arXiv subjects

Eyal Cornfeld

Publications and source records attributed to Eyal Cornfeld.

16 recordsLinked to original sources

arXiv2025

Efficient Quantum Control via Automatic Control Skips

Control of quantum operations is a crucial yet expensive construct for quantum computation. Efficient implementations of controlled operations often avoid applying control to certain subcircuits, which can significantly reduce the number of gates and overall circuit depth. However, these methods are specialized and circuits frequently need to be implemented manually. This paper presents a generic method for finding "skippable" patterns without having to tailor implementations for each algorithm. We prove that finding the optimal operations to be skipped is generally NP-hard. Nevertheless, sub-optimal, polynomial approximation algorithms that find skippable subcircuits can lead to over $50\%$ improvement in circuit metrics for real-world applications.

quant-ph↗

arXiv2025

Qmod: Expressive High-Level Quantum Modeling

Quantum computing hardware is advancing at a rapid pace, yet the lack of high-level programming abstractions remains a serious bottleneck in the development of new applications. Widely used frameworks still rely on gate-level circuit descriptions, causing the algorithm's functional intent to become lost in low-level implementation details, and hindering flexibility and reuse. While various high-level quantum programming languages have emerged in recent years - offering a significant step toward higher abstraction - many still lack support for classical-like expression syntax, and native constructs for useful quantum algorithmic idioms. This paper presents Qmod, a high-level quantum programming language designed to capture algorithmic intent in natural terms while delegating implementation decisions to automation. Qmod introduces quantum numeric variables and expressions, including digital fixed-point arithmetic tuned for compact representations and optimal resource usage. Beyond digital encoding, Qmod also supports non-digital expression modes - phase and amplitude encoding - frequently exploited by quantum algorithms to achieve computational advantages. We describe the language's constructs, demonstrate practical usage examples, and outline future work on evaluating Qmod across a broader set of use cases.

quant-ph↗

arXiv2025

Design and synthesis of scalable quantum programs

We present a scalable, robust approach to creating quantum programs of arbitrary size and complexity. The approach is based on the true abstraction of the problem. The quantum program is expressed in terms of a high-level model together with constraints and objectives on the final program. Advanced synthesis algorithms transform the model into a low-level quantum program that meets the user's specification and is directed at a stipulated hardware. This separation of description from implementation is essential for scale. The technology adapts electronic design automation methods to quantum computing, finding feasible implementations in a virtually unlimited functional space. The results show clear superiority over the compilation and transpilation methods used today. We expect that this technological approach will take over and prevail as quantum software become more demanding, complex, and essential.

quant-ph↗

arXiv2022

Punctured-Chern topological invariants for semi-metallic bandstructures

Topological insulator-based methods underpin the topological classification of gapped bands, including those surrounding semi-metallic nodal defects. However, multiple bands with gap-closing points can also possess non-trivial topology. We construct a general wavefunction-based ``punctured-Chern" invariant to capture such topology. To show its general applicability, we analyze two systems with disparate gapless topology: 1) a recent two-dimensional fragile topological model to capture the various band-topological transitions and 2) a three-dimensional model with a triple-point nodal defect to characterize its semi-metallic topology with \emph{half-integers} that govern physical observables such as anomalous transport. This invariant also gives the classification for Nexus triple-points ($\mathbb{Z}\times\mathbb{Z}$) with certain symmetry restrictions, which is re-confirmed by abstract algebra.

cond-mat.mes-hall↗

arXiv2021

Spin-polarized superconductivity: order parameter topology, current dissipation, and multiple-period Josephson effect

We discuss transport properties of fully spin-polarized triplet superconductors, where only electrons of one spin component (along a certain axis) are paired. Due to the structure of the order parameter space, wherein phase and spin rotations are intertwined, a configuration where the superconducting phase winds by $4π$ in space is topologically equivalent to a configuration with no phase winding. This opens the possibility of supercurrent relaxation by a smooth deformation of the order parameter, where the order parameter remains non-zero at any point in space throughout the entire process. During the process, a spin texture is formed. We discuss the conditions for such processes to occur and their physical consequences. In particular, we show that when a voltage is applied, they lead to an unusual alternating-current Josephson effect whose period is an integer multiple of the usual Josephson period. These conclusions are substantiated in a simple time-dependent Ginzburg-Landau model for the dynamics of the order parameter. One of the potential applications of our analysis is for moiré systems, such as twisted bilayer and double bilayer graphene, where superconductivity is found in the vicinity of ferromagnetism.

cond-mat.supr-con↗

arXiv2021

Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors

The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a complete classification of weakly-interacting electrons' non-crystalline topological phases for all symmetry classes. Over recent years, a plethora of topological phenomena with diverse surface states has been discovered in crystalline materials. In this paper, we obtain an exhaustive classification of topologically distinct groundstates as well as topological phases with anomalous surface states of crystalline topological insulators and superconductors for key space-groups, layer-groups, and rod-groups. This is done in a unified manner for the full tenfold-way of Altland-Zirnbauer non-spatial symmetry classes. We establish a comprehensive paradigm that harnesses the modern mathematical framework of equivariant spectra; it allows us to obtain results applicable to generic topological classification problems. In particular, this paradigm provides efficient computational tools that enable an inherently unified treatment of the full tenfold-way.

cond-mat.mes-hall↗

arXiv2020

Signatures of Topological Superconductivity and Parafermion Zero Modes in Fractional Quantum Hall Edges

Parafermion zero modes are exotic emergent excitations that can be considered as $\mathbb{Z}_n$ generalizations of Majorana fermions. Present in fractional quantum Hall-superconductor hybrid systems, among others, they can serve as potential building blocks in fault-tolerant topological quantum computing. We propose a system that reveals noise and current signatures indicative of parafermion zero modes. The system is comprised of the edge excitations ("quasi-particles") of a fractional quantum Hall bulk at filling factor $ν= 1/m$ (for odd integer $m$) incident upon the interface of a superconductor, and in the presence of back-scattering. Using perturbative calculations, we derive the current that propagates away from this structure, and its corresponding noise correlation function. Renormalization group analysis reveals a flow from a UV fixed point of perfect normal reflection towards an IR fixed point of perfect Andreev reflection. The power law dependence of the differential conductance near these fixed points is determined by $m$. We find that behavior at these two limits is physically distinguishable; whereas near perfect Andreev reflection, the system deviates from equilibrium via tunneling of Cooper pairs between the two edges, near perfect Normal reflection this is done via tunneling of a single quasi-particle to an emergent parafermion zero mode at the superconductor interface. These results are fortified by an exact solution.

cond-mat.mes-hall↗

arXiv2019

Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure

The recent direct experimental measurement of quantum entanglement paves the way towards a better understanding of many-body quantum systems and their correlations. Nevertheless, the experimental and theoretical advances had so far been predominantly limited to bosonic systems. Here, we study fermionic systems. Using experimental setups where multiple copies of the same state are prepared, arbitrary order Renyi entanglement entropies and entanglement negativities can be extracted by utilizing spatially-uniform beam splitters and on-site occupation measurement. As an example, we simulate the use of our protocols for measuring the entanglement growth following a local quench. We also illustrate how our paradigm could be used for experimental quantum simulations of fermions on manifolds with nontrivial spin structures.

cond-mat.stat-mech↗

arXiv2019

Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons

We study the entanglement spectrum of topological systems hosting non-Abelian anyons. Akin to energy levels of a Hamiltonian, the entanglement spectrum is composed of symmetry multiplets. We find that the ratio between different eigenvalues within one multiplet is universal and is determined by the anyonic quantum dimensions. This result is a consequence of the conservation of the total topological charge. For systems with non-Abelian topological order, this generalizes known degeneracies of the entanglement spectrum, which are hallmarks of topological states. Experimental detection of these entanglement spectrum signatures may become possible in Majorana wires using multicopy schemes, allowing the measurement of quantum entanglement and its symmetry resolution.

cond-mat.str-el↗

arXiv2019

Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries

Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery of higher-order hinge and corner states. However, current classification schemes of such phases are either implicit or limited in scope. We present a new scheme for the explicit classification of crystalline topological insulators and superconductors. These phases are protected by crystallographic point group symmetries and are characterized by bulk topological invariants. The classification paradigm generalizes the Clifford algebra extension process of each Altland-Zirnbauer symmetry class and utilizes algebras which incorporate the point group symmetry. Explicit results for all point group symmetries of three-dimensional crystals are presented as well as for all symmorphic layer groups of two-dimensional crystals. We discuss future extensions for treatment of magnetic crystals and defected or higher-dimensional systems as well as weak and fragile invariants.

cond-mat.mes-hall↗

arXiv2018

Imbalance Entanglement: Symmetry Decomposition of Negativity

In the presence of symmetry, entanglement measures of quantum many-body states can be decomposed into contributions arising from distinct symmetry sectors. Here we investigate the decomposability of negativity, a measure of entanglement between two parts of a generally open system in a mixed state. While the entanglement entropy of a subsystem within a closed system can be resolved according to its total preserved charge, we find that negativity of two subsystems may be decomposed into contributions associated with their charge imbalance. We show that this charge-imbalance decomposition of the negativity may be measured by employing existing techniques based on creation and manipulation of many-body twin or triple states in cold atomic setups. Next, using a geometrical construction in terms of an Aharonov-Bohm-like flux inserted in a Riemann geometry, we compute this decomposed negativity in critical one-dimensional systems described by conformal field theory. We show that it shares the same distribution as the charge-imbalance between the two subsystems. We numerically confirm our field theory results via an exact calculations for non-interacting particles based on a double-gaussian representation of the partially transposed density matrix.

cond-mat.stat-mech↗

arXiv2017

Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class

The entanglement entropy in one dimensional critical systems with boundaries has been associated with the noninteger ground state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization group flow, as predicted by the g-theorem. Here, using conformal field theory methods, we exactly calculate the entanglement entropy in the boundary Ising universality class. Our expression can be separated into the well known bulk term and a boundary entanglement term, displaying a universal flow between two boundary conditions, in accordance with the g-theorem. These results are obtained within the replica trick approach, where we show that the associated twist field, a central object generating the geometry of an $n$-sheeted Riemann surface, can be bosonized, giving simple analytic access to multiple quantities of interest. We argue that our result applies to other models falling into the same universality class. This includes the vicinity of the quantum critical point of the two-channel Kondo model, allowing to track in real space the presence of a region containing one half of a qubit with entropy $\frac{1}{2} \log (2)$, associated with a free local Majorana fermion.

cond-mat.stat-mech↗

arXiv2017

Laughlin-like states in bosonic and fermionic atomic synthetic ladders

The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to experimentally address this interplay in quasi-one-dimensional systems. A fundamental question is whether these setups can give access to pristine two-dimensional phenomena, such as the fractional quantum Hall effect, and how. We show that unambiguous signatures of bosonic and fermionic Laughlin-like states can be observed and characterized in synthetic ladders. We theoretically diagnose these Laughlin-like states focusing on the chiral current flowing in the ladder, on the central charge of the low-energy theory, and on the properties of the entanglement entropy. Remarkably, Laughlin-like states are separated from conventional liquids by Lifschitz-type transitions, characterized by sharp discontinuities in the current profiles, which we address using extensive simulations based on matrix-product states. Our work provides a qualitative and quantitative guideline towards the observability and understanding of strongly-correlated states of matter in synthetic ladders. In particular, we unveil how state-of-the-art experimental settings constitute an ideal starting point to progressively tackle two-dimensional strongly interacting systems from a ladder viewpoint, opening a new perspective for the observation of non-Abelian states of matter.

cond-mat.quant-gas↗

arXiv2016

Topological fractional pumping with alkaline-earth(-like) ultracold atoms

Alkaline-earth(-like) ultracold atoms, trapped in optical lattices and in the presence of an external gauge field, can stabilise Mott insulating phases characterised by density and magnetic order. We show that this property can be used to realise a topological fractional pump. Our analysis is based on a many-body adiabatic expansion and on time-dependent matrix-product-states numerical simulations. We characterise the pumping protocol by including both finite-size and non-adiabatic corrections. For a specific form of atom-atom interaction, we present an exactly-solvable model of a fractional pump. Finally, the numerical simulations allow us to thoroughly study a realistic setup amenable of an experimental realisation.

cond-mat.quant-gas↗

arXiv2015

Chiral currents in one-dimensional fractional quantum Hall states

We study bosonic and fermionic quantum two-leg ladders with orbital magnetic flux. In such systems, the ratio, $ν$, of particle density to magnetic flux shapes the phase-space, as in quantum Hall effects. In fermionic (bosonic) ladders, when $ν$ equals one over an odd (even) integer, Laughlin fractional quantum Hall (FQH) states are stabilized for sufficiently long ranged repulsive interactions. As a signature of these fractional states, we find a unique dependence of the chiral currents on particle density and on magnetic flux. This dependence is characterized by the fractional filling factor $ν$, and forms a stringent test for the realization of FQH states in ladders, using either numerical simulations or future ultracold-atom experiments. The two-leg model is equivalent to a single spinful chain with spin-orbit interactions and a Zeeman magnetic field, and results can thus be directly borrowed from one model to the other.

cond-mat.quant-gas↗

arXiv2014

Shot-Noise in Fractional Wires: a Universal Fano-Factor Different than the Tunneling Charge

We consider partially gapped one dimensional (1D) conductors connected to normal leads, as realized in fractional helical wires. At certain electron densities, some distinct charge mode develops a gap due to electron interactions, leading to a fractional conductance. For this state we study the current noise caused by tunneling events inside the wire. We find that the noise's Fano-factor is different from the tunneling charge. This fact arises from charge scattering at the wire-leads interfaces. The resulting noise is, however, universal - it depends only on the identification of the gapped mode, and is insensitive to additional interactions in the wire. We further show that the tunneling charge can be deduced from the finite frequency noise, and yet is interaction dependent due to screening effects.

cond-mat.mes-hall↗