provide a universal description of the behavior of the basic operators of the Schwarzian theory in pure states. When the pure states are energy eigenstates, expectation values of non-extensive operators are thermal. On the other hand, in coherent pure states, these same operators can exhibit ergodic or non-ergodic behavior, which is characterized by elliptic, parabolic or hyperbolic monodromy of an auxiliary equation; or equivalently, which coadjoint Virasoro orbit the state lies on. These results allow us to establish an extended version of the eigenstate thermalization hypothesis (ETH) in theories with a Schwarzian sector. We also elucidate the role of FZZT-type boundary conditions in the Schwarzian theory, shedding light on the physics of microstates associated with ZZ branes and FZZT branes in low dimensional holography.

hep-th↗

arXiv2019

Correlation functions in ${\cal N}=2$ Supersymmetric vector matter Chern-Simons theory

We compute the two, three point function of the opearators in the spin zero multiplet of ${\cal N}=2$ Supersymmetric vector matter Chern-Simons theory at large $N$ and at all orders of 't Hooft coupling by solving the Schwinger-Dyson equation. Schwinger-Dyson method to compute four point function becomes extremely complicated and hence we use bootstrap method to solve for four point function of scaler operator $J_0^{f}=\barψψ$ and $J_0^{b}=\barϕϕ$. Interestingly, due to the fact that $\langle J_0^{f}J_0^{f}J_0^{b} \rangle$ is a contact term, the four point function of $ J_0^{f}$ operator looks like that of free theory up to overall coupling constant dependent factors and up to some bulk AdS contact terms. On the other hand the $J_0^{b}$ four-point function receives an additional contribution compared to the free theory expression due to the $J_0^{f}$ exchange. Interestingly, double discontinuity of this single trace operator $J_0^{f}$ vanishes and hence it only contributes to AdS-contact term.

hep-th↗

arXiv2019

Dual Superconformal Symmetry of ${\cal N}=2$ Chern-Simons theory with Fundamental Matter at Large $N$

Dual conformal symmetry and Yangian symmetry are symmetries of amplitudes that have aided the study of scattering amplitudes in highly supersymmetric theories like ${\cal N}=4$ SYM and ABJM. However, in general such symmetries are absent from the theories with lesser or no supersymmetry. In this paper, we show that the tree level $2\to 2$ scattering amplitude in the 3d ${\cal N}=2$ Chern-Simons theory coupled to a fundamental chiral multiplet is dual superconformal invariant. In the 't Hooft large $N$ limit, the $2\to 2$ scattering amplitude in this theory has been shown to be tree-level exact in non-anyonic channels, while having only an overall multiplicative coupling dependent renormalisation in the anyonic channel. Therefore, the dual superconformal symmetry that we demonstrate in this paper is all loop exact. This is unlike the previously studied highly supersymmetric theories where dual superconformal symmetry is anomalous at loop levels. Furthermore, we reverse the argument to study the extent to which dual superconformal invariance fixes the scattering amplitude in an ${\cal N}=2$ supersymmetric theory. We demonstrate that requiring the dual superconformal invariance completely fixes the momentum dependence of the $2\to2$ amplitude, while the coupling constant dependence remain unfixed. Further, we use a combination of parity invariance, unitarity and self-duality of the amplitude to constrain the coupling dependence of scattering amplitude.

hep-th↗

arXiv2019

Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach

The Sachdev-Ye-Kitaev (SYK) model provides an uncommon example of a chaotic theory that can be analysed analytically. In the deep infrared limit, the original model has an emergent conformal (reparametrisation) symmetry that is broken both spontaneously and explicitly. The explicit breaking of this symmetry comes about due to pseudo-Nambu-Goldstone modes that are not exact zero-modes of the model. In this paper, we study a version of the model which preserves the reparametrisation symmetry at all length scales. We study the heavy-light correlation functions of the operators in the conformal spectrum of the theory. The three point functions of such operators allow us to demonstrate that matrix elements of primaries ${\cal O}_n$ of the CFT$_1$ take the form postulated by the Eigenstate Thermalisation Hypothesis. We also discuss the implications of these results for the states in AdS$_2$ gravity dual.

hep-th↗

arXiv2018

All tree level scattering amplitudes in Chern-Simons theories with fundamental matter

We show that Britto-Cachazo-Feng-Witten (BCFW) recursion relations can be used to compute all tree level scattering amplitudes in terms of $2\rightarrow2$ scattering amplitude in $U(N)$ ${\mathcal N}=2$ Chern-Simons (CS) theory coupled to matter in fundamental representation. As a byproduct, we also obtain a recursion relation for the CS theory coupled to regular fermions, even though in this case standard BCFW deformations do not have a good asymptotic behaviour. Moreover at large $N$, $2\rightarrow 2$ scattering can be computed exactly to all orders in 't Hooft coupling as was done in earlier works by some of the authors. In particular, for ${\mathcal N}=2$ theory, it was shown that $2\rightarrow 2$ scattering is tree level exact to all orders except in the anyonic channel arXiv:1505.06571, where it gets renormalized by a simple function of 't Hooft coupling. This suggests that it may be possible to compute the all loop exact result for arbitrary higher point scattering amplitudes at large $N$.

hep-th↗

arXiv2018

On the Dynamics of Near-Extremal Black Holes

We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti-de Sitter space (AdS$_4$). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.

hep-th↗

arXiv2017

Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models

The Nambu-Goldstone (NG) bosons of the SYK model are described by a coset space Diff/$\mathbb{SL}(2,\mathbb{R})$, where Diff, or Virasoro group, is the group of diffeomorphisms of the time coordinate valued on the real line or a circle. It is known that the coadjoint orbit action of Diff naturally turns out to be the two-dimensional quantum gravity action of Polyakov without cosmological constant, in a certain gauge, in an asymptotically flat spacetime. Motivated by this observation, we explore Polyakov action with cosmological constant and boundary terms, and study the possibility of such a two-dimensional quantum gravity model being the AdS dual to the low energy (NG) sector of the SYK model. We find strong evidences for this duality: (a) the bulk action admits an exact family of asymptotically AdS$_2$ spacetimes, parameterized by Diff/$\mathbb{SL}(2,\mathbb{R})$, in addition to a fixed conformal factor of a simple functional form; (b) the bulk path integral reduces to a path integral over Diff/$\mathbb{SL}(2,\mathbb{R})$ with a Schwarzian action; (c) the low temperature free energy qualitatively agrees with that of the SYK model. We show, up to quadratic order, how to couple an infinite series of bulk scalars to the Polyakov model and show that it reproduces the coupling of the higher modes of the SYK model with the NG bosons.

hep-th↗

arXiv2017

A Note on S-Matrix Bootstrap for Amplitudes with Linear Spectrum

We work out constraints imposed by channel duality and analyticity on tree-level amplitudes of four identical real scalars, with the assumptions of a linear spectrum of exchanged particles and Regge asymptotic behaviour. We reduce the requirement of channel duality to a countably infinite set of equations in the general case. We show that channel duality uniquely fixes the soft Regge behaviour of the amplitudes to that found in String theory, $(-s)^{2t}$. Specialising to the case of tachyonic external particles, we use channel duality to show that the amplitude can be any one in an infinite-dimensional parameter space, and present evidence that unitarity doesn't significantly reduce the dimension of the space of amplitudes.

hep-th↗

arXiv2016

Revisiting AdS/CFT at a finite radial cut-off

We revisit AdS/CFT at finite radial cut-off, specifically in the context of double trace perturbations, $\mathbb{O}_n$= $\mathbb{O}(x) (\partial^2)^{n} {\mathcal O}(x)$, with arbitrary $n$. As well-known, the standard GKPW prescription, applied to a finite radial cut-off, leads to contact terms in correlators. de Haro et al (arXiv:hep-th/0002230) introduced bulk counterterms to remove these. However, this prescription yields additional terms in the correlator corresponding to spurious double trace deformations. Further, if we view GKPW prescription coupled with the prescription in arXiv:hep-th/0002230, in terms of a boundary wavefunction, we find that it is incompatible with radial Schrodinger evolution (in the spirit of holographic Wilsonian RG). We consider a more general wavefunction satisfying the Schrodinger equation, and find that generically such wavefunctions generate both (a) double trace deformations and (b) contact terms. However, we find that there exist special choices of these wavefunctions, amounting to a new AdS/CFT prescription at a finite cut-off, so that both (a) and (b) are removed and we obtain a pure power law behaviour for the correlator. We compare these special wavefunctions with a specific RG scheme in field theory. We give a geometric interpretation of these wavefunctions; these correspond to some specific smearing of boundary points in the Witten diagrams. We present a comprehensive calculation of exact double-trace beta-functions for all couplings $\mathbb{O}_n$ and match with a holographic computation using the method described above. The matching works with a mapping between the field theory and bulk couplings; such a map is highly constrained because the beta-functions are quadratic and exact on both sides. We generalize standard double-trace Wilson-Fisher flow to the space of the infinite number of couplings.

hep-th↗