Quantum Physics (quant-ph)

Abstract: A new measure of information leakage for quantum encoding of classical data is defined. An adversary can access a single copy of the state of a quantum system that encodes some classical data and is interested in correctly guessing a general randomized or deterministic function of the data (e.g., a specific feature or attribute of the data in quantum machine learning) that is unknown to the security analyst. The resulting measure of information leakage, referred to as maximal quantum leakage, is the multiplicative increase of the probability of correctly guessing any function of the data upon observing measurements of the quantum state. Maximal quantum leakage is shown to satisfy post-processing inequality (i.e., applying a quantum channel reduces information leakage) and independence property (i.e., leakage is zero if the quantum state is independent of the classical data), which are fundamental properties required for privacy and security analysis. It also bounds accessible information. Effects of global and local depolarizing noise models on the maximal quantum leakage are established.

Abstract: This chapter explores a deterministic hydrodynamically-inspired ensemble interpretation for free relativistic particles, following the original pilot wave theory conceptualized by de Broglie in 1924 and recent advances in hydrodynamic quantum analogs. We couple a one-dimensional periodically forced Klein-Gordon wave equation and a relativistic particle equation of motion, and simulate an ensemble of multiple uncorrelated particle trajectories. The simulations reveal a chaotic particle dynamic behavior, highly sensitive to the initial random condition. Although particles in the simulated ensemble seem to fill out the entire spatiotemporal domain, we find coherent spatiotemporal structures in which particles are less likely to cross. These structures are characterized by de Broglie's wavelength and the relativistic modulation frequency kc. Markedly, the probability density function of the particle ensemble correlates to the square of the absolute wave field, solved here analytically, suggesting a classical deterministic interpretation of de Broglie's matter waves and Born's rule.

Abstract: We study the donor-bound exciton optical linewidth properties of Al, Ga and In donor ensembles in single-crystal zinc oxide (ZnO). Neutral shallow donors (D$^0$) in ZnO are spin qubits with optical access via the donor-bound exciton (D$^0$X). This spin-photon interface enables applications in quantum networking, memories and transduction. Essential optical parameters which impact the spin-photon interface include radiative lifetime, optical inhomogeneous and homogeneous linewidth and optical depth. The ensemble photoluminescence linewidth ranges from 4-11 GHz, less than two orders of magnitude larger than the expected lifetime-limited linewidth. The ensemble linewidth remains narrow in absorption measurements through the 300 $\mu$m-thick sample, which has an estimated optical depth up to several hundred. Homogeneous broadening of the ensemble line due to phonons is consistent with thermal population relaxation between D$^0$X states. This thermal relaxation mechanism has negligible contribution to the total linewidth at 2 K. We find that inhomogeneous broadening due to the disordered isotopic environment in natural ZnO is significant, ranging from 1.9 GHz - 2.2 GHz. Two-laser spectral anti-hole burning measurements, which can be used to measure the homogeneous linewidth in an ensemble, however, reveal spectral anti-hole linewidths similar to the single laser ensemble linewidth. Despite this broadening, the high homogeneity, large optical depth and potential for isotope purification indicate that the optical properties of the ZnO donor-bound exciton are promising for a wide range of quantum technologies and motivate a need to improve the isotope and chemical purity of ZnO for quantum technologies.

Abstract: In this brief report, we propose a circuit which is locally equivalent to a recently proposed universal two-qubit quantum circuit involving two applications of special perfect entanglers (SPEs) and local y-rotations. Further, we discuss a scheme of implementation of the equivalent circuit using cross-resonance Hamiltonian. Finally, we implement the B-gate circuit using a CNOT gate and a $\sqrt{\text{CNOT}}$ gate. This requires the implementation time which is approximately 64.84% of the time required to implement the same gate using two CNOT gates.

Abstract: In this paper, we describe the unusual low-frequency magnetic resonances in alkali vapor with oriented atomic spins regarding the framework of density matrix formalism. The feature of the resonance is the absence of a constant component in the external magnetic field. To explain steep increase of the spin orientation at certain frequencies, we define special closed atomic spin trajectories governed by periodic magnetic perturbation. Any closed trajectory is characterized by the frequency of spin motion. The resonance effect was numerically verified in the paper. For instance, these trajectories can be observed in an alkali vapor via optical excitation. Surprisingly, the width of the resonance line is found to be narrower, as one may expect.

Abstract: Magic states were originally introduced as a resource that enables universal quantum computation using classically simulable Clifford gates. This concept has been extended to matchgate circuits (MGCs) which are made of two-qubit nearest-neighbour quantum gates defined by a set of algebraic constraints. In our work, we study the Gaussian rank of a quantum state -- defined as the minimum number of terms in any decomposition of that state into Gaussian states -- and associated quantities: the Gaussian Fidelity and the Gaussian Extent. We investigate the algebraic structure of Gaussian states and find and describe the independent sets of constraints upper-bounding the dimension of the manifold of Gaussian states. Furthermore, we describe the form of linearly dependent triples of Gaussian states and find the dimension of the manifold of solutions. By constructing the corresponding $\epsilon$-net for the Gaussian states, we are able to obtain upper bounds on the Gaussian fidelity. We identify a family of extreme points of the feasible set for the Dual Gaussian extent problem and show that Gaussian extent is multiplicative on systems of 4 qubits; and further that it is multiplicative on primal points whose optimal dual witness is in the above family. These extreme points turn out to be closely related to Extended Hamming Codes. We show that optimal dual witnesses are unique almost-surely, when the primal point lies in the interior of the normal cone of an extreme point. Furthermore, we show that the Gaussian rank of two copies of our canonical magic state is 4 for symmetry-restricted decompositions. Numerical investigation suggests that no low-rank decompositions exist of either 2 or 3 copies of the magic state. Finally, we consider approximate Gaussian rank and present approximate decompositions for selected magic states.

Abstract: Significant progress in the construction of physical hardware for quantum computers has necessitated the development of new algorithms or protocols for the application of real-world problems on quantum computers. One of these problems is the power flow problem, which helps us understand the generation, distribution, and consumption of electricity in a system. In this study, the solution of a balanced 4-bus power system supported by the Newton-Raphson method is investigated using a newly developed dissipative quantum neural network hardware. This study presents the findings on how the proposed quantum network can be applied to the relevant problem and how the solution performance varies depending on the network parameters.

Abstract: The maser, a microwave (MW) analog of the laser, is a well-established method for generating and amplifying coherent MW irradiation with ultra-low noise. This is accomplished by creating a state of population inversion between two energy levels separated by MW frequency. Thermodynamically, such a state corresponds to a small but negative temperature. The reverse condition, where only the lower energy level is highly populated, corresponds to a very low positive temperature. In this work, we experimentally demonstrate how to generate such a state in condensed matter at moderate cryogenic temperatures. This state is then used to efficiently remove microwave photons from a cavity, continuously cooling it to the quantum limit, well below its ambient temperature. Such an "anti-maser" device could be extremely beneficial for applications that would normally require cooling to millikelvin temperatures to eliminate any MW photons. For instance, superconducting MW quantum circuits (such as qubits and amplifiers) could, with the use of this device, operate efficiently at liquid helium temperatures.

Abstract: We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. We achieve the promotion of the efficiently simulable FLO subtheory to universal quantum computation by gadgetizing controlled phase gates with arbitrary phases employing non-Gaussian resource states. Our key contribution is the development of a novel phase-sensitive algorithm for simulating FLO circuits. This allows us to decompose the resource states arising from gadgetization into free states at the level of statevectors rather than density matrices. The runtime cost of our algorithm for estimating the Born-rule probability of a given quantum circuit scales polynomially in all circuit parameters, except for a linear dependence on the newly introduced FLO extent, which scales exponentially with the number of controlled-phase gates. More precisely, as a result of finding optimal decompositions of relevant resource states, the runtime doubles for every maximally resourceful (e.g., swap or CZ) gate added. Crucially, this cost compares very favourably with the best known prior algorithm, where each swap gate increases the simulation cost by a factor of approximately 9. For a quantum circuit containing arbitrary FLO unitaries and $k$ controlled-Z gates, we obtain an exponential improvement $O(4.5^k)$ over the prior state-of-the-art.

Abstract: The negatively charged silicon vacancy center (SiV$^-$) in diamond is a promising, yet underexplored candidate for single-spin quantum sensing at sub-kelvin temperatures and tesla-range magnetic fields. A key ingredient for such applications is the ability to perform all-optical, coherent addressing of the electronic spin of near-surface SiV$^-$ centers. We present a robust and scalable approach for creating individual, $\sim$50nm deep SiV$^-$ with lifetime-limited optical linewidths in diamond nanopillars through an easy-to-realize and persistent optical charge-stabilization scheme. The latter is based on single, prolonged 445nm laser illumination that enables continuous photoluminescence excitation spectroscopy, without the need for any further charge stabilization or repumping. Our results constitute a key step towards the use of near-surface, optically coherent SiV$^-$ for sensing under extreme conditions, and offer a powerful approach for stabilizing the charge-environment of diamond color centers for quantum technology applications.

Abstract: The fluctuation relations, which characterize irreversible processes in Nature, are among the most important results in non-equilibrium physics. In short, these relations say that it is exponentially unlikely for us to observe a time-reversed process and, thus, establish the thermodynamic arrow of time pointing from low to high entropy. On the other hand, fundamental physical theories are invariant under time-reversal symmetry. Although in Newtonian and quantum physics the emergence of irreversible processes, as well as fluctuation relations, is relatively well understood, many problems arise when relativity enters the game. In this work, by considering a specific class of spacetimes, we explore the question of how the time-dilation effect enters into the fluctuation relations. We conclude that a positive entropy production emerges as a consequence of both the special relativistic and the gravitational (enclosed in the equivalence principle) time-dilation effects.

Abstract: Registers of trapped neutral atoms, excited to Rydberg states to induce strong long-distance interactions, are extensively studied for direct applications in quantum computing. In this regard, new effective approaches to the creation of multiqubit quantum gates arise high interest. Here, we present a novel gate implementation technique based on RF-induced few-body F\"{o}rster resonances. External radio frequency (RF) control field allows us to manipulate the phase and population dynamics of many-atom system, thus enabling the realization of universal $CCR_{Z}(\phi)$ quantum gates. We numerically demonstrate RF-induced resonant interactions, as well as high-precision three-qubit gates. The extreme controllability of interactions provided by RF makes it possible to implement gates for a wide range of parameters of the atomic system, and significantly facilitates their experimental implementation. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction ($\sim 99.7\%$) using reasonable experimental parameters.

Abstract: Quantum light is considered to be one of the key resources of the coming second quantum revolution expected to give rise to groundbreaking technologies and applications. If the spatio-temporal and polarization structure of modes is known, the properties of quantum light are well understood. This information provides the basis for contemporary quantum optics and its applications in quantum communication and metrology. However, thinking about quantum light at the most fundamental timescale, namely the oscillation cycle of a mode or the inverse frequency of an involved photon, we realize that the corresponding picture has been missing until now. For instance, how to comprehend and characterize a single photon at this timescale? To fill this gap, we demonstrate theoretically how local quantum measurements allow to reconstruct and visualize a quantum field under study at subcycle scales, even when its temporal mode structure is a priori unknown. In particular, generation and tomography of ultrabroadband squeezed states as well as photon-subtracted states derived from them are described, incorporating also single-photon states. Our results set a cornerstone in the emerging chapter of quantum physics termed time-domain quantum optics. We expect this development to elicit new spectroscopic concepts for approaching e.g. fundamental correlations and entanglement in the dynamics of quantum matter, overcoming the temporal limitation set by the oscillation cycles of both light and elementary excitations.

Abstract: Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum states with relivable confidence intervals. In this work, we suggest a computationally efficient and reliable scheme for determining well-justified error bars for quantum tomography. We approximate the probability distribution of the Hilbert-Schmidt distance between the target state and the estimation, which is given by the linear inversion, by calculating its moments. We also present a generalization of this approach for quantum process tomography. We benchmark our approach for a number of quantum tomography protocols using both simulated and experimental data. The obtained results pave a way to the use of the suggested scheme for complete characterization of quantum systems of various nature.

Abstract: Although non-intuitive, an accelerated electron along a particular trajectory can be shown to emit classical electromagnetic radiation in the form of a Fermi-Dirac spectral distribution when observed in a particular angular regime. We investigate the relationship between the distribution, spectrum, and particle count. The result for the moving point charge is classical, as it accelerates along an exactly known trajectory. We map to the semi-classical regime of the moving mirror model with a quantized spin-0 field. The scalars also possess a $\beta$ Bogoliubov coefficient distribution with Fermi-Dirac form in the respective frequency regime.

Abstract: Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a quantum setting, whereby classical functions can be approximated by parameterised quantum circuits. We provide here precise error bounds for specific classes of functions and extend these results to the interesting new setup of randomised quantum circuits, mimicking classical reservoir neural networks. Our results show in particular that a quantum neural network with $\mathcal{O}(\varepsilon^{-2})$ weights and $\mathcal{O} (\lceil \log_2(\varepsilon^{-1}) \rceil)$ qubits suffices to achieve accuracy $\varepsilon>0$ when approximating functions with integrable Fourier transform.

Abstract: Logic gates can be written in terms of complex differential operators where the inputs and outputs are analytic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection between the oscillatory behavior of the system and logic gates. We explain the universal programming language (UPL) used by physical objects to process information. To assure the causality structure in UPL, we introduce the concept of layers that characterizes the computations for each time scale.

Abstract: We describe a framework for the controllability analysis of networks of $n$ quantum systems of an arbitrary dimension $d$, {\it qudits}, with dynamics determined by Hamiltonians that are invariant under the permutation group $S_n$. Because of the symmetry, the underlying Hilbert space, ${\cal H}=(\mathbb{C}^d)^{\otimes n}$, splits into invariant subspaces for the Lie algebra of $S_n$-invariant elements in $u(d^n)$, denoted here by $u^{S_n}(d^n)$. The dynamical Lie algebra ${\cal L}$, which determines the controllability properties of the system, is a Lie subalgebra of such a Lie algebra $u^{S_n}(d^n)$. If ${\cal L}$ acts as $su\left( \dim(V) \right)$ on each of the invariant subspaces $V$, the system is called {\it subspace controllable}. Our approach is based on recognizing that such a splitting of the Hilbert space ${\cal H}$ coincides with the {\it Clebsch-Gordan} splitting of $(\mathbb{C}^d)^{\otimes n}$ into {\it irreducible representations} of $su(d)$. In this view, $u^{S_n}(d^n)$, is the direct sum of certain $su(n_j)$ for some $n_j$'s we shall specify, and its {\it center} which is the Abelian (Lie) algebra generated by the {\it Casimir operators}. Generalizing the situation previously considered in the literature, we consider dynamics with arbitrary local simultaneous control on the qudits and a symmetric two body interaction. Most of the results presented are for general $n$ and $d$ but we recast previous results on $n$ qubits in this new general framework and provide a complete treatment and proof of subspace controllability for the new case of $n=3$, $d=3$, that is, {\it three qutrits}.

Abstract: We propose efficient algorithms for classically simulating fermionic linear optics operations applied to non-Gaussian initial states. By gadget constructions, this provides algorithms for fermionic linear optics with non-Gaussian operations. We argue that this problem is analogous to that of simulating Clifford circuits with non-stabilizer initial states: Algorithms for the latter problem immediately translate to the fermionic setting. Our construction is based on an extension of the covariance matrix formalism which permits to efficiently track relative phases in superpositions of Gaussian states. It yields simulation algorithms with polynomial complexity in the number of fermions, the desired accuracy, and certain quantities capturing the degree of non-Gaussianity of the initial state. We study one such quantity, the fermionic Gaussian extent, and show that it is multiplicative on tensor products when the so-called fermionic Gaussian fidelity is. We establish this property for the tensor product of two arbitrary pure states of four fermions with positive parity.

Abstract: In 1987, Vaidman, Aharanov, and Albert put forward a puzzle called the Mean King's Problem (MKP) that can be solved only by harnessing quantum entanglement. Prime-powered solutions to the problem have been shown to exist, but they have not yet been experimentally realized for any dimension beyond two. We propose a general first-of-its-kind experimental scheme for solving the MKP in prime dimensions (D). Our search is guided by the digital discovery framework PyTheus, which finds highly interpretable graph-based representations of quantum optical experimental setups; using it, we find specific solutions and generalize to higher dimensions through human insight. As proof of principle, we present a detailed investigation of our solution for the three-, five-, and seven-dimensional cases. We obtain maximum success probabilities of 72.8%, 45.8%, and 34.8%, respectively. We, therefore, posit that our computer-inspired scheme yields solutions that exceed the classical probability (1/D) twofold, demonstrating its promise for experimental implementation.

Abstract: Holonomic quantum computing (HQC) functions by transporting an adiabatically degenerate manifold of computational states around a closed loop in a control-parameter space; this cyclic evolution results in a non-Abelian geometric phase which may couple states within the manifold. Realizing the required degeneracy is challenging, and typically requires auxiliary levels or intermediate-level couplings. One potential way to circumvent this is through Floquet engineering, where the periodic driving of a nondegenerate Hamiltonian leads to degenerate Floquet bands, and subsequently non-Abelian gauge structures may emerge. Here we present an experiment in ultracold $^{87}$Rb atoms where atomic spin states are dressed by modulated RF fields to induce periodic driving of a family of Hamiltonians linked through a fully tuneable parameter space. The adiabatic motion through this parameter space leads to the holonomic evolution of the degenerate spin states in $SU(2)$, characterized by a non-Abelian connection. We study the holonomic transformations of spin eigenstates in the presence of a background magnetic field, characterizing the fidelity of these gate operations. Results indicate that while the Floquet engineering technique removes the need for explicit degeneracies, it inherits many of the same limitations present in degenerate systems.

Abstract: Spin network systems can be used to achieve quantum state transfer with high fidelity and to generate entanglement. A new approach to design spin-chain-based spin network systems, for shortrange quantum information processing and phase-sensing, has been proposed recently in [1]. In this paper, we investigate the scalability of such systems, by designing larger spin network systems that can be used for longer-range quantum information tasks, such as connecting together quantum processors. Furthermore, we present more complex spin network designs, which can produce different types of entangled states. Simulations of disorder effects show that even such larger spin network systems are robust against realistic levels of disorder.