arXiv subjects

Łukasz Cywiński

Publications and source records attributed to Łukasz Cywiński.

At least 19 recordsLinked to original sources

arXiv2026

Phenomenological quantum mechanics: I. Phenomenology of quantum observables

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions about the underlying mathematical structures are permitted. We demonstrate that it is indeed possible to derive, on this basis, a complete and fully functional formalism rooted in the structures of Hilbert spaces. However, the resulting formalism--the bi-trajectory formalism--differs significantly from the standard state-focused formulation. In Part I of the paper, we analyze the outcomes of various experiments involving sequential measurements of quantum observables. These outcomes are quantitatively described by phenomenological multi-time probability distributions, estimated from experimental data. Our first conclusion is that the theory describing these experiments must be non-classical: the measured sequences cannot be interpreted as sampling of a uni-trajectory representing the system's observable. The non-classical nature of the investigated systems manifests in a range of observed phenomena, including quantum interference, the quantum Zeno effect, and uncertainty relations between the measured observables.

quant-ph↗

arXiv2026

Phenomenological quantum mechanics: II. Deducing the formalism from experimental observations

We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of sequential measurements of quantum observables; no presuppositions about the underlying mathematical structures are permitted. In the concluding Part II of the paper, we carry out the deduction of the formalism from the phenomenological inputs described in Part I. We show that the resulting formalism exhibits an affinity with Hilbert spaces, and we derive an explicit representation in terms of those mathematical structures. Analogues of the obtained elementary building blocks -- such as projection operators -- are readily identifiable within the standard formalism. However, once these building blocks are assembled according to the blueprint of the deduced bi-trajectory formalism, it becomes evident that the new and the standard formalisms differ substantially at the conceptual level. These differences do not negate the fact that both formalisms are in perfect agreement with respect to empirically testable predictions. Rather, the emergence of a novel, non-standard formulation should be seen as a relatively rare opportunity to reassess, from a fresh perspective, some of the long-standing foundational issues in the theory. The hope is that the new approach may prove more successful in addressing problems that have resisted resolution within the established theoretical framework.

quant-ph↗

arXiv2026

Mapping g-factors and complex intervalley coupling in Si/SiGe by conveyor-mode shuttling

As silicon spin qubit chips are increasing in qubit number and area, methods for the screening of qubit related material parameters become vital. Here we demonstrate the two-dimensional mapping of small variations of the electron g-factor of quantum dots formed in planar Si/SiGe quantum wells with precision better than $10^{-3}$ and with nanometer lateral resolution. We scan the electron g-factor across a 40 nm $\times$ 400 nm area and observe two g-factors per QD site which obey a striking symmetry and bimodal distribution across the area. These two g-factors relate to valley states of the electron in the quantum dot in agreement with a recent theoretical model. Using conveyor-belt shuttling of entangled electron spin pairs, complementary to the mapping of the local valley-splitting, we map the g-factor. We compare g-factor and valley splitting maps measured on the same device, and extract the complex intervalley coupling parameter along the shuttle trajectories applying a theoretical model of g-factor dependence on intervalley coupling. These maps will allow unprecedented insights into the spin-valley dynamics during qubit manipulation, readout and shuttling and serve as a benchmark for the engineering of Si/SiGe heterostructures for large-scale quantum chips.

quant-ph↗

arXiv2026

Impact of the local valley splitting on the coherence of conveyor-belt spin shuttling in $^{28}$Si/SiGe

Silicon quantum chips offer a promising path toward scalable, fault-tolerant quantum computing, with the potential to host millions of qubits. However, scaling up dense quantum-dot arrays and enabling qubit interconnections through shuttling are hindered by uncontrolled lateral variations of the valley splitting energy $E_{VS}$. We map $E_{VS}$ across a $40 \, $nm x $400 \, $nm region of a $^{28}$Si/Si$_{0.7}$Ge$_{0.3}$ shuttle device and analyze the spin coherence of a single electron spin transported by conveyor-belt shuttling. We observe that the $E_{VS}$ varies over a wide range from $1.5 \, μ$eV to $200 \, μ$eV and is dominated by SiGe alloy disorder. In regions of low $E_{VS}$ and at spin-valley resonances, spin coherence is reduced and its dependence on shuttle velocity matches predictions. Rapid and frequent traversal of low-$E_{VS}$ regions induces a regime of enhanced spin coherence explained by motional narrowing. By selecting shuttle trajectories that avoid problematic areas on the $E_{VS}$ map, we achieve transport over tens of microns with coherence limited only by the coupling to a static electron spin entangled with the mobile qubit. Our results provide experimental confirmation of the theory of spin-decoherence of mobile electron spin-qubits and present practical strategies to integrate conveyor-mode qubit shuttling into silicon quantum chips.

quant-ph↗

arXiv2026

Singlet-triplet oscillations in multivalley Si double quantum dots

Charge separation from the $(4,0)$ to the $(3,1)$ state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the $(3,1)$ singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of $g$-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.

cond-mat.mes-hall↗

arXiv2025

Statistical Structure of Charge Disorder in Si/SiGe Quantum Dots

Properties of quantum dot based spin qubits have significant inter-device variability due to unavoidable presence of various types of disorder in semiconductor nanostructures. A significant source of this variability is charge disorder at the semiconductor-oxide interface, which causes unpredictable, yet, as we show here, correlated fluctuations in such essential properties of quantum dots like their mutual tunnel couplings, and electronic confinement energies. This study presents a systematic approach to characterize and mitigate the effects of such disorder. We utilize finite element modeling of a Si/SiGe double quantum dot to generate a large statistical ensemble of devices, simulating the impact of trapped interface charges. This work results in a predictive statistical model capable of generating realistic artificial data for training machine learning algorithms. By applying Principal Component Analysis to this dataset, we identify the dominant modes through which disorder affects the multi-dimensional parameter space of the device. Our findings show that the parameter variations are not arbitrary, but are concentrated along a few principal axes, i.e. there are significant correlations between many properties of the devices. We finally compare that against control modes generated by sweeping the gate voltages, revealing limitations of the plunger-only control. This work provides a framework for enhancing the controllability and operational yield of spin qubit devices, by systematically addressing the nature of electrostatic disorder that leads to statistical correlations in properties of double quantum dots.

cond-mat.mes-hall↗

arXiv2024

Decoherence of electron spin qubit during transfer between two semiconductor quantum dots at low magnetic fields

Electron shuttling is one of the current avenues being pursued to scale semiconductor quantum dot-based spin qubits. Adiabatic spin qubit transfer along a chain of tunnel-coupled quantum dots is one of the possible schemes. In this scheme, we theoretically analyze the dephasing of a spin qubit that is adiabatically transferred between two tunnel-coupled quantum dots. We focus on the regime where the Zeeman splitting is lower than the tunnel coupling, such that interdot tunneling with spin flip is absent. We analyze the sources of errors in spin-coherent electron transfer for Si- and GaAs-based quantum dots. In addition to the obvious effect of fluctuations in spin splitting within each dot, leading to finite $T_{2}^{*}$ for the stationary spin qubit, we consider the effects activated by detuning sweeps: failure of charge transfer due to charge noise and phonons, spin relaxation due to the enhancement of spin-orbit mixing at the tunnel-induced anticrossing of states localized in the two dots, and spin dephasing caused by low- and high-frequency noise coupling to the electron's charge. We show that the latter effect is activated by differences in Zeeman splittings between the two dots. Importantly, all the error mechanisms are more dangerous at low tunnel couplings. Our results indicate that away from micromagnets, maximizing the fidelity of coherent transfer aligns with minimizing charge transfer error that was previously considered in J. A. Krzywda and L. Cywiński, Phys. Rev. B 104 075439 (2021). For silicon, we suggest having tunnel coupling fulfilling $ 2t_c \gtrsim 60 \, μ$eV when one aims to coherently transfer a spin qubit across a $\sim \!10$ $μ$m long array of $\sim \! 100$ quantum dots with error less than $10^{-3}$.

cond-mat.mes-hall↗

arXiv2024

Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics

The multitime probability distributions obtained by repeatedly probing a quantum system via the measurement of an observable generally violate Kolmogorov's consistency property. Therefore, one cannot interpret such distributions as the result of the sampling of a single trajectory. We show that, nonetheless, they do result from the sampling of one pair of trajectories. In this sense, rather than give up on trajectories, quantum mechanics requires to double down on them. To this purpose, we prove a generalization of the Kolmogorov extension theorem that applies to families of complex-valued bi-probability distributions (that is, defined on pairs of elements of the original sample spaces), and we employ this result in the quantum mechanical scenario. We also discuss the relation of our results with the quantum comb formalism.

quant-ph↗

arXiv2024

Simulation of 1/f charge noise affecting a quantum dot in a Si/SiGe structure

Due to presence of magnetic field gradient needed for coherent spin control, dephasing of single-electron spin qubits in silicon quantum dots is often dominated by $1/f$ charge noise. We investigate theoretically fluctuations of ground state energy of an electron in gated quantum dot in realistic Si/SiGe structure. We assume that the charge noise is caused by motion of charges trapped at the semiconductor-oxide interface. We consider a realistic range of trapped charge densities, $ρ\! \sim \! 10^{10}$ cm$^{-2}$, and typical lenghtscales of isotropically distributed displacements of these charges, $δr \! \leq \! 1$ nm, and identify pairs $(ρ,δr)$ for which the amplitude and shape of the noise spectrum is in good agreement with spectra reconstructed in recent experiments on similar structures.

cond-mat.mes-hall↗

arXiv2024

Correlations of spin splitting and orbital fluctuations due to 1/f charge noise in the Si/SiGe Quantum Dot

Fluctuations of electric fields can change the position of a gate-defined quantum dot in a semiconductor heterostructure. In the presence of magnetic field gradient, these stochastic shifts of electron's wavefunction lead to fluctuations of electron's spin splitting. The resulting spin dephasing due to charge noise limits the coherence times of spin qubits in isotopically purified Si/SiGe quantum dots. We investigate the spin splitting noise caused by such process caused by microscopic motion of charges at the semiconductor-oxide interface. We compare effects of isotropic and planar displacement of the charges, and estimate their densities and typical displacement magnitudes that can reproduce experimentally observed spin splitting noise spectra. We predict that for defect density of $10^{10}$ cm$^{-2}$, visible correlations between noises in spin splitting and in energy of electron's ground state in the quantum dot, are expected.

cond-mat.mes-hall↗

arXiv2024

Objectivity of classical quantum stochastic processes

We investigate what can be concluded about a quantum system when sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition and thus appear to an observer as a sampling of a classical trajectory. We identify a set of physical conditions imposed on the system dynamics, that when satisfied, lead to the aforementioned trajectory interpretation of the measurement results. We then show that when another quantum system is coupled to the observable, the operator representing it can be replaced by external noise. Crucially, the realizations of this surrogate (classical) stochastic process follow the same trajectories as those measured by the observer. Therefore, it can be said that the trajectory interpretation suggested by the Kolmogorov consistent measurements also applies in contexts other than sequential measurements.

quant-ph↗

arXiv2023

Mapping of valley-splitting by conveyor-mode spin-coherent electron shuttling

In Si/SiGe heterostructures, the low-lying excited valley state seriously limit operability and scalability of electron spin qubits. For characterizing and understanding the local variations in valley splitting, fast probing methods with high spatial and energy resolution are lacking. Leveraging the spatial control granted by conveyor-mode spin-coherent electron shuttling, we introduce a method for two-dimensional mapping of the local valley splitting by detecting magnetic field dependent anticrossings of ground and excited valley states using entangled electron spin-pairs as a probe. The method has sub-μeV energy accuracy and a nanometer lateral resolution. The histogram of valley splittings spanning a large area of 210 nm by 18 nm matches well with statistics obtained by the established but time-consuming magnetospectroscopy method. For the specific heterostructure, we find a nearly Gaussian distribution of valley splittings and a correlation length similar to the quantum dot size. Our mapping method may become a valuable tool for engineering Si/SiGe heterostructures for scalable quantum computing.

quant-ph↗

arXiv2023

Limitations on the maximal level of entanglement of two singlet-triplet qubits in GaAs quantum dots

We analyze in detail a procedure of entangling of two singlet-triplet ($S$-$T_{0}$) qubits operated in a regime when energy associated with the magnetic field gradient, $ΔB_{z}$, is an order of magnitude smaller than the exchange energy, $J$, between singlet and triplet states [Shulman M. et al., Science 336, 202 (2012)]. We have studied theoretically a single $S$-$T_{0}$ qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for time dependence of components of its Bloch vector for quasistatical fluctuations of $ΔB_{z}$ and quasistatical or dynamical $1/f^β$-type fluctuations of $J$. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two $S$-$T_{0}$ qubits. Particularly, we have obtained an analytical expression for evolution of two qubits affected by $1/f^β$-type fluctuations of $J$. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment, the $S$-$T_{0}$ qubits were affected by uncorrelated $1/f^β$ charge noises.

cond-mat.mes-hall↗

arXiv2023

Spin-EPR-pair separation by conveyor-mode single electron shuttling in Si/SiGe

Long-ranged coherent qubit coupling is a missing function block for scaling up spin qubit based quantum computing solutions. Spin-coherent conveyor-mode electron-shuttling could enable spin quantum-chips with scalable and sparse qubit-architecture. Its key feature is the operation by only few easily tuneable input terminals and compatibility with industrial gate-fabrication. Single electron shuttling in conveyor-mode in a 420 nm long quantum bus has been demonstrated previously. Here we investigate the spin coherence during conveyor-mode shuttling by separation and rejoining an Einstein-Podolsky-Rosen (EPR) spin-pair. Compared to previous work we boost the shuttle velocity by a factor of 10000. We observe a rising spin-qubit dephasing time with the longer shuttle distances due to motional narrowing and estimate the spin-shuttle infidelity due to dephasing to be 0.7 % for a total shuttle distance of nominal 560 nm. Shuttling several loops up to an accumulated distance of 3.36 $μ$m, spin-entanglement of the EPR pair is still detectable, giving good perspective for our approach of a shuttle-based scalable quantum computing architecture in silicon.

quant-ph↗

arXiv2023

Blueprint of a scalable spin qubit shuttle device for coherent mid-range qubit transfer in disordered Si/SiGe/SiO$_2$

Silicon spin qubits stand out due to their very long coherence times, compatibility with industrial fabrication, and prospect to integrate classical control electronics. To achieve a truly scalable architecture, a coherent mid-range link that moves the electrons between qubit registers has been suggested to solve the signal fan-out problem. Here, we present a blueprint of such a $\approx 10\,μ$m long link, called a spin qubit shuttle, which is based on connecting an array of gates into a small number of sets. To control these sets, only a few voltage control lines are needed and the number of these sets and thus the number of required control signals is independent of the length of this link. We discuss two different operation modes for the spin qubit shuttle: A qubit conveyor, i.e. a potential minimum that smoothly moves laterally, and a bucket brigade, in which the electron is transported through a series of tunnel-coupled quantum dots by adiabatic passage. We find the former approach more promising considering a realistic Si/SiGe device including potential disorder from the charged defects at the Si/SiO$_2$ layer, as well as typical charge noise. Focusing on the qubit transfer fidelity in the conveyor shuttling mode, we discuss in detail motional narrowing, the interplay between orbital and valley excitation and relaxation in presence of $g$-factors that depend on orbital and valley state of the electron, and effects from spin-hotspots. We find that a transfer fidelity of 99.9 \% is feasible in Si/SiGe at a speed of $\sim$10 m/s, if the average valley splitting and its inhomogeneity stay within realistic bounds. Operation at low global magnetic field $\approx 20$ mT and material engineering towards high valley splitting is favourable for reaching high fidelities of transfer.

cond-mat.mes-hall↗

arXiv2022

Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system

We consider a quantum probe $P$ undergoing pure dephasing due to its interaction with a quantum system $S$. The dynamics of $P$ is then described by a well-defined sub-algebra of operators of $S,$ i.e. the "accessible" algebra on $S$ from the point of view of $P.$ We consider sequences of $n$ measurements on $P,$ and investigate the relationship between Kolmogorov consistency of probabilities of obtaining sequences of results with various $n,$ and commutativity of the accessible algebra. For a finite-dimensional $S$ we find conditions under which the Kolmogorov consistency of measurement on $P,$ given that the state of $S$ can be arbitrarily prepared, is equivalent to the commutativity of this algebra. These allow us to describe witnesses of nonclassicality (understood here as noncommutativity) of part of $S$ that affects the probe. For $P$ being a qubit, the witness is particularly simple: observation of breaking of Kolmogorov consistency of sequential measurements on a qubit coupled to $S$ means that the accessible algebra of $S$ is noncommutative.

quant-ph↗

arXiv2021

Qubit decoherence under two-axis coupling to low-frequency noises

Many solid-state qubit systems are afflicted by low frequency noise mechanisms that operate along two perpendicular axes of the Bloch sphere. Depending on the qubit's control fields, either noise can be longitudinal or transverse to the qubit's quantization axis, thus affecting its dynamics in distinct ways, generally contributing to decoherence that goes beyond pure dephasing. Here we present a theory that provides a unified platform to study dynamics of a qubit subjected to two perpendicular low-frequency noises (assumed to be Gaussian and uncorrelated) under dynamical decoupling pulse sequences. The theory is demonstrated by the commonly encountered case of power-law noise spectra, where approximate analytical results can be obtained.

quant-ph↗

arXiv2021

Interplay of charge noise and coupling to phonons in adiabatic electron transfer between quantum dots

Long-distance transfer of quantum information in architectures based on quantum dot spin qubits will be necessary for their scalability. One way of achieving it is to simply move the electron between two quantum registers. Precise control over the electron shuttling through a chain of tunnel-coupled quantum dots is possible when interdot energy detunings are changed adiabatically. Deterministic character of shuttling is however endangered by coupling of the transferred electron to thermal reservoirs: sources of fluctuations of electric fields, and lattice vibrations. We theoretically analyse how the electron transfer between two quantum dots is affected by electron-phonon scattering, and interaction with sources of $1/f$ and Johnson charge noise in both detuning and tunnel coupling. The electron-phonon scattering turns out to be irrelevant in Si quantum dots, while a competition between the effects of charge noise and Landau-Zener effect leads to an existence of optimal detuning sweep rate, at which probability of leaving the electron behind is minimal. In GaAs quantum dots, on the other hand, coupling to phonons is strong enough to make the phonon-assisted processes of interdot transfer dominate over influence of charge noise. The probability of leaving the electron behind depends then monotonically on detuning sweep rate, and values much smaller than in silicon can be obtained for slow sweeps. However, after taking into account limitations on transfer time imposed by need for preservation of electron's spin coherence, minimal probabilities of leaving the electron behind in both GaAs- and Si-based double quantum dots turn out to be of the same order of magnitude. Bringing them down below $10^{-3}$ requires temperatures $\leq \! 100$ mK and tunnel couplings above $20$ $μ$eV.

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