arXiv subjects

Rahul Sahay

Publications and source records attributed to Rahul Sahay.

16 recordsLinked to original sources

arXiv2026

Computing with qLDPC Codes by Climbing the Chain Map Hierarchy

We develop a framework for logical computation with qLDPC codes that places logical Pauli, Clifford, and non-Clifford operations on the same footing. This brings the simple homological description of Pauli logicals to the patchwork landscape of logical Clifford and non-Clifford operations, providing a tool for the discovery of new logical gates. In particular, we define the chain map hierarchy: a family of chain complexes whose homology classes encode logical unitary and code surgery operations at any level of the Clifford hierarchy, precisely analogous to the chain complex description of Pauli logicals. Consequently, intuition for Pauli logicals can be leveraged to discover new logical operations on qLDPC codes. For instance, the familiar ability to deform Pauli logicals with stabilizers---i.e. boundaries of the chain complex---becomes a way to search for constant-depth unitary implementations of (non-)Clifford logical gates. Using this strategy, we discover constant-depth unitary implementations of the full logical Clifford group on any number of blocks of the 2D toric code, including within a single block, and addressable logical CCZ gates on any triple of logical qubits on any number of blocks of the 3D toric code. Beyond manifold codes, we find addressable non-Clifford gates on codes with many encoded qubits. The chain map hierarchy naturally encompasses and extends other constructions of logical gadgets, for instance providing a universal parameterization of cup products. As such, our work provides a unified, useful, and intuitive language for computing with qLDPC codes.

quant-ph↗

arXiv2026

Engineering quantum criticality and dynamics on an analog-digital simulator

Understanding emergent phenomena in out-of-equilibrium interacting many-body systems is an exciting frontier in physical science. While quantum simulators represent a promising approach to this long-standing problem, in practice it can be challenging to directly realize the required interactions, measure arbitrary observables, and mitigate errors. Here we use coherent mapping between the Rydberg and hyperfine qubits in a neutral atom array simulator to engineer and probe complex quantum dynamics. We combine efficient analog dynamics with fully programmable state preparation and measurement, leverage non-destructive readout for loss information and atomic qubit reuse, and use an atom reservoir for replacing lost atoms. With this analog-digital approach, we first demonstrate dynamical engineering of ring-exchange and particle hopping dynamics via Floquet driving and measure the spectral function of single excitations by evolving initial superposition states. Extending these techniques to a 271-site kagome lattice, we employ closed-loop optimization to target an out-of-equilibrium critical quantum spin liquid of the Rokhsar-Kivelson type. We observe the key features of such a state, including the absence of local order, many-body coherences between nearly equal-amplitude dimer configurations over up to 18 sites, and universal correlations consistent with predictions from field theory. Together, these results pave the way for using dynamical control in analog-digital quantum simulators to study complex quantum many-body systems.

quant-ph↗

arXiv2026

Non-Abelian Quantum Low-Density Parity Check Codes and Non-Clifford Operations from Gauging Logical Gates via Measurements

In this work, we introduce constructions for non-Abelian qLDPC codes obtained by gauging transversal Clifford gates using measurement and feedback. In particular, we identify two qualitatively different approaches to gauging qLDPC codes to obtain their non-Abelian counterparts. The first approach applies to codes that exhibit a generalized form of Poincar\'e duality and leads to a qLDPC non-Abelian Clifford stabilizer code, whose stabilizers are reminiscent of the action of a Type-III twisted quantum double. Our second approach applies to general qLDPC codes, and uses a graph of ancilla qubits which may be tailored to properties of the input codes to gauge a single transversal gate. For both constructions, the resulting gauged codes are shown to have properties analogous to 2D non-Abelian topological order -- e.g. the analog of a single anyon on a torus. We conclude by demonstrating that our gauging procedures enable magic state preparation via the measurement of logical Clifford gates. Consequently, our gauging constructions offer a protocol for performing non-Clifford operations on any qLDPC code.

quant-ph↗

arXiv2025

Spin Polarons in Flat Band Ferromagnets

Spin polarons are bound states of electrons and spin-flips that form above spin polarized electronic insulators.These bound states conventionally form in one of two settings: in frustrated lattices with dispersive bands -- where the motion of an electron preferences binding a nearby spin-flip -- or in topological flat bands -- where the Chern number enforces an effective dipolar interaction between electrons and spin flips. In this work, we report the formation of a spin polaron in a context that doesn't fall cleanly into either of these paradigms. In particular, we study the one-dimensional Mielke-Tasaki chain, a paradigmatic model of flat band ferromagnetism, which has an exact ferromagnetic ground state, trivial band topology, and quenched kinetic energy in its lowest band. Despite these features, our density matrix renormalization group simulations reveal the presence of spin polarons upon electron doping this model. More surprisingly, combining these numerics with analytic calculations, we show that polaron binding occurs when the interaction-induced kinetic energy of the model is zero -- contrary to intuition from kinetic magnetism -- and the glue binding the electrons and spin-flips arises from weak mixing with the model's dispersive band -- contrary to what occurs in topological flat bands. Our results open the doors to exploring how the quantum geometry of flat bands drives the formation of exotic charge carriers.

cond-mat.str-el↗

arXiv2025

Topological Phase Transitions and Mixed State Order in a Hubbard Quantum Simulator

Topological phase transitions challenge conventional paradigms in many-body physics by separating phases that are locally indistinguishable yet globally distinct. Using a quantum simulator of interacting erbium atoms in an optical lattice, we observe such a transition between one-dimensional crystalline symmetry-protected topological phases (CSPTs). We detect the critical point through non-local string order parameters and reveal its connection to the transition predicted between the Mott and Haldane insulators. Moreover, we demonstrate a striking property: stacking two identical systems eliminates the transition, confirming the predicted group structure and invertibility of SPTs. Finally, while introducing symmetry-breaking disorder also removes the transition, disorder averaging restores it. Consequently, the adjacent phases realize a form of mixed-state quantum order wherein the criticality between them depends on the observer's information. Our results demonstrate how topology and information influence quantum phase transitions, opening the doors to probing novel critical phenomena in programmable quantum matter.

cond-mat.quant-gas↗

arXiv2025

Enforced Gaplessness from States with Exponentially Decaying Correlations

It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply gaplessness. This is exemplified by the deformed toric code $\propto \exp(\beta \sum_{\ell} Z_{\ell}) |\mathsf{TC}\rangle$, where $|\mathsf{TC}\rangle$ is a fixed-point toric code wavefunction. Although it has a confined regime for $\beta > \beta_c$, recent work has drawn attention to its perimeter law loop correlations. Here, we show that these unusual loop correlations -- namely, perimeter law coexisting with a 1-form symmetry whose disorder operator has long-range order -- imply that any local parent Hamiltonian must either be gapless or have a degeneracy scaling with system size. Moreover, we construct a variational low-energy state for arbitrary local frustration-free Hamiltonians, upper bounding the finite-size gap by $O(1/L^3)$ on periodic boundary conditions. Strikingly, these variational states look like loop waves -- non-quasiparticle analogs of spin waves -- generated from the ground state by non-local loop operators. Our findings have implications for identifying the subset of Hilbert space to which gapped ground states belong, and the techniques have wide applicability. For instance, a corollary of our first result is that Glauber dynamics for the ordered phase of the two-dimensional classical Ising model on the torus must have a gapless Markov transition matrix, with our second result bounding its gap.

cond-mat.str-el↗

arXiv2025

Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes

The dynamical preparation of exotic many-body quantum states is a persistent goal of analog quantum simulation, often limited by experimental coherence times. Recently, it was shown that fast, non-adiabatic Hamiltonian parameter sweeps can create finite-size ``lakes'' of quantum order in certain settings, independent of what is present in the ground state phase diagram. Here, we show that going further out of equilibrium via external driving can substantially accelerate the preparation of these quantum lakes. Concretely, when lakes can be prepared, existing counterdiabatic driving techniques -- originally designed to target the ground state -- instead naturally target the lakes state. We demonstrate this both for an illustrative single qutrit and a model of a $\mathbb{Z}_2$ Rydberg quantum spin liquid. In the latter case, we construct experimental drive sequences that accelerate preparation by almost an order of magnitude at fixed laser power. We conclude by using a Landau-Ginzburg model to provide a semi-classical picture for how our method accelerates state preparation.

quant-ph↗

arXiv2024

Finite-Depth Preparation of Tensor Network States from Measurement

Although tensor network states constitute a broad range of exotic quantum states, their realization is challenging and often requires resources whose depth scales with system size. In this work, we explore criteria on the local tensors for enabling deterministic state preparation via a single round of measurements and on-site unitary feedback. We use these criteria to construct families of measurement-preparable states in one and two dimensions, tuning between distinct symmetry-breaking, symmetry-protected, and intrinsic topological phases of matter. For instance, in one dimension we chart out a three-parameter family of preparable states which interpolate between the AKLT, cluster, GHZ and other states of interest. Our protocol even allows one to engineer preparable quantum states with a range of desired correlation lengths and entanglement properties. In addition to such constructive approaches, we present diagnostics for verifying whether a given tensor network state is preparable using measurements. We conclude by charting out generalizations, such as considering multiple rounds of measurements, implementing matrix product operators, and using incomplete basis measurements.

quant-ph↗

arXiv2024

Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements

Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However, a detailed understanding has been restricted to fixed-point representatives of phases of matter. Here, we go beyond this and characterize the patterns of many-body entanglement that can be deterministically created from measurement. Focusing on one spatial dimension, a framework is developed for the case where a single round of measurements is the only entangling operation. We show this creates matrix product states and identify necessary and sufficient tensor conditions for preparability, which uniquely determine the preparation protocol. We use these conditions to both classify preparable quantum states and characterize their physical constraints. In particular, we find a trade-off between the richness of the preparable entanglement spectrum and correlation functions, which leads to a no-go theorem for preparing certain quantum states. More broadly, we connect properties of the preparation protocol to the resulting phase of matter, including trivial, symmetry-breaking, and symmetry-protected topological phases -- for both uniform and modulated symmetries. This work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter, away from their fixed points, in quantum devices.

quant-ph↗

arXiv2024

Emergent Holographic Forces from Tensor Networks and Criticality

The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is challenging. We formulate an efficiently implementable multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT providing a mapping between a (1+1)-dimensional critical spin system and a (2+1)-dimensional bulk theory. Using a combination of numerics and analytics, we show that the bulk theory arising from this optimized tensor network furnishes excitations with attractive interactions. Remarkably, these excitations have one- and two-particle energies matching the predictions for matter coupled to AdS gravity at long distances, thus displaying key features of AdS physics. We show that these potentials arise as a direct consequence of entanglement renormalization and discuss how this approach can be used to efficiently simulate bulk dynamics using realistic quantum devices.

quant-ph↗

arXiv2023

Superconductivity in a Topological Lattice Model with Strong Repulsion

The highly tunable nature of synthetic quantum materials -- both in the solid-state and cold atom contexts -- invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moir\'e materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce a minimal 2D lattice model that incorporates exactly these features: time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall (QSH) insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. At the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the QSH insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be $p$-wave -- reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

cond-mat.str-el↗

arXiv2022

Quantum Spin Puddles and Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics

While many-body systems can host long-ranged entangled quantum spin liquids (QSLs), the ingredients for realizing these as ground states can be prohibitively difficult. In many circumstances, one requires (i) a constrained Hilbert space and (ii) an extensive quantum superposition. The paradigmatic example is the toric code, or $\mathbb{Z}_2$ spin liquid, which is a superposition of closed loop states. We show how non-equilibrium Hamiltonian dynamics can provide a streamlined route toward creating such QSLs. Rather than cooling into the ground state of a Hamiltonian, we show how a simple parameter sweep can dynamically project a family of initial product states into the constrained space, giving rise to a QSL. For the toric code, this is achieved in systems with a separation in energy scales between the $e$- and $m$-anyons, where one can sweep in a way that is adiabatic (sudden) with respect to the former (latter). Although this separation of scales does not extend to the thermodynamic limit, we analytically and numerically show that this method efficiently prepares a spin liquid in finite-sized regions, which we brand ``quantum spin lakes.'' This mechanism elucidates recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. In fact, the slow dynamics of $m$-anyons suggest that we can capture spin lake preparation by simulating the dynamics on tree lattices, which we confirm with tensor network simulations. Finally, we use this mechanism to propose new experiments, e.g., for preparing a finite-sized $U(1)$ spin liquid as a honeycomb Rokhsar-Kivelson dimer model using Rydberg atoms -- which is remarkable given its equilibrium counterpart is unstable in $2 + 1$D. Our work opens up a new avenue in the study of non-equilibrium physics, as well as the exploration of exotic states of finite extent in NISQ devices.

cond-mat.str-el↗

arXiv2022

Extracting the Quantum Hall Conductance from a Single Bulk Wavefunction

We propose a new formula that extracts the quantum Hall conductance from a single (2+1)D gapped wavefunction. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow: i.e., unitary dynamics generated from the entanglement structure of the wavefunction. The formula is shown to satisfy all formal properties of the Hall conductance: it is odd under time-reversal and reflection, even under charge conjugation, universal and topologically rigid in the thermodynamic limit. Further evidence for relating the formula to the Hall conductance is obtained from conformal field theory arguments. Finally, we numerically check the formula by applying it to a non-interacting Chern band where excellent agreement is obtained.

cond-mat.str-el↗

arXiv2021

Noise Electrometry of Polar and Dielectric Materials

A qubit sensor with an electric dipole moment acquires an additional contribution to its depolarization rate when it is placed in the vicinity of a polar or dielectric material as a consequence of electrical noise arising from polarization fluctuations in the latter. Here, we characterize this relaxation rate as a function of experimentally tunable parameters such as sample-probe distance, probe-frequency, and temperature, and demonstrate that it offers a window into dielectric properties of insulating materials over a wide range of frequencies and length scales. We discuss the experimental feasibility of our proposal and illustrate its ability to probe a variety of phenomena, ranging from collective polar excitations to phase transitions and disorder-dominated physics in relaxor ferroelectrics. Our proposal paves the way for a novel table-top probe of polar and dielectric materials in a parameter regime complementary to existing tools and techniques.

cond-mat.mtrl-sci↗

arXiv2020

Emergent ergodicity at the transition between many-body localized phases

Strongly disordered systems in the many-body localized (MBL) phase can exhibit ground state order in highly excited eigenstates. The interplay between localization, symmetry, and topology has led to the characterization of a broad landscape of MBL phases ranging from spin glasses and time crystals to symmetry protected topological phases. Understanding the nature of phase transitions between these different forms of eigenstate order remains an essential open question. Here, we conjecture that no direct transition between distinct MBL orders can occur; rather, a thermal phase always intervenes. Motivated by recent advances in Rydberg-atom-based quantum simulation, we propose an experimental protocol where the intervening thermal phase can be diagnosed via the dynamics of local observables.

cond-mat.dis-nn↗

arXiv2017

Curves of Constant Curvature and Torsion in the 3-Sphere

We describe the curves of constant (geodesic) curvature and torsion in the three-dimensional round sphere. These curves are the trajectory of a point whose motion is the superposition of two circular motions in orthogonal planes. The global behavior may be periodic or the curve may be dense in a Clifford torus embedded in the three-sphere. This behavior is very different from that of helices in three-dimensional Euclidean space, which also have constant curvature and torsion.

math.DG↗