arXiv subjects

János K. Asbóth

Publications and source records attributed to János K. Asbóth.

14 recordsLinked to original sources

arXiv2025

The EU Quantum Flagship's Key Performance Indicators for Quantum Computing

As quantum processors continue to scale in size and complexity, the need for well-defined, reproducible, and technology-agnostic performance metrics becomes increasingly critical. Here we present a suite of scalable quantum computing benchmarks developed as key performance indicators (KPIs) within the EU Quantum Flagship. These proposed benchmarks are designed to assess holistic system performance rather than isolated components, and to remain applicable across both noisy intermediate-scale quantum (NISQ) devices and future fault-tolerant architectures. We introduce four core benchmarks addressing complementary aspects of quantum computing capability: large multi-qubit circuit execution via a Clifford Volume benchmark, scalable multipartite entanglement generation through GHZ-state preparation, a benchmark based on the application of Shor's period-finding subroutine to simple functions, and a protocol quantifying the benefit of quantum error correction using Bell states. Each benchmark is accompanied by clearly specified protocols, reporting standards, and scalable evaluation methods. Together, these KPIs provide a coherent framework for transparent and fair performance assessment across quantum hardware platforms and for tracking progress late-NISQ toward early fault-tolerant quantum computation.

quant-ph↗

arXiv2025

Optimal number of stabilizer measurement rounds in an idling surface code patch

Logical qubits can be protected against environmental noise by encoding them into a highly entangled state of many physical qubits and actively intervening in the dynamics with stabilizer measurements. In this work, we numerically optimize the rate of these interventions: the number of stabilizer measurement rounds for a logical qubit encoded in a surface code patch and idling for a given time. We model the environmental noise on the circuit level, including gate errors, readout errors, amplitude and phase damping. We find, qualitatively, that the optimal number of stabilizer measurement rounds is getting smaller for better qubits and getting larger for better gates or larger code sizes. We discuss the implications of our results to some of the leading architectures, superconducting qubits, and neutral atoms.

quant-ph↗

arXiv2024

Characterization of errors in a CNOT between surface code patches

As current experiments already realize small quantum circuits on error corrected qubits, it is important to fully understand the effect of physical errors on the logical error channels of these fault-tolerant circuits. Here, we investigate a lattice-surgery-based CNOT operation between two surface code patches under phenomenological error models. (i) For two-qubit logical Pauli measurements -- the elementary building block of the CNOT -- we optimize the number of stabilizer measurement rounds, usually taken equal to $d$, the size (code distance) of each patch. We find that the optimal number can be greater or smaller than $d$, depending on the rate of physical and readout errors, and the separation between the code patches. (ii) We fully characterize the two-qubit logical error channel of the lattice-surgery-based CNOT. We find a symmetry of the CNOT protocol, that results in a symmetry of the logical error channel. We also find that correlations between X and Z errors on the logical level are suppressed under minimum weight decoding.

quant-ph↗

arXiv2024

Coherent errors in stabilizer codes caused by quasistatic phase damping

Quantum error correction is a key challenge for the development of practical quantum computers, a direction in which significant experimental progress has been made in recent years. In solid-state qubits, one of the leading information loss mechanisms is dephasing, usually modelled by phase flip errors. Here, we introduce quasistatic phase damping, a more subtle error model which describes the effect of Larmor frequency fluctuations due to 1/f noise. We show how this model is different from a simple phase flip error model, in terms of multi-cycle error correction. Considering the surface code, we provide numerical evidence for an error threshold, in the presence of quasistatic phase damping and readout errors. We discuss the implications of our results for spin qubits and superconducting qubits.

quant-ph↗

arXiv2023

Floquet-Anderson localization in the Thouless pump and how to avoid it

We investigate numerically how onsite disorder affects conduction in the periodically driven Rice-Mele model, a prototypical realization of the Thouless pump. Although the pump is robust against disorder in the fully adiabatic limit, much less is known about the case of finite period time $T$, which is relevant also in light of recent experimental realizations. We find that at any fixed period time and nonzero disorder, increasing the system size $L\to\infty$ always leads to a breakdown of the pump, indicating Anderson localization of the Floquet states. Our numerics indicate, however, that in a properly defined thermodynamic limit, where $L/T^θ$ is kept constant, Anderson localization can be avoided, and the charge pumped per cycle has a well-defined value -- as long as the disorder is not too strong. The critical exponent $θ$ is not universal, rather, its value depends on the disorder strength. Our findings are relevant for practical, experimental realizations of the Thouless pump, for studies investigating the nature of its current-carrying Floquet eigenstates, as well as the mechanism of the full breakdown of the pump, expected if the disorder exceeds a critical value.

cond-mat.dis-nn↗

arXiv2023

Coherent errors and readout errors in the surface code

We consider the combined effect of readout errors and coherent errors, i.e., deterministic phase rotations, on the surface code. We use a recently developed numerical approach, via a mapping of the physical qubits to Majorana fermions. We show how to use this approach in the presence of readout errors, treated on the phenomenological level: perfect projective measurements with potentially incorrectly recorded outcomes, and multiple repeated measurement rounds. We find a threshold for this combination of errors, with an error rate close to the threshold of the corresponding incoherent error channel (random Pauli-Z and readout errors). The value of the threshold error rate, using the worst case fidelity as the measure of logical errors, is 2.6%. Below the threshold, scaling up the code leads to the rapid loss of coherence in the logical-level errors, but error rates that are greater than those of the corresponding incoherent error channel. We also vary the coherent and readout error rates independently, and find that the surface code is more sensitive to coherent errors than to readout errors. Our work extends the recent results on coherent errors with perfect readout to the experimentally more realistic situation where readout errors also occur.

quant-ph↗

arXiv2023

Multiparticle quantum walk: a dynamical probe of topological many-body excitations

Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting $N$ particles with multiple flavors in the interacting SU$(N)$ Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the $N$-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes.

quant-ph↗

arXiv2021

Two particles on a chain with disordered interaction: Localization and dissociation of bound states and mapping to chaotic billiards

We consider two particles hopping on a chain with a contact interaction between them. At strong interaction, there is a molecular bound state separated by a direct gap from a continuous band of atomic states. Introducing weak disorder in the interaction, the molecular state becomes Anderson localized. At stronger disorder, part of the molecular band delocalizes and dissociates due to its hybridization to the atomic band. We characterize these different regimes by computing the density of states, the inverse participation ratio, the level-spacing statistics and the survival probability of an initially localized state. The atomic band is best described as that of a rough billiard for a single particle on a square lattice that shows signatures of quantum chaos. In addition to typical "chaotic states", we find states that are localized along only one direction. These "separatrix states" are more localized than chaotic states, and similar in this respect to scarred states, but their existence is due to the separatrix iso-energy line in the interaction-free dispersion relation, rather than to unstable periodic orbits.

cond-mat.dis-nn↗

arXiv2021

Topologically protected, correlated end spin formation in carbon nanotubes

For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogues of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, as well as the size of the end spins: for $S=1/2$ end spins their interaction is antiferromagnetic, while for $S>1/2$ it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.

cond-mat.str-el↗

arXiv2021

Topological delocalization in the completely disordered two-dimensional quantum walk

We investigate numerically and theoretically the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states. Spatial disorder can lead to Anderson localization, inhibiting the spread of quantum walks, putting them at a disadvantage against their diffusively spreading classical counterparts. We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization but to a diffusive spread instead. This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases. We base this explanation on the relationship of this general quantum walk to a simpler case more studied in the literature and for which disorder-induced delocalization of a topological origin has been observed. We review topological delocalization for the simpler quantum walk, using time evolution of the wave functions and level spacing statistics. We apply scattering theory to two-dimensional quantum walks and thus calculate the topological invariants of disordered quantum walks, substantiating the topological interpretation of the delocalization and finding signatures of the delocalization in the finite-size scaling of transmission. We show criticality of the Haar random quantum walk by calculating the critical exponent $η$ in three different ways and find $η$ $\approx$ 0.52 as in the integer quantum Hall effect. Our results showcase how theoretical ideas and numerical tools from solid-state physics can help us understand spatially random quantum walks.

quant-ph↗

arXiv2019

Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model

Topological properties of quantum systems could provide protection of information against environmental noise, and thereby drastically advance their potential in quantum information processing. Most proposals for topologically protected quantum gates are based on many-body systems, e.g., fractional quantum Hall states, exotic superconductors, or ensembles of interacting spins, bearing an inherent conceptual complexity. Here, we propose and study a topologically protected quantum gate, based on a one-dimensional single-particle tight-binding model, known as the Su-Schrieffer-Heeger chain. The proposed $Y$ gate acts in the two-dimensional zero-energy subspace of a Y junction assembled from three chains, and is based on the spatial exchange of the defects supporting the zero-energy modes. With numerical simulations, we demonstrate that the gate is robust against hopping disorder but is corrupted by disorder in the on-site energy. Then we show that this robustness is topological protection, and that it arises as a joint consequence of chiral symmetry, time-reversal symmetry and the spatial separation of the zero-energy modes bound to the defects. This setup will most likely not lead to a practical quantum computer, nevertheless it does provide valuable insight to aspects of topological quantum computing as an elementary minimal model. Since this model is non-interacting and non-superconducting, its dynamics can be studied experimentally, e.g., using coupled optical waveguides.

cond-mat.mes-hall↗

arXiv2019

Creating anomalous Floquet Chern insulators with magnetic quantum walks

We propose a realistic scheme to construct anomalous Floquet Chern topological insulators using spin-1/2 particles carrying out a discrete-time quantum walk in a two-dimensional lattice. By Floquet engineering the quantum-walk protocol, an Aharonov-Bohm geometric phase is imprinted onto closed-loop paths in the lattice, thus realizing an abelian gauge field---the analog of a magnetic flux threading a two-dimensional electron gas. We show that in the strong field regime, when the flux per plaquette is a sizable fraction of the flux quantum, magnetic quantum walks give rise to nearly flat energy bands featuring nonvanishing Chern numbers. Furthermore, we find that because of the nonperturbative nature of the periodic driving, a second topological number---the so-called RLBL invariant---is necessary to fully characterize the anomalous Floquet topological phases of magnetic quantum walks and to compute the number of topologically protected edge modes expected at the boundaries between different phases. In the second part of this article, we discuss an implementation of this scheme using neutral atoms in two-dimensional spin-dependent optical lattices, which enables the generation of arbitrary magnetic-field landscapes, including those with sharp boundaries. The robust atom transport, which is observed along boundaries separating regions of different field strength, reveals the topological character of the Floquet Chern bands.

quant-ph↗

arXiv2016

Topological bound states of a quantum walk with cold atoms

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically non-trivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

cond-mat.quant-gas↗

arXiv2015

A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions

This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological band insulators in one and two dimensions. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. We use noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the model is introduced first and then its properties are discussed and subsequently generalized. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.

cond-mat.mes-hall↗