QUROPE Quantum Information Processing and Communication in Europe

By leveraging the no-cloning principle of quantum mechanics, unclonable cryptography enables us to achieve novel cryptographic protocols that are otherwise impossible classically. Two most notable examples of unclonable cryptography are quantum copy-protection and unclonable encryption. Despite receiving a lot of attention in recent years, two important open questions still remain: copy-protection for point functions in the plain model, which is usually considered as feasibility demonstration, and unclonable encryption with unclonable indistinguishability security in the plain model. In this work, by relying on previous works of Coladangelo, Liu, Liu, and Zhandry (Crypto'21) and Culf and Vidick (Quantum'22), we establish a new monogamy-of-entanglement property for subspace coset states, which allows us to obtain the following new results:

- We show that copy-protection of point functions exists in the plain model, with different challenge distributions (including arguably the most natural ones).

- We show, for the first time, that unclonable encryption with unclonable indistinguishability security exists in the plain model.

Magic describes the distance of a quantum state to its closest stabilizer state. It is -- like entanglement -- a necessary resource for a potential quantum advantage over classical computing. We study magic, quantified by stabilizer entropy, in a hybrid quantum circuit with projective measurements and a controlled injection of non-Clifford resources. We discover a phase transition between a (sub)-extensive and area law scaling of magic controlled by the rate of measurements. The same circuit also exhibits a phase transition in entanglement that appears, however, at a different critical measurement rate. This mechanism shows how, from the viewpoint of a potential quantum advantage, hybrid circuits can host multiple distinct transitions where not only entanglement, but also other non-linear properties of the density matrix come into play.

We developed a general theoretical approach and a user-ready computer code that permit to study the dynamics of collisional energy transfer and ro-vibrational energy exchange in complex molecule-molecule collisions. The method is a mixture of classical and quantum mechanics. The internal ro-vibrational motion of collision partners is treated quantum mechanically using time-dependent Schrodinger equation that captures many quantum phenomena including state quantization and zero-point energy, propensity and selection rules for state-to-state transitions, quantum symmetry and interference phenomena. A significant numerical speed up is obtained by describing the translational motion of collision partners classically, using the Ehrenfest mean-field trajectory approach. Within this framework a family of approximate methods for collision dynamics is developed. Several benchmark studies for diatomic and triatomic molecules, such as H$_2$O and ND$_3$ collided with He, H$_2$ and D$_2$, show that the results of MQCT are in good agreement with full-quantum calculations in a broad range of energies, especially at high collision energies where they become nearly identical to the full quantum results. Numerical efficiency of the method and massive parallelism of the MQCT code permit us to embrace some of the most complicated collisional systems ever studied, such as C$_6$H$_6$ + He, CH$_3$COOH + He and H$_2$O + H$_2$O. Application of MQCT to the collisions of chiral molecules such as CH$_3$CHCH$_2$O + He, and to the molecule-surface collisions is also possible and will be pursued in the future.

Quantum light sources are crucial foundational components for various quantum technology applications. With the rapid development of quantum technology, there has been a growing demand for materials that are capable of hosting quantum emitters. One such material platform are fluorescent defects in hexagonal boron nitride (hBN) inducing deep sub-levels within the band gap. The question arises if other layered wide bandgap (2D) materials offer similar single photon emitting defects. Here, we investigate and compare the fabrication of quantum emitters in exfoliated multi-layer mica flakes with hBN and other wide bandgap 3D crystals (silicon carbide and gallium nitride) which are known to host quantum emitters. We use our primary fabrication technique of localized electron irradiation using a standard scanning electron microscope. To complement our experimental work, we employ density functional theory simulations to study the atomic structures of intrinsic defects and their photophysical properties. While our fabrication technique can create hBN quantum emitters with a high yield and high single photon purity, it is unable to fabricate emitters in the other solid-state crystals under investigation. This allows us to draw conclusions on the emitter fabrication mechanism, which could be relying on the activation of already present defects by charge state manipulation. We therefore provide an important step toward the identification of hBN emitters and their formation process.

The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for more exotic phases, such as fractons. Intriguingly, for the former, recent work suggests that bulk topological order manifests in a non-local structure in the boundary Hilbert space; however, a concrete understanding of how and where this perspective applies remains limited. Here, we provide an explicit and general framework for understanding the bulk-boundary correspondence in Pauli topological stabilizer codes. We show -- for any boundary termination of any two-dimensional topological stabilizer code -- that the boundary Hilbert space cannot be realized via local degrees of freedom, in a manner precisely determined by the anyon data of the bulk topological order. We provide a simple method to compute this "obstruction" using a well-known mapping to polynomials over finite fields. Leveraging this mapping, we generalize our framework to fracton models in three-dimensions, including both the X-Cube model and Haah's code. An important consequence of our results is that the boundaries of topological phases can exhibit emergent symmetries that are impossible to otherwise achieve without an unrealistic degree of fine tuning. For instance, we show how linear and fractal subsystem symmetries naturally arise at the boundaries of fracton phases.

We introduce a class of quantum non-Markovian processes -- dubbed process trees -- that exhibit polynomially decaying temporal correlations and memory distributed across time scales. This class of processes is described by a tensor network with tree-like geometry whose component tensors are (1) {causality-preserving} maps (superprocesses) and (2) {locality-preserving} temporal change of scale transformations. We show that the long-range correlations in this class of processes tends to originate almost entirely from memory effects, and can accommodate genuinely quantum power-law correlations in time. Importantly, this class allows efficient computation of multi-time correlation functions. To showcase the potential utility of this model-agnostic class for numerical simulation of physical models, we show how it can approximate the strong memory dynamics of the paradigmatic spin-boson model, in term of arbitrary multitime features. In contrast to an equivalently costly matrix product operator (MPO) representation, the ansatz produces a fiducial characterization of the relevant physics. Our work lays the foundation for the development of more efficient numerical techniques in the field of strongly interacting open quantum systems, as well as the theoretical development of a temporal renormalization group scheme.

We propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi index $n\geq1$, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. For $n<1$, however, our proposal predicts a new phase with leading order (in Newton's constant $G$) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over fixed-area states, the difference between the two proposals can be understood to come from the order of optimization: for $n<1$, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to the $n<1$ Renyi entropies.

Quantum information transfer is fundamental for scalable quantum computing in any potential platform and architecture. Hole spin qubits, owing to their intrinsic spin-orbit interaction (SOI), promise fast quantum operations which are fundamental for the implementation of quantum gates. Yet, the influence of SOI in quantum transfer protocols remains an open question. Here, we investigate, using Shortcuts to Adiabaticity, the long-range transfer of hole spin states and quantum distribution of entangled pairs in a semiconductor quantum dot array. We demonstrate that electric field manipulation allows dynamical control of the SOI, enabling simultaneous implementation of quantum gates during the transfer, with the potential to significantly accelerate quantum algorithms. By harnessing the ability to perform quantum gates in parallel with the transfer, we employ dynamical decoupling schemes to focus and preserve the spin state, leading to higher transfer fidelity.

We explore the decoherence of the gapless/critical boundary of a topological order, through interactions with the bulk reservoir of "ancilla anyons." We take the critical boundary of the $2d$ toric code as an example. The intrinsic nonlocal nature of the anyons demands the strong and weak symmetry condition for the ordinary decoherence problem be extended to the strong or weak gauge invariance conditions. We demonstrate that in the $\textit{doubled}$ Hilbert space, the partition function of the boundary is mapped to two layers of the $2d$ critical Ising model with an inter-layer line defect that depends on the species of the anyons causing the decoherence. The line defects associated with the tunneling of bosonic $e$ and $m$ anyons are relevant, and result in long-range correlations for either the $e$ or $m$ anyon respectively on the boundary in the doubled Hilbert space. In contrast, the defect of the $f$ anyon is marginal and leads to a line of fixed points with varying effective central charges, and power-law correlations having continuously varying scaling dimensions. We also demonstrate that decoherence-analogues of Majorana zero modes are localized at the spatial interface of the relevant $e$ and $m$ anyon decoherence channels, which leads to a universal logarithmic scaling of the R\'enyi entropy of the boundary.

The study of percolation phenomena has various applications in natural sciences and, therefore, efficient algorithms have been developed to estimate the corresponding percolation thresholds. For instance, this applies to the widely-used bond-site percolation model for which the Newman-Ziff algorithm enables an efficient simulation. Here, we consider several non-standard percolation models that have applications in measurement-based photonic quantum computing with graph states. We focus on prominent architectures where large-scale graph states are created by fusion networks connecting many small resource states. We investigate percolation models that provide an estimate of the tolerance to photon loss in such systems and we develop efficient algorithms to analyze them through modifications of the Newman-Ziff algorithm. We consider non-adaptive fusion networks with all fusions being performed at once, and adaptive ones where fusions are repeated conditioned on the outcome of previous fusion attempts. We demonstrate our algorithms by using them to characterize several fusion networks and provide the corresponding source code.

Two-way microwave-optical quantum transduction is an essential capability to connect distant superconducting qubits via optical fiber, and to enable quantum networking at a large scale. In Bl\'esin, Tian, Bhave, and Kippenberg's article, ``Quantum coherent microwave-optical transduction using high overtone bulk acoustic resonances" (Phys. Rev. A, 104, 052601 (2021)), they lay out a quantum transduction system that accomplishes this by combining a piezoelectric interaction to convert microwave photons to GHz-scale phonons, and an optomechanical interaction to up-convert those phonons into telecom-band photons using a pump laser set to an adjacent telecom-band tone. In this work, we discuss these coupling interactions from first principles in order to discover what device parameters matter most in determining the transduction efficiency of this new platform, and to discuss strategies toward system optimization for near-unity transduction efficiency, as well as how noise impacts the transduction process.

In addition, we address the post-transduction challenge of separating single photons of the transduced light from a classically bright pump only a few GHz away in frequency by proposing a novel optomechanical coupling mechanism using phonon-photon four-wave mixing via stress-induced optical nonlinearity and its thermodynamic connection to higher-orders of electrostriction. Where this process drives transduction by consuming pairs instead of individual pump photons, it will allow a clean separation of the transduced light from the classically bright pump driving the transduction process.

We explain how the so-called Einstein locality is to be understood in the Schr\"odinger picture of quantum mechanics. This notion is perfectly compatible with the Bell non-locality exhibited by entangled states. Contrary to some beliefs that quantum mechanics is incomplete, it is, in fact, its overcompleteness as exemplified by different pictures of quantum physics, that points to the same underlying reality.

The possibility of using the generator coordinate method (GCM) using hybrid quantum-classical algorithms with reduced quantum resources is discussed. The task of preparing the basis states and calculating the various kernels involved in the GCM is assigned to the quantum computer, while the remaining tasks, such as finding the eigenvalues of a many-body problem, are delegated to classical computers for post-processing the generated kernels. This strategy reduces the quantum resources required to treat a quantum many-body problem. We apply the method to the Lipkin model. Using the permutation symmetry of the Hamiltonian, we show that, ultimately, only two qubits is enough to solve the problem regardless of the particle number. The classical computing post-processing leading to the full energy spectrum can be made using standard generalized eigenvalues techniques by diagonalizing the so-called Hill-Wheeler equation. As an alternative to this technique, we also explored how the quantum state deflation method can be adapted to the GCM problem. In this method, variational principles are iteratively designed to access the different excited states with increasing energies. The methodology proposed here is successfully applied to the Lipkin model with a minimal size of two qubits for the quantum register. The performances of the two classical post-processing approaches with respect to the statistical noise induced by the finite number of measurements and quantum devices noise are analyzed. Very satisfactory results for the full energy spectra are obtained once noise correction techniques are employed.

Microwave quantum information networks require reliable transmission of single photon propagating modes over lossy channels. In this article we propose a microwave noise-less linear amplifier (NLA) suitable to circumvent the losses incurred by a flying photon undergoing an amplitude damping channel (ADC). The proposed model is constructed by engineering a simple one-dimensional four node cluster state. Contrary to conventional NLAs based on quantum scissors (QS), single photon amplification is realized without the need for photon number resolving detectors (PNRDs). Entanglement between nodes comprising the device's cluster is achieved by means of a controlled phase gate (CPHASE). Furthermore, photon measurements are implemented by quantum non demolition detectors (QNDs), which are currently available as a part of circuit quantum electrodynamics (cQED) toolbox. We analyze the performance of our device practically by considering detection inefficiency and dark count probability. We further examine the potential usage of our device in low power quantum sensing applications and remote secret key generation (SKG). Specifically, we demonstrate the device's ability to prepare loss-free resources offline, and its capacity to overcome the repeater-less bound of SKG. We compare the performance of our device against a QS-NLA for the aforementioned applications, and highlight explicitly the operating conditions under which our device can outperform a QS-NLA. The proposed device is also suitable for applications in the optical domain.

Quantum approximate optimization algorithm (QAOA) has attracted much attention as an algorithm that has the potential to efficiently solve combinatorial optimization problems. Among them, a fermionic QAOA (FQAOA) for solving constrained optimization problems has been developed [Yoshioka, Sasada, Nakano, and Fujii, Phys. Rev. Research vol. 5, 023071, 2023]. In this algorithm, the constraints are essentially imposed as fermion number conservation at arbitrary approximation level. We take the portfolio optimization problem as an application example and propose a new driver Hamiltonian on an one-dimensional cyclic lattice. Our FQAOA with the new driver Hamiltonian reduce the number of gate operations in quantum circuits. Experiments on a trapped-ion quantum computer using 16 qubits on Amazon Braket demonstrates that the proposed driver Hamiltonian effectively suppresses noise effects compared to the previous FQAOA.

Simulation of the single-particle tunneling problem by means of the Suzuki-Trotter approximation (STA) is analyzed. Considered is a particle hopping across a chain of sites in presence of a smooth position-dependent potential profile with several local minima that arrange a tunneling problem between the localized states in different minima. The STA error is found to manifest itself in three ways: i) perturbative energy shifts, ii) nonperturbartive renormalization of the tunneling rates, and iii) perturbative leakage of the total probability to other states. Generally, the first type of error is the most essential, as detuning of the tunneling resonance has to be compared with exponentially small tunneling rates. In absence of detuning (e.g. if the resonance is protected by symmetry), STA leads to exponential enhancement of the tunneling rates. The last type of error classifies the overall defect in the wave function and delineates the region of sufficiently weak distortion of the wave function due to STA. The conducted analysis confirms the naive criteria of applicability $\max\{T,P\}\ll\delta t^{-1}$ (with $T,P$ being the typical scales of kinetic and potential terms, respectively), while also revealing the structure of error and its behavior with system parameters. Analysis of the case of large Trotter step is also performed, with the main result being the reconstruction of low-energy spectrum due to coupling between states with energy difference close to $2\pi/\delta t$. The connection of the obtained results with rigorous upper error bounds on the STA error is discussed, with particular emphasis on why these rigorous bounds are not always saturated. We also point out that the proposed problem can be directly implemented on existing quantum devices [arXiv:2012.00921]. In particular, we give a detailed description of an experimental design that demonstrates the described physics.

We simulate the dynamics of systems with $N$ = 1-20 qubits coupled to a cavity in order to assess their potential for quantum metrology of a parameter in the open systems limit. The qubits and the cavity are both allowed to have losses and the system is studied under various coupling strength regimes. The focus is primarily on the coupling between the qubits using the quantum Fisher information as the measured parameter. Some results on estimating the qubit-cavity detuning parameter are also presented. We investigate the scaling of the uncertainty in the estimate of the qubit-cavity coupling with the number of qubits and for different initial states of the qubits that act as the quantum probe. As initial probe states, we consider Dicke states with varying excitation numbers, the GHZ state, and separable X-polarized states. It is shown that in the strong coupling regime, i.e., when the coupling between the qubits and the cavity is greater than the decay parameters of both the qubits and the cavity, Dicke states with a large excitation number can achieve the Heisenberg limit, with the precision scaling improving as the excitation number increases. A particularly intriguing finding of our study is that in the weak coupling regime, as well as in situations where either the qubit or cavity decay parameters exceed the coupling, the separable $X$-polarized state is the best in terms of scaling and is even able to achieve the Heisenberg limit in these lossy regimes for the range of $N$ considered.

Liouville theorem (LT) reveals robust incompressibility of distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., LT is only conditionally true (e.g., for perfect Harmonic potential). We develop quantum Liouville theorem (rigorous incompressibility) for arbitrary potentials (interacting or not) in Hamiltonians. Haar measure, instead of symplectic measure dp^dq used in Wigner's scheme, plays a central role. The argument is based on general measure theory, independent of specific spaces or coordinates. Comparison of classical and quantum is made: for instance, we address why Haar measure and metric preservation do not work in the classical case. Applications of theorems in statistics, topological phase transition, ergodic theory, etc. are discussed.

The optimization of system parameters is a ubiquitous problem in science and engineering. The traditional approach involves setting to zero the partial derivatives of the objective function with respect to each parameter, in order to extract the optimal solution. However, the system parameters often take the form of complex matrices. In such situations, conventional methods become unwieldy. The `Wirtinger Calculus' provides a relatively simple methodology for such optimization problems. In this tutorial, we provide a pedagogical introduction to Wirtinger Calculus. To illustrate the utility of this framework in quantum information theory, we also discuss a few example applications.

Near-concentric cavities are excellent tools for enhancing atom--light interaction as they combine a small mode volume with a large optical access for atom manipulation. However, they are sensitive to longitudinal and transverse misalignment. To address this sensitivity, we present a compact near-concentric optical cavity system with a residual cavity length variation $\delta L_{C, rms}$=36(9) pm. A key part of this system is a cage-like tensegrity mirror support structure that allows to correct for longitudinal and transverse misalignment. The system is stable enough to allow the use of mirrors with higher cavity finesse to enhance the atom--light coupling strength in cavity-QED applications.