CyberSec Research

This work classifies stabilizer codes by the set of diagonal Clifford gates that can be implemented transversally on them. We show that, for any stabilizer code, its group of diagonal transversal Clifford gates on $\ell$ code blocks must be one of six distinct families of matrix groups. We further develop the theory of classifying stabilizer codes by via matrix algebras of endomorphisms first introduced by Rains, and give a complete classification of the diagonal Clifford symmetries of $\ell$ code blocks. A number of corollaries are given in the final section.

This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum systems. Aimed at students and researchers seeking a clear mathematical treatment, the study begins with the foundational principles of quantum mechanics and quantum computation before presenting the Lie-Trotter product formula and its higher-order generalizations. In particular, Suzuki's recursive method is explored to achieve improved error scaling. Through theoretical analysis and illustrative examples, the advantages and limitations of these techniques are discussed, with an emphasis on their application to $k$-local Hamiltonians and their role in overcoming classical computational bottlenecks. The work concludes with a brief overview of current advances and open challenges in Hamiltonian simulation.

Strontium-88 is a versatile atomic species often used in quantum optics, precision metrology, and quantum computing. Consolidated atomic data is essential for the planning, execution, and evaluation of experiments. In this reference, we present physical and optical properties of neutral $^{88}$Sr relevant to these applications. Here we focus on experimental results and supplement these with theoretical values. We present equations to convert values and derive important parameters. Tabulated results include key parameters for commonly used transitions in $^{88}$Sr ($^1\mathrm{S}_0 \rightarrow \, ^1\mathrm{P}_1$, $^1\mathrm{S}_0 \rightarrow \, ^3\mathrm{P}_{0,1,2}$, and $^3\mathrm{P}_{0,1,2} \rightarrow \, ^3\mathrm{S}_1$). This dataset serves as an up-to-date reference for studies involving bosonic $^{88}$Sr.

The Hubbard model at $U\to\infty$ has recently been shown to have resonant valence bond (RVB) ground states on the corner-sharing sawtooth and pyrochlore lattices in the dilute doping limit of a single vacancy. In an effort to further generalize those results, I study how the ground state is modified when not all corners are shared between two tetrahedra as in the quasi-1D lattices of a pyrochlore stripe, and how to approach the problem in the case of finite doping. Using a non-Abelian version of the flux inequality, the tetrahedron chain is shown to have degenerate RVB-like ground states. The Bethe ansatz (BA) is adapted to solve the sawtooth chain with spinless or spin-polarized fermions and multiple holons, which is the first example of applying BA to a quasi-1D lattice.

For chaotic scattering systems we investigate the left-right Husimi representation, which combines left and right resonance states. We demonstrate that the left-right Husimi representation is invariant in the semiclassical limit under the corresponding closed classical dynamics, which we call quantum invariance. Furthermore, we show that it factorizes into a classical multifractal structure times universal quantum fluctuations. Numerical results for a dielectric cavity, the three-disk scattering system, and quantum maps confirm both the quantum invariance and the factorization.

We investigate the response of a Ramsey interferometric quantum sensor based on a frustrated, three-spin system (a Kitaev trimer) to a classical time-dependent field (signal). The system eigenspectrum is symmetric about a critical point, $|\vec{b}| = 0$, with four of the spectral components varying approximately linearly with the magnetic field and four exhibiting a nonlinear dependence. Under the adiabatic approximation and for appropriate initial states, we show that the sensor's response to a zero-mean signal is such that below a threshold, $|\vec{b}| < b_\mathrm{th}$, the sensor does not respond to the signal, whereas above the threshold, the sensor acts as a detector that the signal has occurred. This thresholded response is approximately omnidirectional. Moreover, when deployed in an entangled multisensor configuration, the sensor achieves sensitivity at the Heisenberg limit. Such detectors could be useful both as standalone units for signal detection above a noise threshold and in two- or three-dimensional arrays, analogous to a quantum bubble chamber, for applications such as particle track detection and long-baseline telescopy.

Photonic and polaritonic systems offer a fast and efficient platform for accelerating machine learning (ML) through physics-based computing. To gain a computational advantage, however, polaritonic systems must: (1) exploit features that specifically favor nonlinear optical processing; (2) address problems that are computationally hard and depend on these features; (3) integrate photonic processing within broader ML pipelines. In this letter, we propose a polaritonic machine learning approach for solving graph-based data problems. We demonstrate how lattices of condensates can efficiently embed relational and topological information from point cloud datasets. This information is then incorporated into a pattern recognition workflow based on convolutional neural networks (CNNs), leading to significantly improved learning performance compared to physics-agnostic methods. Our extensive benchmarking shows that photonic machine learning achieves over 90\% accuracy for Betti number classification and clique detection tasks - a substantial improvement over the 35\% accuracy of bare CNNs. Our study introduces a distinct way of using photonic systems as fast tools for feature engineering, while building on top of high-performing digital machine learning.

Collective coherent noise poses challenges for fault-tolerant quantum error correction (FTQEC), as it falls outside the usual stochastic noise models. While constant excitation (CE) codes can naturally avoid coherent noise, a complete fault-tolerant framework for the use of these codes under realistic noise models has been elusive. Here, we introduce a complete fault-tolerant architecture for CE CSS codes based on dual-rail concatenation. After showing that transversal CNOT gates violate CE code constraints, we introduce CE-preserving logical CNOT gates and modified Shor- and Steane-type syndrome extraction schemes using zero-controlled NOT gates and CE-compatible ancilla. This enables fault-tolerant syndrome-extraction circuits fully compatible with CE constraints. We also present an extended stabilizer simulation algorithm that efficiently tracks both stochastic and collective coherent noise. Using our framework, we identify minimal CE codes, including the $[[12,1,3]]$ and $[[14,3,3]]$ codes, and demonstrate that the $[[12,1,3]]$ code achieves strong performance under coherent noise. Our results establish the first complete FTQEC framework for CE codes, demonstrating their robustness to coherent noise. This highlights the potential of CE codes as a possible solution for quantum processors dominated by collective coherent noise.

In this work we present a comprehensive method of characterization and optimization of laser irradiation within a confocal microscope tailored to quantum sensing experiments using nitrogen-vacancy (NV) centres. While confocal microscopy is well-suited for such experiments, precise control and understanding of several optical parameters are essential for reliable single-emitter studies. We investigate the laser beam intensity profile, single-photon emission statistics, fluorescence response under varying polarization and saturation conditions, spectral characteristics, and the temporal profiles of readout and reinitialization pulses. The beam quality is assessed using the beam propagation factor $M^2$, determined via the razorblade technique. Optical fluorescence spectrum is recorded to confirm NV centre emission. To confirm single-emitter operation, we measure second-order autocorrelation function $g^{(2)}(\tau)$. Saturation behaviour is analysed by varying laser power and recording the corresponding fluorescence, while polarization dependence is studied using a half-wave ($\lambda/2$) plate. Temporal laser pulse profile is examined by modulating the power of an acousto-optic modulator. After optimizing all relevant parameters, we demonstrate the microscope's capabilities in driving spin transitions of a single NV centre. This work establishes a straightforward and effective protocol for laser excitation optimization, enhancing the performance and reliability of NV-based quantum sensors.

Classical Shadow Tomography (Huang, Kueng and Preskill, Nature Physics 2020) is a method for creating a classical snapshot of an unknown quantum state, which can later be used to predict the value of an a-priori unknown observable on that state. In the short time since their introduction, classical shadows received a lot of attention from the physics, quantum information, and quantum computing (including cryptography) communities. In particular there has been a major effort focused on improving the efficiency, and in particular depth, of generating the classical snapshot. Existing constructions rely on a distribution of unitaries as a central building block, and research is devoted to simplifying this family as much as possible. We diverge from this paradigm and show that suitable distributions over \emph{states} can be used as the building block instead. Concretely, we create the snapshot by entangling the unknown input state with an independently prepared auxiliary state, and measuring the resulting entangled state. This state-based approach allows us to consider a building block with arguably weaker properties that has not been studied so far in the context of classical shadows. Notably, our cryptographically-inspired analysis shows that for \emph{efficiently computable} observables, it suffices to use \emph{pseudorandom} families of states. To the best of our knowledge, \emph{computational} classical shadow tomography was not considered in the literature prior to our work. Finally, in terms of efficiency, the online part of our method (i.e.\ the part that depends on the input) is simply performing a measurement in the Bell basis, which can be done in constant depth using elementary gates.

Current count-rate models for single-photon avalanche diodes (SPADs) typically assume an instantaneous recovery of the quantum efficiency following dead-time, leading to a systematic overestimation of the effective detection efficiency for high photon flux. To overcome this limitation, we introduce a generalized analytical count-rate model for free-running SPADs that models the non-instantaneous, exponential recovery of the quantum efficiency following dead-time. Our model, framed within the theory of non-homogeneous Poisson processes, only requires one additional detector parameter -- the exponential-recovery time constant $\tau_\mathrm{r}$. The model accurately predicts detection statistics deep into the saturation regime, outperforming the conventional step-function model by two orders of magnitude in terms of the impinging photon rate. For extremely high photon flux, we further extend the model to capture paralyzation effects. Beyond photon flux estimation, our model simplifies SPAD characterization by enabling the extraction of quantum efficiency $\eta_0$, dead-time $\tau_\mathrm{d}$, and recovery time constant $\tau_\mathrm{r}$ from a single inter-detection interval histogram. This can be achieved with a simple setup, without the need for pulsed lasers or externally gated detectors. We anticipate broad applicability of our model in quantum key distribution (QKD), time-correlated single-photon counting (TCSPC), LIDAR, and related areas. Furthermore, the model is readily adaptable to other types of dead-time-limited detectors. A Python implementation is provided as supplementary material for swift adoption.

We present a method to suppress crosstalk from implementing controlled-Z gates via local addressing in neutral atom quantum computers. In these systems, a fraction of the laser light that is applied locally to implement gates typically leaks to other atoms. We analyze the resulting crosstalk in a setup of two gate atoms and one neighboring third atom. We then perturbatively derive a spin-echo-inspired gate protocol that suppresses the leading order of the amplitude error, which dominates the crosstalk. Numerical simulations demonstrate that our gate protocol improves the fidelity by two orders of magnitude across a broad range of experimentally relevant parameters. To further reduce the infidelity, we develop a circuit to cancel remaining phase errors. Our results pave the way for using local addressing for high-fidelity quantum gates on Rydberg-based quantum computers.

We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \langle\mathbf{v}^2,\mathbf{w}^2\rangle \leq \|\mathbf{v}\|^2\|\mathbf{w}\|^2 - \langle\mathbf{v},\mathbf{w}\rangle^2$ for all $\mathbf{v},\mathbf{w} \in \mathbb{R}^n$. We present three new proofs of this inequality that better illustrate "why" it is true and generalize it in several different ways: we generalize from vectors to matrices, we explore which exponents other than 2 result in the inequality holding, and we derive a version of the inequality involving three or more vectors.

Understanding how a quantum many-body state is maintained stably as a nonequilibrium steady state is of fundamental and practical importance for exploration and exploitation of open quantum systems. We establish a general equivalent condition for an open quantum many-body system governed by the Gorini-Kossakowski-Sudarshan-Lindblad dynamics under local drive and/or dissipation to have a quantum independent and identically distributed (i.i.d.) steady state. We present a sufficient condition for a system to have a quantum i.i.d. steady state by identifying a set of operators that commute with arbitrary quantum i.i.d. states. In particular, a set of quantum i.i.d. states is found to be an invariant subset of time evolution superoperators for systems that satisfy the sufficient condition. These findings not only identify a class of models with exactly solvable steady states but also lead to a no-go theorem that precludes quantum entanglement and spatial correlations in a broad class of quantum many-body steady states in a dissipative environment.

The negatively charged diamond nitrogen-vacancy ($\mathrm{{NV}^-}$) center plays a central role in many cutting edge quantum sensing applications; despite this, much is still unknown about the energy levels in this system. The ionization energy of the $\mathrm{^{1}E}$ singlet state in the $\mathrm{{NV}^-}$ has only recently been measured at between 2.25 eV and 2.33 eV. In this work, we further refine this energy by measuring the $\mathrm{^{1}E}$ energy as a function of laser wavelength and diamond temperature via magnetically mediated spin-selective photoluminescence (PL) quenching; this PL quenching indicating at what wavelength ionization induces population transfer from the $\mathrm{^{1}E}$ into the neutral $\mathrm{{NV}^0}$ charge configuration. Measurements are performed for excitation wavelengths between 450 nm and 470 nm and between 540 nm and 566 nm in increments of 2 nm, and for temperatures ranging from about 50 K to 150 K in 5 K increments. We determine the $\mathrm{^{1}E}$ ionization energy to be between 2.29 and 2.33 eV, which provides about a two-fold reduction in uncertainty of this quantity. Distribution level: A. Approved for public release; distribution unlimited.

Excited states play a central role in determining the physical properties of quantum matter, yet their accurate computation in many-body systems remains a formidable challenge for numerical methods. While neural quantum states have delivered outstanding results for ground-state problems, extending their applicability to excited states has faced limitations, including instability in dense spectra and reliance on symmetry constraints or penalty-based formulations. In this work, we rigorously formalize the framework introduced by Pfau et al.~\cite{pfau2024accurate} in terms of Grassmann geometry of the Hilbert space. This allows us to generalize the Stochastic Reconfiguration method for the simultaneous optimization of multiple variational wave functions, and to introduce the multidimensional versions of operator variances and overlaps. We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.

Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that embeds any linear, non-Hermitian flow $\dot x = A x$ with $A=-iH+K$ into a strictly unitary evolution on an enlarged Hilbert space: \[ ( (l| \otimes I ) \mathcal T e^{-i \int ( I_A\otimes H +i F\otimes K) dt} ( |r) \otimes I ) = \mathcal T e^{\int A dt}, \] provided the triple $( F, (l|, |r) )$ satisfies the compact moment identities $(l| F^{k}|r) =1$ for all $k\ge 0$ in the ancilla space. This algebraic criterion recovers both \emph{Schr\"odingerization} [Phys. Rev. Lett. 133, 230602 (2024)] and the linear-combination-of-Hamiltonians (LCHS) scheme [Phys. Rev. Lett. 131, 150603 (2023)], while also unveiling whole families of new dilations built from differential, integral, pseudo-differential, and difference generators. Each family comes with a continuous tuning parameter \emph{and} is closed under similarity transformations that leave the moments invariant, giving rise to an overwhelming landscape of design space that allows quantum dilations to be co-optimized for specific applications, algorithms, and hardware. As concrete demonstrations, we prove that a simple finite-difference dilation in a finite interval attains near-optimal oracle complexity. Numerical experiments on Maxwell viscoelastic wave propagation confirm the accuracy and robustness of the approach.

A qubit-oscillator junction connecting as a series two bosonic heat baths at different temperatures can display heat valve and diode effects. In particular, the rectification can change in magnitude and even in sign, implying an inversion of the preferential direction for the heat current with respect to the temperature bias. We perform a systematic study of these effects in a circuit QED model of qubit-oscillator system and find that the features of current and rectification crucially depend on the qubit-oscillator coupling. While at small coupling, transport occurs via a resonant mechanism between the sub-systems, in the ultrastrong coupling regime the junction is a unique, highly hybridized system and the current becomes largely insensitive to the detuning. Correspondingly, the rectification undergoes a change of sign. In the nonlinear transport regime, the coupling strength determines whether the current scales sub- or super-linearly with the temperature bias and whether the rectification, which increases in magnitude with the bias, is positive or negative. We also find that steady-state coherence largely suppresses the current and enhances rectification. An insight on these behaviors with respect to changes in the system parameters is provided by analytical approximate formulas.