Quantum Physics (quant-ph)

Abstract: We consider the impact of the unitary averaging framework on single and two-mode linear optical gates. We demonstrate that this allows a trade-off between the probability of success and gate fidelity, with perfect fidelity gates being achievable for a finite decrease in the probability of success, at least in principle. Furthermore, we show that the encoding and decoding errors in the averaging scheme can also be suppressed up to the first order. We also look at how unitary averaging can work in conjunction with existing error correction schemes. Specifically, we consider how parity encoding might be used to counter the extra loss due to the decreased probability of success, with the aim of achieving fault tolerance. We also consider how unitary averaging might be utilised to expand the parameter space in which fault tolerance may be achievable using standard fault tolerant schemes.

Abstract: Quantum entanglement provides a novel way to test short-distance quantum physics in a non-relativistic regime. We provide entanglement-based protocols to potentially test the magnetically induced dipole-dipole interaction and the Casimir-Polder potential between the two nano-crystals kept in a Schrodinger Cat state. Our scheme is based on the Stern-Gerlach (SG) apparatus, where we can witness the entanglement mediated by these interactions for the nano-crystal mass m~10^-19 kg with a spatial superposition size of order 0.1 micron in a trap relying on diamagnetic levitation. We show that it is possible to close the SG interferometer in position and momentum with a modest gradient in the magnetic field.

Abstract: We examine the effectiveness and resilience of achieving quantum gates employing three approaches stemming from quantum control methods: counterdiabatic driving, Floquet engineering, and inverse engineering. We critically analyse their performance in terms of the gate infidelity, the associated resource overhead based on energetic cost, the susceptibility to time-keeping errors, and the degradation under environmental noise. Despite significant differences in the dynamical path taken, we find a broadly consistent behavior across the three approaches in terms of the efficacy of implementing the target gate and the resource overhead. Furthermore, we establish that the functional form of the control fields plays a crucial role in determining how faithfully a gate operation is achieved. Our results are demonstrated for single qubit gates, with particular focus on the Hadamard gate, and we discuss the extension to $N$-qubit operations.

Abstract: Single quantum emitters embedded in solid-state hosts are an ideal platform for realizing quantum information processors and quantum network nodes. Among the currently-investigated candidates, Er$^{3+}$ ions are particularly appealing due to their 1.5 $\mu$m optical transition in the telecom band as well as their long spin coherence times. However, the long lifetimes of the excited state -- generally in excess of 1 ms -- along with the inhomogeneous broadening of the optical transition result in significant challenges. Photon emission rates are prohibitively small, and different emitters generally create photons with distinct spectra, thereby preventing multi-photon interference -- a requirement for building large-scale, multi-node quantum networks. Here we solve this challenge by demonstrating for the first time linear Stark tuning of the emission frequency of a single Er$^{3+}$ ion. Our ions are embedded in a lithium niobate crystal and couple evanescently to a silicon nano-photonic crystal cavity that provides an up to 143 increase of the measured decay rate. By applying an electric field along the crystal c-axis, we achieve a Stark tuning greater than the ion's linewidth without changing the single-photon emission statistics of the ion. These results are a key step towards rare earth ion-based quantum networks.

Abstract: We present a Fermionic Cellular Automaton model which describes massless Dirac fermion in 1+1 dimension coupled with local, number preserving interaction. The diagonalization of the two particle sector shows that specific values of the total momentum and of the coupling constant allows for the formation of bound states.

Abstract: The task of discriminating between two known quantum channels is a well known binary hypothesis testing task. We present a variational quantum algorithm with a parameterized state preparation and two-outcome positive operator valued measure (POVM) which defines the acceptance criteria for the hypothesis test. Both the state preparation and measurement are simultaneously optimized using success probability of single-shot discrimination as an objective function which can be calculated using localized measurements. Under constrained signal mode photon number quantum illumination we match the performance of known optimal 2-mode probes by simulating a bosonic circuit. Our results show that variational algorithms can prepare optimal states for binary hypothesis testing with resource constraints.

Abstract: Giant atoms are attracting interest as an emerging paradigm in the quantum optics of engineered waveguides. Here we propose to realize a synthetic giant atom working in the optical regime starting from a pair of interacting Rydberg atoms driven by a coherent field and coupled to a photonic crystal waveguide. Giant-atom effects can be observed as a phase-dependent decay of the double Rydberg excitation during the initial evolution of this atomic pair while (internal) atomic entanglement is exhibited at later times. Such an intriguing entanglement onset occurs in the presence of intrinsic atomic decay toward non-guided vacuum modes and is accompanied by an anti-bunching correlation of the emitted photons. Our findings may be relevant to quantum information processing, besides broadening the giant-atom waveguide physics with optically driven natural atoms.

Abstract: We study the process of resonant generation of high-order harmonics in a closed cavity in the model of vacuum nonlinear electrodynamics. Concretely, we study the possibility of resonant generation of the third harmonic induced by a single electromagnetic mode in a radiofrequency cavity, as well as resonant generation of a combined frequency mode induced by two pump modes ($\omega_1$ and $\omega_2$). We explicitly show that the third harmonic as well as the $2\omega_1+\omega_2$ combined frequency mode are not resonantly amplified, while the $2\omega_1-\omega_2$ signal mode is amplified for certain cavity geometry. We discuss the process from the point of view of quantum theory.

Abstract: Quantum entanglement and squeezing have significantly improved phase estimation and imaging in interferometric settings beyond the classical limits. However, for a wide class of non-interferometric phase imaging/retrieval methods vastly used in the classical domain e.g., ptychography and diffractive imaging, a demonstration of quantum advantage is still missing. Here, we fill this gap by exploiting entanglement to enhance imaging of a pure phase object in a non-interferometric setting, only measuring the phase effect on the free-propagating field. This method, based on the so-called "transport of intensity equation", is quantitative since it provides the absolute value of the phase without prior knowledge of the object and operates in wide-field mode, so it does not need time-consuming raster scanning. Moreover, it does not require spatial and temporal coherence of the incident light. Besides a general improvement of the image quality at a fixed number of photons irradiated through the object, resulting in better discrimination of small details, we demonstrate a clear reduction of the uncertainty in the quantitative phase estimation. Although we provide an experimental demonstration of a specific scheme in the visible spectrum, this research also paves the way for applications at different wavelengths, e.g., X-ray imaging, where reducing the photon dose is of utmost importance.

Abstract: We study the one-dimensional system subjected to a linearly varying imaginary vector potential, which is described by the single-particle continuous Schr\"odinger equation and is analytically solved. The eigenenergy spectrum is found to be real under open boundary condition (OBC) but forms a parabola in the complex energy plane under periodic boundary condition (PBC). The eigenstates always exhibit a modulated Gaussian distribution and are all pinned on the same position, which is determined by the imaginary vector potential and boundary conditions. These behaviors are in sharp contrast to the non-Hermitian skin effect (NHSE) in systems with constant imaginary vector potential, where the eigenstates are exponentially distributed under OBC but become extended under PBC. We further demonstrate that even though the spectrum under PBC is an open curve, the Gaussian type of NHSE still has a topological origin and is characterized by a nonvanishing winding number in the PBC spectrum. The energies interior to the parabola can support localized edge states under semi-infinite boundary condition. The corresponding tight-binding lattice models also show similar properties, except that the PBC spectrum form closed loops. Our work opens a door for the study of quantum systems with spatially varying imaginary vector potentials.

Abstract: We consider a system of composite bosons given by strongly bound fermion pairs tunneling through sites that form a low-dimensional network. It has been shown that the ground state of this system can have condensate-like properties in the very dilute regime for two-dimensional lattices but displays fermionization for one-dimensional lattices. Studying graphs with fractal dimensions, we explore intermediate situations between these two cases and observe a correlation between increasing dimension and increasing condensate-like character. However, this is only the case for graphs for which the average path length grows with power smaller than 1 in the number of sites, and which have an unbounded circuit rank. We thus conjecture that these two conditions are relevant for condensation of composite bosons in arbitrary networks, and should be considered jointly with the well-established criterion of high entanglement between constituents.

Abstract: Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. By combining these with multivariate matrix trace inequalities, we recover and sometimes strengthen various existing entanglement monogamy inequalities. In particular, we give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement by relating it to the relative entropy of entanglement measured with one-way local operations and classical communication, as well as for the faithfulness of conditional entanglement of mutual information by relating it to the separably measured relative entropy of entanglement. We discuss variations of these results using the relative entropy to states with positive partial transpose, and multipartite setups. Our results simplify and generalize previous derivations in the literature that employed operational arguments about the asymptotic achievability of information-theoretic tasks.

Abstract: In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then generalized to the case of a particle confined in an infinite well in arbitrary dimensions. It is known, that boundary value problems in the phase space formulation of the quantum mechanics are surprisingly tricky. The complications arise from nonlocality of the expression involved in calculation of the Wigner function. Several ways of treating such problems were proposed. They are rather complicated and even exotic, involving, for example, corrections to the kinetic energy proportional to the derivatives of the Dirac delta--function. The presented in the manuscript approach is simpler both from analytical point of view and regarding numerical calculation. The solution is brought to a form of convolution of the free particle solution with some function, defined by the shape of the well. This procedure requires calculation of an integral, which can be done by developed analytical and numerical method.

Abstract: Entanglement of spatially separated quantum states is usually defined with respect to a reference frame provided by some external observer. Thus, if one wishes to localize the quantum information within a spatially separated entangled state, one must enact an entanglement extraction protocol also defined with respect to that external frame. Entanglement extraction for Gaussian ground states in such an external frame construction has been shown to require a minimum energy and is hence an interesting process for gravitational physics, where examinations of localization vs. energy cost have a long history. General covariance however, precludes dependence on external frames. In order to enact an extraction protocol in a generally covariant theory, dependence on the external reference frame must first be removed and the states made relational. We examine the implementation of an extraction protocol for Gaussian states, who's center-of-mass and relational degrees of freedom are entangled, in a relational toy model where translation invariance stands in for full diffeomorphism invariance. Constructing fully relational states and the corresponding extraction/localization can, in principle, be done in two ways. External frame position information can be removed through $G$-twirling over translations or one can spontaneously break the translation symmetry via the gradient of an auxiliary field, or $Z$-model. We determine the energetics of quantum information localization after the states have been made fully relational via both the $G$-twirl and $Z$-model. We also show one can smoothly transition between the two approaches via positive operator valued measurements (POVM).

Abstract: We show that an exciton on a discrete chain of sites can be guided by effective measurements induced by an ambient, non-equilibrium medium that is synchronised to the exciton transport. For experimental verification, we propose a hybrid cold atom platform, carrying the exciton as electronic excitation on a chain of atoms, which are surrounded by a slow light medium supporting polaritons. The chain is coupled to the medium through long-range Rydberg interactions. Despite the guiding mechanism being incoherent, the exciton pulse can be coherently transported with high fidelity. The implementation requires careful alignment of chain and medium but then no further time-dependent control. Our concept can be ported to other exciton and polariton carrying media or devices, and will enable switches and waveguides operating with the two quasi particles involved, as we demonstrate.

Abstract: Quantum teleportation is the name of a problem: how can the real-valued parameters encoding the state at Alice's location make their way to Bob's location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick. Investigating the phenomenon with Schr\"odinger states and reduced density matrices shall always leave loose ends because they are not local and complete descriptions of quantum systems. Upon demonstrating that the Heisenberg picture admits a local and complete description, Deutsch and Hayden rendered its explanatory power manifest by revealing the trick behind teleportation, namely, by providing an entirely local account. Their analysis is re-exposed and further developed.

Abstract: Dempster rule of combination (DRC) is widely used for uncertainty reasoning in intelligent information system, which is generalized to complex domain recently. However, as the increase of identification framework elements, the computational complexity of Dempster Rule of Combination increases exponentially. To address this issue, we propose a novel quantum Dempster rule of combination (QDRC) by means of Toffoli gate. The QDRC combination process is completely implemented using quantum circuits.

Abstract: We report the investigation of the influence of atomic motion on the fluorescence dynamics of dilute atomic ensemble driven by resonant pulse radiation. We show that even for sub-Doppler temperatures, the motion of atoms can significantly affect the nature of both superradiation and subradiation. We also demonstrate that, in the case of an ensemble of moving scatterers, it is possible to observe the nonmonotonic time dependence of the fluorescence rate. This leads to the fact that, in certain time intervals, increasing in temperature causes not an decrease but increase of the fluorescence intensity in the cone of coherent scattering. We have analyzed the role of the frequency diffusion of secondary radiation as a result of multiple light scattering in an optically dense medium. It is shown that spectrum broadening is the main factor which determines radiation trapping upon resonant excitation. At later time, after the trapping stage, the dynamics is dominated by close pairs of atoms (dimers). The dynamics of the excited states of these dimers has been studied in detail. It is shown that the change in the lifetime of the given adiabatic term of the diatomic quasi-molecule induced by the change in the interatomic distance as well as possible non-adiabatic transitions between sub- and superradiant states caused by atomic motion can lead not to the anticipated weakening of subradiation effect but to its enhancement.

Abstract: We benchmark the performances of Qrack, an open-source software library for the high-performance classical simulation of (gate-model) quantum computers. Qrack simulates, in the Schr\"odinger picture, the exact quantum state of $n$ qubits evolving under the application of a circuit composed of elementary quantum gates. Moreover, Qrack can also run approximate simulations in which a tunable reduction of the quantum state fidelity is traded for a significant reduction of the execution time and memory footprint. In this work, we give an overview of both simulation methods (exact and approximate), highlighting the main physics-based and software-based techniques. Moreover, we run computationally heavy benchmarks on a single GPU, executing large quantum Fourier transform circuits and large random circuits. Compared with other classical simulators, we report competitive execution times for the exact simulation of Fourier transform circuits with up to 27 qubits. We also demonstrate the approximate simulation of all amplitudes of random circuits acting on 54 qubits with 7 layers at average fidelity higher $\approx 4\%$, a task commonly considered hard without super-computing resources.

Abstract: The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich range of possible quantum Fisher information, only a handful are typically used and studied. This review aims at collecting a number of results scattered in the literature that can be useful to people who begin the study of Fisher information and to those who are already working on it to have a more organic understanding of the topic. Moreover, we complement the review with new results about the relation between Fisher information and physical evolutions. Extending the study done in [1], we prove that all the physically realisable dynamics can be defined solely in terms of their relation with respect to the Fisher information metric. Moreover, other properties as Markovianity, retrodiction or detailed balance can be expressed in the same formalism. These results show a fact that was partially overseen in the literature, namely the inherently dynamical nature of Fisher information.

Abstract: In this work, we migrate the quantum error mitigation technique of Zero-Noise Extrapolation (ZNE) to fault-tolerant quantum computing. We employ ZNE on \emph{logically encoded} qubits rather than \emph{physical} qubits. This approach will be useful in a regime where quantum error correction (QEC) is implementable but the number of qubits available for QEC is limited. Apart from illustrating the utility of a traditional ZNE approach (circuit-level unitary folding) for the QEC regime, we propose a novel noise scaling ZNE method specifically tailored to QEC: \emph{distance scaled ZNE (DS-ZNE)}. DS-ZNE scales the distance of the error correction code, and thereby the resulting logical error rate, and utilizes this code distance as the scaling `knob' for ZNE. Logical qubit error rates are scaled until the maximum achievable code distance for a fixed number of physical qubits, and lower error rates (i.e., effectively higher code distances) are achieved via extrapolation techniques migrated from traditional ZNE. Furthermore, to maximize physical qubit utilization over the ZNE experiments, logical executions at code distances lower than the maximum allowed by the physical qubits on the quantum device are parallelized to optimize device utilization. We validate our proposal with numerical simulation and confirm that ZNE lowers the logical error rates and increases the effective code distance beyond the physical capability of the quantum device. For instance, at a physical code distance of 11, the DS-ZNE effective code distance is 17, and at a physical code distance of 13, the DS-ZNE effective code distance is 21. When the proposed technique is compared against unitary folding ZNE under the constraint of a fixed number of executions of the quantum device, DS-ZNE outperforms unitary folding by up to 92\% in terms of the post-ZNE logical error rate.