arXiv subjects

Yuri D. Lensky

Publications and source records attributed to Yuri D. Lensky.

12 recordsLinked to original sources

arXiv2026

Practical gates by Majorana fermion motion

Quantum error correction protocols protect against local errors by storing logical information non-locally. This poses a challenge: how to design efficient logical gates on the non-local ``hidden'' logical information, and how to implement these gates using the local physical operations. We develop a general description of planar Pauli stabilizer codes and protocols for logical operations in terms of point-like particles called Majorana fermions. Information is stored in the pairwise fermion parities of spatially separated Majorana fermions. The description in terms of Majorana fermions captures not only large distance asymptotics, but also all scales down to the lattice constants. We exploit this locality to densely pack logical information in spacetime. The simplest application is to a static case: dense memory. More importantly, we implement fault-tolerant Majorana motion and leverage this primitive to design braiding-based logical gates. This approach reduces space overhead of logical operations resulting in an improved logical error rate given fixed number of physical qubits. We illustrate a practical use of our approach by designing and benchmarking of 2-qubit Clifford gates. We find numerically that our protocol outperforms lattice surgery in this setting for near-term error rates and realistic device constraints. More generally, introduction of compact motion of Majorana fermions as an efficient computational primitive opens a promising new route for the design of low overhead error correction protocols.

quant-ph↗

arXiv2025

Observation of disorder-free localization using a (2+1)D lattice gauge theory on a quantum processor

Disorder-induced phenomena in quantum many-body systems pose significant challenges for analytical methods and numerical simulations at relevant time and system scales. To reduce the cost of disorder-sampling, we investigate quantum circuits initialized in states tunable to superpositions over all disorder configurations. In a translationally-invariant lattice gauge theory (LGT), these states can be interpreted as a superposition over gauge sectors. We observe localization in this LGT in the absence of disorder in one and two dimensions: perturbations fail to diffuse despite fully disorder-free evolution and initial states. However, Rényi entropy measurements reveal that superposition-prepared states fundamentally differ from those obtained by direct disorder sampling. Leveraging superposition, we propose an algorithm with a polynomial speedup in sampling disorder configurations, a longstanding challenge in many-body localization studies.

quant-ph↗

arXiv2025

Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories

Lattice gauge theories (LGTs) can be employed to understand a wide range of phenomena, from elementary particle scattering in high-energy physics to effective descriptions of many-body interactions in materials. Studying dynamical properties of emergent phases can be challenging as it requires solving many-body problems that are generally beyond perturbative limits. Here, we investigate the dynamics of local excitations in a $\mathbb{Z}_2$ LGT using a two-dimensional lattice of superconducting qubits. We first construct a simple variational circuit which prepares low-energy states that have a large overlap with the ground state; then we create charge excitations with local gates and simulate their quantum dynamics via a discretized time evolution. As the electric field coupling constant is increased, our measurements show signatures of transitioning from deconfined to confined dynamics. For confined excitations, the electric field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT from which we uncover two distinct regimes inside the confining phase: for weak confinement the string fluctuates strongly in the transverse direction, while for strong confinement transverse fluctuations are effectively frozen. In addition, we demonstrate a resonance condition at which dynamical string breaking is facilitated. Our LGT implementation on a quantum processor presents a novel set of techniques for investigating emergent excitations and string dynamics.

quant-ph↗

arXiv2024

Attention to Quantum Complexity

The imminent era of error-corrected quantum computing urgently demands robust methods to characterize complex quantum states, even from limited and noisy measurements. We introduce the Quantum Attention Network (QuAN), a versatile classical AI framework leveraging the power of attention mechanisms specifically tailored to address the unique challenges of learning quantum complexity. Inspired by large language models, QuAN treats measurement snapshots as tokens while respecting their permutation invariance. Combined with a novel parameter-efficient mini-set self-attention block (MSSAB), such data structure enables QuAN to access high-order moments of the bit-string distribution and preferentially attend to less noisy snapshots. We rigorously test QuAN across three distinct quantum simulation settings: driven hard-core Bose-Hubbard model, random quantum circuits, and the toric code under coherent and incoherent noise. QuAN directly learns the growth in entanglement and state complexity from experimentally obtained computational basis measurements. In particular, it learns the growth in complexity of random circuit data upon increasing depth from noisy experimental data. Taken to a regime inaccessible by existing theory, QuAN unveils the complete phase diagram for noisy toric code data as a function of both noise types. This breakthrough highlights the transformative potential of using purposefully designed AI-driven solutions to assist quantum hardware.

quant-ph↗

arXiv2024

Machine learning reveals features of spinon Fermi surface

With rapid progress in simulation of strongly interacting quantum Hamiltonians, the challenge in characterizing unknown phases becomes a bottleneck for scientific progress. We demonstrate that a Quantum-Classical hybrid approach (QuCl) of mining sampled projective snapshots with interpretable classical machine learning can unveil signatures of seemingly featureless quantum states. The Kitaev-Heisenberg model on a honeycomb lattice under external magnetic field presents an ideal system to test QuCl, where simulations have found an intermediate gapless phase (IGP) sandwiched between known phases, launching a debate over its elusive nature. We use the correlator convolutional neural network, trained on labeled projective snapshots, in conjunction with regularization path analysis to identify signatures of phases. We show that QuCl reproduces known features of established phases. Significantly, we also identify a signature of the IGP in the spin channel perpendicular to the field direction, which we interpret as a signature of Friedel oscillations of gapless spinons forming a Fermi surface. Our predictions can guide future experimental searches for spin liquids.

cond-mat.str-el↗

arXiv2023

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory: by collapsing the wavefunction it can enable phenomena such as teleportation and thereby alter the "arrow of time" that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time that go beyond established paradigms for characterizing phases, either in or out of equilibrium. On present-day NISQ processors, the experimental realization of this physics is challenging due to noise, hardware limitations, and the stochastic nature of quantum measurement. Here we address each of these experimental challenges and investigate measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping, to avoid mid-circuit measurement and access different manifestations of the underlying phases -- from entanglement scaling to measurement-induced teleportation -- in a unified way. We obtain finite-size signatures of a phase transition with a decoding protocol that correlates the experimental measurement record with classical simulation data. The phases display sharply different sensitivity to noise, which we exploit to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realize measurement-induced physics at scales that are at the limits of current NISQ processors.

quant-ph↗

arXiv2023

Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics. For all elementary and quasiparticles observed to date - including fermions, bosons, and Abelian anyons - this principle guarantees that the braiding of identical particles leaves the system unchanged. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of employing the anyons for quantum computation and utilize braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and - through the future inclusion of error correction to achieve topological protection - could open a path toward fault-tolerant quantum computing.

quant-ph↗

arXiv2022

Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code

Stabilizer codes allow for non-local encoding and processing of quantum information. Deformations of stabilizer surface codes introduce new and non-trivial geometry, in particular leading to emergence of long sought after objects known as projective Ising non-Abelian anyons. Braiding of such anyons is a key ingredient of topological quantum computation. We suggest a simple and systematic approach to construct effective unitary protocols for braiding, manipulation and readout of non-Abelian anyons and preparation of their entangled states. We generalize the surface code to a more generic graph with vertices of degree 2, 3 and 4. Our approach is based on the mapping of the stabilizer code defined on such a graph onto a model of Majorana fermions charged with respect to two emergent gauge fields. One gauge field is akin to the physical magnetic field. The other one is responsible for emergence of the non-Abelian anyonic statistics and has a purely geometric origin. This field arises from assigning certain rules of orientation on the graph known as the Kasteleyn orientation in the statistical theory of dimer coverings. Each 3-degree vertex on the graph carries the flux of this "Kasteleyn" field and hosts a non-Abelian anyon. In our approach all the experimentally relevant operators are unambiguously fixed by locality, unitarity and gauge invariance. We illustrate the power of our method by making specific prescriptions for experiments verifying the non-Abelian statistics.

quant-ph↗

arXiv2020

Rescuing a black hole in the large-$q$ coupled SYK model

In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-$q$ theory with the bulk low energy effective theory. In particular, we study the special case of a ``rescued black hole'', which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS$_2$ vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-$q$ and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.

hep-th↗

arXiv2020

Size of bulk fermions in the SYK model

The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS$_2$ bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk $\text{SL}(2; \mathbb{R})$ generators.

hep-th↗

arXiv2018

Chaos and High Temperature Pure State Thermalization

Classical arguments for thermalization of isolated systems do not apply in a straightforward way to the quantum case. Recently, there has been interest in diagnostics of quantum chaos in many- body systems. In the classical case, chaos is a popular explanation for the legitimacy of the methods of statistical physics. In this work, we relate a previously proposed criteria of quantum chaos in the unitary time evolution operator to the entanglement entropy growth for a far-from-equilibrium initial pure state. By mapping the unitary time evolution operator to a doubled state, chaos can be characterized by suppression of mutual information between subsystems of the past and that of the future. We show that when this mutual information is small, a typical unentangled initial state will evolve to a highly entangled final state. Our result provides a more concrete connection between quantum chaos and thermalization in many-body systems.

cond-mat.stat-mech↗

arXiv2014

Topological Valley Currents in Gapped Dirac Materials

Gapped 2D Dirac materials, in which inversion symmetry is broken by a gap-opening perturbation, feature a unique valley transport regime. The system ground state hosts dissipationless persistent valley currents existing even when topologically protected edge modes are absent or when they are localized due to edge roughness. Topological valley currents in such materials are dominated by bulk currents produced by electronic states just beneath the gap rather than by edge modes. Dissipationless currents induced by an external bias are characterized by a quantized half-integer valley Hall conductivity. The under-gap currents dominate magnetization and the charge Hall effect in a light-induced valley-polarized state.

cond-mat.mes-hall↗