arXiv subjects

Guido Burkard

Publications and source records attributed to Guido Burkard.

At least 37 records · Page 2Linked to original sources

arXiv2025

Effective 2D Envelope Function Theory for Silicon Quantum Dots

We present a rigorous method to reduce the three-dimensional (3D) description of a quantum dot in silicon to an effective two-dimensional (2D) envelope function theory for electron spin qubits. By systematically integrating out the strongly confined vertical dimension using a Born-Oppenheimer-inspired ansatz at the envelope-function level, we derive an effective in-plane potential that faithfully captures the essential electrostatics of the full 3D system. Considering the lowest two eigenstates of the out-of-plane direction, this reduction leads to the natural and explicit emergence of the valley degree of freedom within a 2D formalism, which is derived here from first principles. We validate the accuracy of the method through comparisons with full 3D simulations and demonstrate its superiority over naive 2D slicing, particularly in the presence of interface roughness. Crucially, the reduction in dimensionality leads to substantial computational savings, making our approach particularly well suited for simulating two-electron systems, e.g., for the extraction of parameters such as the exchange coupling. Beyond its practical utility, the rigorous 2D envelope function theory that is introduced in this study incorporates valley physics in a physically grounded manner, offering conceptual clarity on the role of valley states in qubit operation and measurement.

quant-ph↗

arXiv2025

Fast quantum gates for exchange-only qubits using simultaneous exchange pulses

The benefit of exchange-only qubits compared to other spin qubit types is the universal control using only voltage controlled exchange interactions between neighboring spins. As a compromise, qubit operations have to be constructed from non-orthogonal rotation axes of the Bloch sphere and result in rather long pulsing sequences. This paper aims to develop a faster implementation of single-qubit gates using simultaneous exchange pulses and manifests their potential for the construction of two-qubit gates. We introduce pulse sequences in which single-qubit gates could be executed faster and show that subsequences on three spins in two-qubit gates could be implemented in fewer steps. Our findings can particularly speed up gate sequences for realistic idle times between sequential pulses and we show that this advantage increases with more interconnectivity of the quantum dots. We further demonstrate how a phase operation can introduce a relative phase between the computational and some of the leakage states, which can be advantageous for the construction of two-qubit gates. In addition to our theoretical analysis, we experimentally demonstrate and characterize a simultaneous exchange implementation of $X$ rotations in a SiGe quantum dot device and compare to the state of the art with sequential exchange pulses.

quant-ph↗

arXiv2025

Partial Landau-Zener transitions and applications to qubit shuttling

The transition dynamics of two-state systems with time-dependent energy levels, first considered by Landau, Zener, Majorana, and Stückelberg, is one of the basic models in quantum physics and has been used to describe various physical systems. We propose here a generalization of the Landau-Zener (LZ) problem characterized by distinct paths of the instantaneous eigenstates as the system evolves in time while keeping the instantaneous eigenenergies exactly as in the standard LZ model. We show that these paths play an essential role in the transition probability $P$ between the two states, and can lead to a substantial reduction of $P$, being possible even to achieve $P=0$ in an instructive extreme case, and also to large $P$ even in the absence of any anticrossing point. The partial LZ model can describe valley transition dynamics during charge and spin shuttling in semiconductor quantum dots.

quant-ph↗

arXiv2025

Time-domain field correlation measurements enable tomography of highly multimode quantum states of light

Recent progress in ultrafast optics facilitates the investigation of the dynamics of highly multimode quantum states of light, as demonstrated by the application of electro-optic sampling to quantum states of the electromagnetic field. Yet, the complete tomographic reconstruction of optical quantum states with prior unknown statistics and dynamics is still challenging, since state-of-the-art tomographic methods require the measurement of many orthogonal, distinguishable modes. Here, we propose a tomography scheme based on time-domain quadrature correlation measurements and theoretically demonstrate its ability to reconstruct highly multimode Gaussian states. In contrast to (eight-port) homodyne detection, the two local oscillator pulses are shorter in time and are (independently) time-delayed against the pulsed quantum state. The distinguishable mode structure is obtained in post-processing from the correlation measurement data by orthogonalization. We show that the number of reconstructable modes increases with the number of time delays used and decreases with the temporal extent of the local oscillator. We extend and optimise our proposed correlation measurement to electro-optic sampling by adding a nonlinear crystal prior to the homodyne detection, potentially achieving subcycle resolution in the mid-infrared to THz regime. By analysing the (quantum) correlations present in the measurement data, we show how thermalisation of the quantum state during detection leads to the requirement of correlation measurements. The thermalisation is especially pronounced in the strong squeezing limit, for which we developed a non-perturbative theory. Furthermore, we open an avenue to extending our tomography scheme to non-Gaussian states by theoretically establishing the complete measurement statistics and showing how to obtain spectral information about pulsed Fock states from the joint statistics.

quant-ph↗

arXiv2025

Phonon-limited valley life times in single-particle bilayer graphene quantum dots

The valley degree of freedom in 2D semiconductors, such as gapped bilayer graphene (BLG) and transition metal dichalcogenides, is a promising carrier of quantum information in the emerging field of valleytronics. While valley dynamics have been extensively studied for moderate band gap 2D~semiconductors using optical spectroscopy techniques, very little is known about valley lifetimes in narrow band gap BLG, which is difficult to study using optical techniques. Here, we report single-particle valley relaxation times ($T_1$) exceeding several microseconds in electrostatically defined BLG quantum dots (QDs) using a pulse-gating technique. The observed dependence of $T_1$ on perpendicular magnetic field can be understood qualitatively and quantitatively by a model in which $T_1$ is limited by electron-phonon coupling. We identify the coupling to acoustic phonons via the bond length change and via the deformation potential as the limiting mechanisms.

cond-mat.mes-hall↗

arXiv2025

Spin relaxation in a single-electron bilayer graphene quantum dot

We study the spin relaxation in a single-electron bilayer graphene quantum dot due to the spin-orbit coupling. The spin relaxation is assisted by the emission of acoustic phonons via the bond-length change and deformation potential mechanisms and $1/f$ charge noise. In the perpendicular magnetic-field dependence of the spin relaxation rate $T_1^{-1}$, we predict a monotonic increase of $T_1^{-1}$ at higher fields where the electron-phonon coupling via the deformation potential plays a dominant role in spin relaxation. We show a less pronounced dip in $T_1^{-1}$ at lower magnetic fields due to the competition between the electron-phonon coupling due to bond-length change and $1/f$ charge noise. Finally, detailed comparisons of the magnetic-field dependence of the spin relaxation with the existing experiments by Banszerus et al. [Nat. Commun. 13, 3637 (2022)] and Gächter et al. [PRX Quantum 3, 020343 (2022)] are reported.

cond-mat.mes-hall↗

arXiv2025

Suppression of coherent errors during entangling operations in NV centers in diamond

We consider entangling operations in a single nitrogen-vacancy (NV) center in diamond where the hyperfine-coupled nuclear spin qubits are addressed with radio-frequency (rf) pulses conditioned on the state of the central electron spin. Limiting factors for the gate fidelity are coherent errors due to off-resonant driving of neighboring transitions in the dense, hyperfine-split energy spectrum of the defect and non-negligible perpendicular hyperfine tensor components that narrow the choice of $^{13}\rm C$ nuclear spin qubits. We address these issues by presenting protocols based on synchronization effects that allow for a complete suppression of both error sources in state-of-the-art CNOT gate schemes. This is possible by a suitable choice of parameter sets that incorporate the error into the scheme instead of avoiding it. These results contribute to the recent progress toward scalable quantum computation with defects in solids.

quant-ph↗

arXiv2025

The singlet-triplet and exchange-only flopping-mode spin qubits

Semiconductor-based spin qubits embedded into a superconducting microwave cavity constitute a fast-progressing and promising platform for realizing fast and fault-tolerant qubit control with long-range two-qubit coupling. The flopping-mode spin qubit consists of a single electron in a double quantum dot; it combines a charge qubit with a spin qubit. With its strong and tunable cavity coupling, the flopping-mode qubit is proven to be well-suited for low-power qubit control and cavity-mediated long-range quantum gates. The singlet-triplet (ST) and exchange-only (EO) qubits are multi-electron realizations that go without broadband control and are protected from some types of noise, but are challenging to couple to each other and to microwave cavities. We combine the flopping-mode concept with the ST and EO qubits and propose two new flopping-mode qubits that consist of three (four) quantum dots, occupied by two (three) electrons near the (1,0,1) - (0,1,1) [(1,0,1,1) -- (0,1,1,1)] charge transition. The two-electron system augments the $ST_0$ spin qubit with a charge qubit that interacts transversally and longitudinally with a cavity. Both couplings are highly tunable, and the longitudinal coupling distinguishes the flopping-mode ST qubit from the regular flopping-mode qubit. The longitudinal coupling allows for non-dissipative universal control similar to superconducting transmon qubits. The EO flopping-mode qubit comprises four dots occupied by three electrons and opens a new possibility to perform two-qubit gates for EO qubits that are challenging to perform directly with the exchange coupling. We use input-output theory to provide means of extracting the coupling strengths from cavity transmission data.

cond-mat.mes-hall↗

arXiv2025

Recipes for the Digital Quantum Simulation of Lattice Spin Systems

We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the efficiency gained by parallel execution of an extensive number of commuting terms. We provide resource estimates and quantum circuit elements for the most important cases and classes of spin systems. As resource estimates we indicate the total number of gates $N$ and simulation time $T$, expressed in terms of the number $n$ of spin 1/2 lattice sites (qubits), target accuracy $ε$, and simulated time $t$. We provide circuit constructions that realize the simulation time $T^{(1)}\propto nt^2/ε$ and $T^{(2q)}\propto t^{1+η}n^η/ε^η$ for arbitrarily small $η=1/2q$ for the first-order and higher-order Trotter expansions. We also discuss the potential impact of scaled gates, which have not yet been fully explored.

quant-ph↗

arXiv2025

Revealing correlated noise with single-qubit operations

Spatially correlated noise poses a significant challenge to fault-tolerant quantum computation by breaking the assumption of independent errors. Existing methods such as cycle benchmarking and quantum process tomography can characterize noise correlations but require substantial resources. We propose straightforward and efficient techniques to detect and quantify these correlations by leveraging collective phenomena arising from environmental correlations in a qubit register. In these techniques, single-qubit state preparations, single-qubit gates, and single-qubit measurements, combined with classical post-processing, suffice to uncover correlated relaxation and dephasing. Specifically, we use that correlated relaxation is connected to the superradiance effect which we show to be accessible by single-qubit measurements. Analogously, the established parity oscillation protocol can be refined to reveal correlated dephasing through characteristic changes in the oscillation line shape, without requiring the preparation of complex and entangled states.

quant-ph↗

arXiv2025

Crosstalk analysis in single hole-spin qubits within highly anisotropic g-tensors

Spin qubits based on valence band hole states are highly promising for quantum information processing due to their strong spin-orbit coupling and ultrafast operation speed. As these systems scale up, achieving high-fidelity single-qubit operations becomes essential. However, mitigating crosstalk effects from neighboring qubits in larger arrays, particularly for anisotropic qubits with strong spin-orbit coupling, presents a significant challenge. We investigate the impact of crosstalk on qubit fidelities during single-qubit operations and derive an analytical equation that serves as a synchronization condition to eliminate crosstalk in anisotropic media. Our analysis proposes optimized driving field conditions that can robustly synchronize Rabi oscillations and minimize crosstalk, showing a strong dependence on qubit anisotropy and the orientation of the external magnetic field. Taking experimental data into our analysis, we identify a set of parameter values that enable nearly crosstalk-free single-qubit gates, thereby paving the way for scalable quantum computing architectures.

cond-mat.other↗

arXiv2025

Strain-enabled control of the vanadium qudit in silicon carbide

Vanadium in silicon carbide is a promising spin photon interface candidate with optical transitions in the telecom range and a long lived electron spin, hosted in an advanced semiconductor platform. In this detailed investigation of the defect's 16-dimensional ground state spin manifold at millikelvin temperatures, a wide range of previously unreported transitions are observed which are accurately described using a theoretical model that includes strain. Using a superconducting microcoil we achieve Rabi frequencies exceeding 20 MHz and perform the first coherent manipulation of a direct hyperfine transition. These insights further underscore the defect's potential for strain engineering and sensing, as well as for fault-tolerant qudit encoding.

quant-ph↗

arXiv2024

Modeling Quantum Volume Using Randomized Benchmarking of Room-Temperature NV Center Quantum Registers

Accurately estimating the performance of quantum hardware is crucial for comparing different platforms and predicting the performance and feasibility of quantum algorithms and applications. In this paper, we tackle the problem of benchmarking a quantum register based on the NV center in diamond operating at room temperature. We define the connectivity map as well as single qubit performance. Thanks to an all-to-all connectivity the 2 and 3 qubit gates performance is promising and competitive among other platforms. We experimentally calibrate the error model for the register and use it to estimate the quantum volume, a metric used for quantifying the quantum computational capabilities of the register, of 8. Our results pave the way towards the unification of different architectures of quantum hardware and evaluation of the joint metrics.

quant-ph↗

arXiv2024

Spin shuttling in a silicon double quantum dot

The transport of quantum information between different nodes of a quantum device is among the challenging functionalities of a quantum processor. In the context of spin qubits, this requirement can be met by coherent electron spin shuttling between semiconductor quantum dots. Here we theoretically study a minimal version of spin shuttling between two quantum dots. To this end, we analyze the dynamics of an electron during a detuning sweep in a silicon double quantum dot (DQD) occupied by one electron. Possibilities and limitations of spin transport are investigated. Spin-orbit interaction and the Zeeman effect in an inhomogeneous magnetic field play an important role for spin shuttling and are included in our model. Interactions that couple the position, spin and valley degrees of freedom open a number of avoided crossings in the spectrum allowing for diabatic transitions and interfering paths. The outcomes of single and repeated spin shuttling protocols are explored by means of numerical simulations and an approximate analytical model based on the solution of the Landau--Zener problem. We find that a spin infidelity as low as $1-F_s\lesssim 0.002$ with a relatively fast level velocity of $α= 600\, μ$eV/ns is feasible for optimal choices of parameters or by making use of constructive interference.

cond-mat.mes-hall↗

arXiv2024

Interplay of Pauli blockade with electron-photon coupling in quantum dots

Both quantum transport measurements in the Pauli blockade regime and microwave cavity transmission measurements are important tools for spin-qubit readout and characterization. Based on a generalized input-output theory we derive a theoretical framework to investigate how a double quantum dot (DQD) in a transport setup interacts with a coupled microwave resonator while the current through the DQD is rectified by Pauli blockade. We show that the output field of the resonator can be used to infer the leakage current and thus obtain insight into the blockade mechanisms. In the case of a silicon DQD, we show how the valley quasi-degeneracy can impose limitations on this scheme. We also demonstrate that a large number of unknown DQD parameters including (but not limited to) the valley splitting can be estimated from the resonator response simultaneous to a transport experiment, providing more detailed knowledge about the microscopic environment of the DQD. Furthermore, we describe and quantify a back-action of the resonator photons on the steady state leakage current.

cond-mat.mes-hall↗

arXiv2024

Theory of the Simultaneous Transient Dispersive Readout of Multiple Spin Qubits

We propose a paradigm of multiplexed dispersive qubit measurement performed while the qubits dephase. A Laplace transformation of the time-dependent cavity response allows to separate contributions from multiple qubits coupled to the same resonator mode, thus allowing for simultaneous single-shot read out. With realistic parameters for silicon spin qubits we find a competitive readout fidelity, while the measurement time compares favourably to conventional dispersive readout. We extend the multiplexed readout method to quantum non-demolition measurements using auxiliary qubits.

cond-mat.mes-hall↗

arXiv2024

Proposal for a cavity-induced measurement of the exchange coupling in quantum dots

In spin qubit arrays the exchange coupling can be harnessed to implement two-qubit gates and to realize intermediate-range qubit connectivity along a spin bus. In this work, we propose a scheme to characterize the exchange coupling between electrons in adjacent quantum dots. We investigate theoretically the transmission of a microwave resonator coupled to a triple quantum dot (TQD) occupied by two electrons. We assume that the right quantum dot (QD) is always occupied by one electron while the second electron can tunnel between the left and center QD. If the two electrons are in adjacent dots they interact via the exchange coupling. By means of analytical calculations we show that the transmission profile of the resonator directly reveals the value of the exchange coupling strength between two electrons. From perturbation theory up to second order we conclude that the exchange can still be identified in the presence of magnetic gradients. A valley splitting comparable to the inter-dot tunnel coupling will lead to further modifications of the cavity transmission dips that also depend on the valley phases.

cond-mat.mes-hall↗

arXiv2024

Entanglement generation using single-photon pulse reflection in realistic networks

A general entanglement generation protocol between remote stationary qubits using single-photon reflection in a photonic network is explored theoretically. The nodes of the network consist of single qubits that are typically represented by the spin of a color center, each localized in a separate optical cavity and linked to other nodes via photonic links such as optical fibers. We derive a model applicable to a wide range of parameters and scenarios to describe the nodes and the local spin-photon interaction accounting for the pulsed (finite bandwidth) nature of flying single photons while optimizing the rate and fidelity. We investigate entanglement generation between remote qubits and tailor protocols to a variety of physical implementations with different properties. Of particular interest is the regime of weak coupling and low cooperativity between spin and cavity which is relevant in the cases of the nitrogen and silicon vacancy centers in diamond. We also take into account the variability of the properties between realistic (stationary) nodes.

quant-ph↗