arXiv subjects

Anton V. Khvalyuk

Publications and source records attributed to Anton V. Khvalyuk.

4 recordsLinked to original sources

arXiv2026

Influence of Trotterization error on single-particle tunneling

Existing superconducting quantum devices struggle to simulate spatial quantum tunneling as it is exponentially slow and inherently nonlocal. The Suzuki-Trotter algorithm (STA) offers a practical solution for existing quantum hardware by approximating nonlocal evolution with a local two-qubit gate sequence that requires no ancilla qubits and preserves physical interpretability. However, estimating the required gate count from naive fidelity-based error bounds yields values exceeding the constraints imposed by noise and decoherence in real devices. Here, we fully characterize STA for a semiclassical tunneling model by adapting the Wentzel-Kramers-Brillouin approximation. We find that, in the general case, tunneling is suppressed by resonance detuning. In contrast, if STA preserves the target resonance, tunneling rates are exponentially enhanced via non-perturbative renormalization, dramatically reducing the gate count required to observe tunneling and thus benefiting from large Trotter steps$\unicode{x2013}$equally natural for existing quantum hardware. However, for the latter regime, we further find that Floquet mixing of quasi-energy levels reconstructs the low-energy spectrum and strongly deforms tunneling dynamics by introducing additional allowed regions. Based on the semiclassical picture, we conjecture interplay of tunneling and large-step STA in the presence of topology-altering modifications, such as staggered potential modulation$\unicode{x2013}$a subject of future work. Our findings enable direct tunneling simulations on existing superconducting platforms, providing a controlled platform for studying the nontrivial interplay of tunneling and STA, with the possibility of addressing the effects of noise, disorder, and interaction.

quant-ph↗

arXiv2026

Dissipation due to Bulk Localized Low-Energy Modes in Strongly Disordered Superconductors

Strongly disordered superconductors (SDSCs) are widely used in qubits, microwave resonators, photon detectors, and other superconducting quantum devices. In SDSC-based devices, coherence times are limited by low-temperature microwave dissipation in the material. However, the standard Mattis-Bardeen theory fails in SDSCs because their single-particle spectrum exhibits a hard pseudogap $Δ_{P}$ both below and above the transition temperature $T_{c}$. We develop a novel microscopic theory of the dependence of \emph{ac }dissipation in such systems on temperature $T$ and frequency $ω$. We analyze the resonator quality factor $Q(ω,T)$ in the practically relevant range $\hbarω,\,T\llΔ\leqΔ_{P}$, where $Δ$ is the typical superconducting order parameter, distinct from $Δ_{P}$. We show that low-$ω$ dissipation is dominated by a new type of bulk localized collective modes arising from spatial inhomogeneity of the superconducting state. Consequently, $Q(ω)$ decreases strongly with $ω$ and exhibits two-level-system-like growth with $T$ for $T\ll T_{c}$. Our theory provides a microscopic understanding of existing and future experiments on thin films of $\mathrm{InO}_{x}$, TiN, NbN, and similar SDSCs, and is phenomenologically relevant to granular aluminum films. The results suggest strategies to mitigate intrinsic microwave losses in SDSC-based quantum devices.

cond-mat.supr-con↗

arXiv2024

Near-power-law temperature dependence of the superfluid stiffness in strongly disordered superconductors

In BCS superconductors, the superfluid stiffness is virtually constant at low temperature and only slightly affected by the exponentially low density of thermal quasiparticles. Here, we present an experimental and theoretical study on the temperature dependence of superfluid stiffness $Θ\left(T\right)$ in a strongly disordered pseudo-gaped superconductor, amorphous $\text{InO}_{x}$, which exhibits non-BCS behavior. Experimentally, we report an unusual power-law suppression of the superfluid stiffness $δΘ\left(T\right)\propto T^{b}$ at $T\ll T_{c}$, with $b\sim1.6$, which we measured via the frequency shift of microwave resonators. Theoretically, by combining analytical and numerical methods to a model of a disordered superconductor with pseudogap and spatial inhomogeneities of the superconducting order parameter, we found a qualitatively similar low-temperature power-law behavior with exponent $b\sim1.6-3$ being disorder-dependent. This power-law suppression of the superfluid density occurs mainly due to the broad distribution of the superconducting order parameter that is known to exist in such superconductors [arXiv:1012.3630], even moderately far from the superconductor-insulator transition. The presence of the power-law dependence $δΘ\left(T\right)\propto T^{b}$ at low $T\ll T_{c}$ demonstrates the existence of low-energy collective excitations; in turn, it implies the presence of a new channel of dissipation in inhomogeneous superconductors caused by sub-gap excitations that are not quasiparticles. Our findings have implications for the use of strongly disordered superconductors as superinductance in quantum circuits.

cond-mat.supr-con↗

arXiv2022

Distribution of the order parameter in strongly disordered superconductors: An analytic theory

We developed an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to superconducting-insulator transition. Single-electron eigenstates are assumed to be Anderson-localized, with a large localization volume. Superconductivity develops due to coherent delocalization of originally localized pre-formed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number $Z\gg1$ of similar neighboring pairs. We derived integral equations for the probability distribution $P\left(Δ\right)$ of local superconducting order parameter $Δ\left(\boldsymbol{r}\right)$ and analyzed their solutions in the limit of small dimensionless Cooper coupling constant $λ\ll1$. The shape of the order-parameter distribution is found to depend crucially upon the effective number of nearest neighbors $Z_{\text{eff}}=2ν_{0}Δ_{0}Z$. The solution we provide is valid both at large and small $Z_{\text{eff}}$; the latter case is nontrivial as the function $P\left(Δ\right)$ is heavily non-Gaussian. The discovery of a broad parameter range where the distribution function $P\left(Δ\right)$ is non-Gaussian but also non-critical (in the sense of SIT criticality) is one of our key findings. The analytic results are supplemented by numerical data, and good agreement between them is observed.

cond-mat.supr-con↗