arXiv subjects

András Pályi

Publications and source records attributed to András Pályi.

At least 19 recordsLinked to original sources

arXiv2026

Readout sweet spots for spin qubits with strong spin-orbit interaction

Qubit readout schemes often deviate from ideal projective measurements, introducing critical issues that limit quantum computing performance. In this work, we model charge-sensing-based readout for semiconductor spin qubits in double quantum dots, and identify key error mechanisms caused by the back-action of the charge sensor. We quantify how the charge noise of the sensor, residual tunneling, and $g$-tensor modulation degrade readout fidelity, induce a mixed post-measurement state, and cause leakage from the computational subspace. For state-of-the-art systems with strong spin-orbit interaction and electrically tunable $g$-tensors, we identify a readout sweet spot, that is, a special device configuration where readout is closest to projective. Our framework provides a foundation for developing effective readout error mitigation strategies, with broad applications for optimizing readout performance for a variety of charge-sensing techniques, advancing quantum protocols, and improving adaptive circuits for error correction.

quant-ph↗

arXiv2026

Four-state discrimination for a pair of spin qubits via gate reflectometry

Single-electron spin qubits defined in quantum dots are used as building blocks of a semiconductor-based quantum computer. Readout in a scaled-up version of such a quantum computer is expected to rely on the Pauli Spin Blockade (PSB) mechanism. A desired functionality of PSB readout is that it reveals two bits of information on the two spin qubits that are involved in the process, such that the four computational basis states can be discriminated. In this work, we propose and quantitatively analyze an experimental procedure, based on gate reflectometry, which enables this four-state discrimination in a single measurement. We provide an intuitive recipe to maximize the contrast between the quantum capacitances of the four basis states. Focusing on silicon double quantum dots equipped with a micromagnet, we quantify how amplifier noise and phonon-mediated relaxation influence readout fidelity. Our results highlight a realistic opportunity to mitigate the overhead of readout ancilla qubits in a spin-based quantum computer.

cond-mat.mes-hall↗

arXiv2026

The geometry of the Hermitian matrix space and the Schrieffer--Wolff transformation

In quantum mechanics, the Schrieffer--Wolff (SW) transformation (also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. We present a geometric interpretation of the SW transformation: We prove that it induces a local coordinate chart in the space of Hermitian matrices near a $k$-fold degeneracy submanifold. Inspired by this result, we establish a `distance theorem': we show that the standard deviation of $k$ neighboring eigenvalues of a Hamiltonian equals the distance of this Hamiltonian from the corresponding $k$-fold degeneracy submanifold, divided by $\sqrt{k}$. Furthermore, we investigate one-parameter perturbations of a degenerate Hamiltonian, and prove that the standard deviation and the pairwise differences of the eigenvalues lead to the same order of splitting of the energy eigenvalues, which in turn is the same as the order of distancing from the degeneracy submanifold. As applications, we prove the `protection' of Weyl points using the transversality theorem, and infer geometrical properties of certain degeneracy submanifolds based on results from quantum error correction and topological order.

quant-ph↗

arXiv2026

RING: Rabi oscillations induced by nonresonant geometric drive

Coherent control of two-level quantum systems is typically achieved using resonant driving fields, forming the basis for qubit operations. Here, we report a mechanism for inducing complete Rabi oscillations in monochromatically driven two-level quantum systems, when the drive frequency is much larger than the Larmor frequency of the qubit. This effect$\unicode{x2015}$Rabi oscillations induced by nonresonant geometric drive (RING)$\unicode{x2015}$requires that the control field is elliptical, enclosing a nonzero area per cycle. We illustrate the effect with numerical simulations, and provide an analytical understanding via a simple effective Hamiltonian obtained from Floquet theory and perturbation theory. We show that RING enables coherent oscillations without relying on resonant energy exchange, allows for high-pass noise filtering, provides access to non-Abelian phases in finite magnetic fields. We detail a realization in electrically driven spin-orbit qubits and argue that the RING mechanism enables amplification of the Rabi frequency using the same gate voltage amplitudes at higher drive frequencies. Our results broaden the landscape of quantum control techniques, by highlighting a pathway to achieving coherent oscillations under off-resonant driving conditions.

cond-mat.mes-hall↗

arXiv2026

Acoustic phonons, spin-phonon coupling and spin relaxation via the lattice reorientation mechanism in hexagonal germanium nanowires

Spin relaxation via electron-phonon interaction is an important decoherence mechanism for spin qubits. In this work, we study spin relaxation in hexagonal (2H) germanium, a novel direct-gap semiconductor showing great potential to combine highly coherent spin qubits with optical functionality. Focusing on electrostatically defined quantum dots in hexagonal germanium nanowires, we (i) identify geometries where spin qubit experiments are feasible, (ii) compute the nanowire phonon modes, and (iii) describe spin relaxation of hole spin qubits due to phonon-induced lattice reorientation, a direct spin-phonon coupling mechanism that is absent in cubic semiconductors typically used for spin qubits (GaAs, cubic Si, cubic Ge). We obtain the spin relaxation time as a function of nanowire cross section, quantum dot confinement length, and magnetic field. For realistic parameters, we find relaxation times above 10 ms, and reveal that the magnetic field direction maximizing the relaxation time depends on the qubit Larmor frequency. Our results facilitate the design of nanowire quantum dot experiments with long qubit relaxation times.

cond-mat.mes-hall↗

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

Birth Quota of Non-Generic Degeneracy Points

Weyl points are generic and stable features in the energy spectrum of Hamiltonians that depend on a three-dimensional parameter space. Non-generic isolated two-fold degeneracy points, such as multi-Weyl points, split into Weyl points upon a generic perturbation that removes the fine-tuning or protecting symmetry. The number of the resulting Weyl points is at least $|Q|$, where $Q$ is the topological charge associated to the non-generic degeneracy point. Here, we show that such a non-generic degeneracy point also has a birth quota, i.e., a maximum number of Weyl points that can be born from it upon any perturbation. The birth quota is a local multiplicity associated to the non-generic degeneracy point, an invariant of map germs known from singularity theory. This holds not only for the case of a three-dimensional parameter space with a Hermitian Hamiltonian, but also for the case of a two-dimensional parameter space with a chiral-symmetric Hamiltonian. We illustrate the power of this result for band structures of two- and three-dimensional crystals. Our work establishes a strong and powerful connection between singularity theory and topological band structures, and more broadly, parameter-dependent quantum systems.

cond-mat.mes-hall↗

arXiv2025

Multifold degeneracy points of quantum systems and singularities of matrix varieties

Parameter-dependent quantum systems often exhibit energy degeneracy points, whose comprehensive description naturally lead to the application of methods from singularity theory. A prime example is an electronic band structure where two energy levels coincide in a point of momentum space. It may happen, and this case is the focus of our work, that three or more levels coincide at a parameter point, called multifold degeneracy. Upon a generic perturbation, such a multifold degeneracy point is dissolved into a set of Weyl points, that is, generic two-fold degeneracy points. In this work, we provide an upper bound to the number of Weyl points born from the multifold degeneracy point. To compute this upper bound, we describe the geometric degeneracy variety in the space of complex matrices. We compute its multiplicity at certain singular points corresponding to a multifold degeneracy, and the multiplicity of holomorphic map germs with respect to this variety. Our work covers physics and mathematics aspects in detail, and attempts to bridge the two disciplines and communities. For self-containedness, we survey examples of multi-fold degeneracies in quantum systems and condensed-matter physics, as well as the established tools of local algebraic geometry that we use to identify the upper bound.

math-ph↗

arXiv2025

Multi-shot readout error benchmark of the nitrogen-vacancy center's electronic qubit

The ground-state electronic spin of a negatively charged nitrogen-vacancy center in diamond can be used for room-temperature experiments showing coherent qubit functionality. At room temperature, photoluminescence-based qubit readout has a low single-shot fidelity; however, the populations of the qubit's two basis states can be inferred using multi-shot readout. In this work, we calculate the dependence of the error of a multi-shot inference method on various parameters of the readout process. This multi-shot readout error scales as $Δ/\sqrt{N}$, with $N$ being the number of shots, suggesting to use the coefficient $Δ$ as a simple multi-shot readout error benchmark. Our calculation takes into account background photons, photon loss, and initialization error. Our model enables the identification of the readout error budget, i.e., the role various imperfections play in setting the readout error. Our results enable experimentalists and engineers to focus their efforts on those hardware improvements that yield the highest performance gain for multi-shot readout.

cond-mat.mes-hall↗

arXiv2025

Protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a quantum-dot loop

A quantum system constrained to a degenerate energy eigenspace can undergo a nontrival time evolution upon adiabatic driving, described by a non-Abelian Berry phase. This type of dynamics may provide logical gates in quantum computing that are robust against timing errors. A strong candidate to realize such holonomic quantum gates is an electron or hole spin qubit trapped in a spin-orbit-coupled semiconductor, whose twofold Kramers degeneracy is protected by time-reversal symmetry. Here, we propose and quantitatively analyze protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a loop of quantum dots. One of these protocols allows to characterize the local internal Zeeman field directions in the dots of the loop. We expect a near-term realisation of these protocols, as all key elements have been already demonstrated in spin-qubit experiments. These experiments would be important to assess the potential of holonomic quantum gates for spin-based quantum information processing.

cond-mat.mes-hall↗

arXiv2025

Limitations of the $g$-tensor formalism of semiconductor spin qubits

The $g$-tensor formalism is a powerful method for describing the electrical driving of semiconductor spin qubits. However, up to now, this technique has only been applied to the simplest qubit dynamics, resonant monochromatic driving by a single gate. Here we study the description of (i) monochromatic driving using two driving gates and bichromatic driving via (ii) one or (iii) two gates. Assuming a general Hamiltonian with qubit states well separated from excited orbital states, we find that when (i) two driving gates are used for monochromatic driving or (ii) a single one for bichromatic, the $g$-tensor formalism successfully captures the leading-order dynamics. We express the Rabi frequency and the Bloch-Siegert shift using the $g$-tensor and its first and second derivatives with respect to the gate voltage. However, when (iii) bichromatic driving is realized using two distinct driving gates, we see a breakdown of $g$-tensor formalism: the Rabi frequency cannot be expressed using the $g$-tensor and its derivatives. We find that beyond the $g$-tensor and its derivatives, three additional parameters are needed to capture the dynamics. We demonstrate our general results by assuming an electron (hole) confined in a circular quantum dot, subjected to Rashba spin-orbit interaction.

cond-mat.mes-hall↗

arXiv2025

Bichromatic Rabi Control of Semiconductor Qubits

Electrically driven spin resonance is a powerful technique for controlling semiconductor spin qubits. However, it faces challenges in qubit addressability and off-resonance driving in larger systems. We demonstrate coherent bichromatic Rabi control of quantum dot hole spin qubits, offering a spatially selective approach for large qubit arrays. By applying simultaneous microwave bursts to different gate electrodes, we observe multichromatic resonance lines and resonance anticrossings that are caused by the ac Stark shift. Our theoretical framework aligns with experimental data, highlighting interdot motion as the dominant mechanism for bichromatic driving.

cond-mat.mes-hall↗

arXiv2024

Compiling the surface code to crossbar spin qubit architectures

Spin qubits in quantum dots provide a promising platform for realizing large-scale quantum processors since they have a small characteristic size of a few tens of nanometers. One difficulty of controlling e.g., a few thousand qubits on a single chip is the large number of control lines. The crossbar control architecture has been proposed to reduce the number of control lines exploiting shared control among the qubits. Here, we compile the surface code cycle to a pulse sequence that can be executed in the crossbar architecture. We decompose the quantum circuits of the stabilizer measurements in terms of native gates of the spin-qubit architecture. We provide a routing and scheduling protocol, and construct a gate voltage pulse sequence for the stabilizer measurement cycle. During this protocol, coherent phase errors can occur on idle qubits, due to the operational constraints of the crossbar architecture. We characterize these crosstalk errors during the stabilizer measurement cycle, and identify an experimentally relevant parameter regime where the crosstalk errors are below the surface code threshold. Our results provide design guidelines for near-term qubit experiments with crossbar architectures.

cond-mat.mes-hall↗

arXiv2024

Stability of Weyl node merging processes under symmetry constraints

Changes in the number of Weyl nodes in Weyl semimetals occur through merging processes, usually involving a pair of oppositely charged nodes. More complicated processes involving multiple Weyl nodes are also possible, but they typically require fine tuning and are thus less stable. In this work, we study how symmetries affect the allowed merging processes and their stability, focusing on the combination of a two-fold rotation and time-reversal ($C_2\mathcal{T}$) symmetry. We find that, counter-intuitively, processes involving a merging of three nodes are more generic than processes involving only two nodes. Our work suggests that multi-Weyl-merging may be observed in a large variety of quantum materials, and we discuss SrSi$_2$ and bilayer graphene as potential candidates

cond-mat.mes-hall↗

arXiv2024

Classification and magic magnetic-field directions for spin-orbit-coupled double quantum dots

The spin of a single electron confined in a semiconductor quantum dot is a natural qubit candidate. Fundamental building blocks of spin-based quantum computing have been demonstrated in double quantum dots with significant spin-orbit coupling. Here, we show that spin-orbit-coupled double quantum dots can be categorised in six classes, according to a partitioning of the multi-dimensional space of their $g$-tensors. The class determines physical characteristics of the double dot, i.e., features in transport, spectroscopy and coherence measurements, as well as qubit control, shuttling, and readout experiments. In particular, we predict that the spin physics is highly simplified due to pseudospin conservation, whenever the external magnetic field is pointing to special directions (`magic directions'), where the number of special directions is determined by the class. We also analyze the existence and relevance of magic loops in the space of magnetic-field directions, corresponding to equal local Zeeman splittings. These results present an important step toward precise interpretation and efficient design of spin-based quantum computing experiments in materials with strong spin-orbit coupling.

cond-mat.mes-hall↗

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↗

arXiv2024

Resource analysis for quantum-aided Byzantine agreement with the four-qubit singlet state

In distributed computing, a Byzantine fault is a condition where a component behaves inconsistently, showing different symptoms to different components of the system. Consensus among the correct components can be reached by appropriately crafted communication protocols even in the presence of byzantine faults. Quantum-aided protocols built upon distributed entangled quantum states are worth considering, as they are more resilient than traditional ones. Based on earlier ideas, here we establish a parameter-dependent family of quantum-aided weak broadcast protocols. We compute upper bounds on the failure probability of the protocol, and define and illustrate a procedure that minimizes the quantum resource requirements. Following earlier work demonstrating the suitability of noisy intermediate scale quantum (NISQ) devices for the study of quantum networks, we experimentally create our resource quantum state on publicly available quantum computers. Our work highlights important engineering aspects of the future deployment of quantum communication protocols with multi-qubit entangled states.

quant-ph↗

arXiv2024

Coupling a single spin to high-frequency motion

Coupling a single spin to high-frequency mechanical motion is a fundamental bottleneck of applications such as quantum sensing, intermediate and long-distance spin-spin coupling, and classical and quantum information processing. Previous experiments have only shown single spin coupling to low-frequency mechanical resonators, such as diamond cantilevers. High-frequency mechanical resonators, having the ability to access the quantum regime, open a range of possibilities when coupled to single spins, including readout and storage of quantum states. Here we report the first experimental demonstration of spin-mechanical coupling to a high-frequency resonator. We achieve this all-electrically on a fully suspended carbon nanotube device. A new mechanism gives rise to this coupling, which stems from spin-orbit coupling, and it is not mediated by strain. We observe both resonant and off-resonant coupling as a shift and broadening of the electric dipole spin resonance (EDSR), respectively. We develop a complete theoretical model taking into account the tensor form of the coupling and non-linearity in the motion. Our results propel spin-mechanical platforms to an uncharted regime. The interaction we reveal provides the full toolbox for promising applications ranging from the demonstration of macroscopic superpositions, to the operation of fully quantum engines, to quantum simulators.

cond-mat.mes-hall↗