QUROPE Quantum Information Processing and Communication in Europe

Image classification is a crucial task in machine learning. In recent years, this field has witnessed rapid development, with a series of image classification models being proposed and achieving state-of-the-art (SOTA) results. Parallelly, with the advancement of quantum technologies, quantum machine learning has attracted a lot of interest. In particular, a class of algorithms known as variational quantum algorithms (VQAs) has been extensively studied to improve the performance of classical machine learning. In this paper, we propose a novel image classification framework using VQAs. The major advantage of our framework is the elimination of the need for the global pooling operation typically performed at the end of classical image classification models. While global pooling can help to reduce computational complexity, it often results in a significant loss of information. By removing the global pooling module before the output layer, our approach allows for effectively capturing more discriminative features and fine-grained details in images, leading to improved classification performance. Moreover, employing VQAs enables our framework to have fewer parameters compared to the classical framework, even in the absence of global pooling, which makes it more advantageous in preventing overfitting. We apply our method to different SOTA image classification models and demonstrate the superiority of the proposed quantum architecture over its classical counterpart through a series of experiments on public datasets.

Leveraging the extraordinary phenomena of quantum superposition and quantum correlation, quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers. This paper tackles two pivotal challenges in the realm of quantum computing: firstly, the development of an effective encoding protocol for translating classical data into quantum states, a critical step for any quantum computation. Different encoding strategies can significantly influence quantum computer performance. Secondly, we address the need to counteract the inevitable noise that can hinder quantum acceleration. Our primary contribution is the introduction of a novel variational data encoding method, grounded in quantum regression algorithm models. By adapting the learning concept from machine learning, we render data encoding a learnable process. Through numerical simulations of various regression tasks, we demonstrate the efficacy of our variational data encoding, particularly post-learning from instructional data. Moreover, we delve into the role of quantum correlation in enhancing task performance, especially in noisy environments. Our findings underscore the critical role of quantum correlation in not only bolstering performance but also in mitigating noise interference, thus advancing the frontier of quantum computing.

Random noise and crosstalk are the major factors limiting the readout fidelity of superconducting qubits, especially in multi-qubit systems. Neural networks trained on labeled measurement data have proven useful in mitigating the effects of crosstalk at readout, but their effectiveness is currently limited to binary discrimination of joint-qubit states by their architectures. We propose a time-resolved modulated neural network that adapts to full-state tomography of individual qubits, enabling time-resolved measurements such as Rabi oscillations. The network is scalable by pairing a module with each qubit to be detected for joint-state tomography. Experimental results demonstrate a 23% improvement in fidelity under low signal-to-noise ratio, along with a 49% reduction in variance in Rabi measurements.

Uncertainty principle is one of the most essential features in quantum mechanics and plays profound roles in quantum information processing. We establish tighter summation form uncertainty relations based on metric-adjusted skew information via operator representation of observables, which improve the existing results. By using the methodologies of sampling coordinates of observables, we also present tighter product form uncertainty relations. Detailed examples are given to illustrate the advantages of our uncertainty relations.

We investigate a non-interacting many-particle bosonic system, placed in a slightly asymmetric double-well potential. We first consider the dynamics of a single particle and determine its time-dependent probabilities to be in the left or the right well of the potential. These probabilities obey the standard Josephson equations, which in their many-particle interpretation also describe a globally coherent system, such as a Bose-Einstein condensate. This system exhibits the widely studied Josephson oscillations of the population imbalance between the wells. In our study we go beyond the regime of global coherence by developing a formalism based on an effective density matrix. This formalism gives rise to a generalization of Josephson equations, which differ from the standard ones by an additional parameter, that has the meaning of the degree of fragmentation. We first consider the solution of the generalized Josephson equations in the particular case of thermal equilibrium at finite temperatures, and extend our discussion to the non-equilibrium regime afterwards. Our model leads to a constraint on the maximum amplitude of Josephson oscillations for a given temperature and the total number of particles. A detailed analysis of this constraint for typical experimental scenarios is given.

Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded operators remains unclear. Here, we present a general theory for error estimation, including higher-order product formulas, with explicit input state dependency. Our approach overcomes two limitations of the existing operator-norm estimates in the literature. First, previous bounds are too pessimistic as they quantify the worst-case scenario. Second, previous bounds become trivial for unbounded operators and cannot be applied to a wide class of Trotter scenarios, including atomic and molecular Hamiltonians. Our method enables analytical treatment of Trotter errors in chemistry simulations, illustrated through a case study on the hydrogen atom. Our findings reveal: (i) for states with fat-tailed energy distribution, such as low-angular-momentum states of the hydrogen atom, the Trotter error scales worse than expected (sublinearly) in the number of Trotter steps; (ii) certain states do not admit an advantage in the scaling from higher-order Trotterization, and thus, the higher-order Trotter hierarchy breaks down for these states, including the hydrogen atom's ground state; (iii) the scaling of higher-order Trotter bounds might depend on the order of the Hamiltonians in the Trotter product for states with fat-tailed energy distribution. Physically, the enlarged Trotter error is caused by the atom's ionization due to the Trotter dynamics. Mathematically, we find that certain domain conditions are not satisfied by some states so higher moments of the potential and kinetic energies diverge. Our analytical error analysis agrees with numerical simulations, indicating that we can estimate the state-dependent Trotter error scaling genuinely.

We investigate both theoretically and numerically the wavepacket's dynamics in momentum space for a Floquet non-Hermitian system with a periodically-kicked driven potential. We have deduced the exact expression of a time-evolving wavepacket under the condition of quantum resonance. With this analytical expression, we can investigate thoroughly the temporal behaviors of the directed transport, energy diffusion and quantum scrambling. We find interestingly that, by tuning the relative phase between the real part and imaginary part of the kicking potential, one can manipulate the directed propagation, energy diffusion and quantum scrambling efficiently: when the phase equals to $\pi/2$, we observe a maximum directed current and energy diffusion, while a minimum scrambling phenomenon protected by the $\mathcal{PT}$-symmetry; when the phase is $\pi$, both the directed transport and the energy diffusion are suppressed, in contrast, the quantum scrambling is enhanced by the non-Hermiticity. Possible applications of our findings are discussed.

We conduct a theoretical investigation on the existence of Barren Plateaus for alternated disentangled UCC (dUCC) ansatz, a relaxed version of Trotterized UCC ansatz. In the infinite depth limit, we prove that if only single excitations are involved, the energy landscape of any electronic structure Hamiltonian concentrates polynomially. In contrast, if there are additionally double excitations, the energy landscape concentrates exponentially, which indicates the presence of BP. Furthermore, we perform numerical simulations to study the finite depth scenario. Based on the numerical results, we conjecture that the widely used first-order Trotterized UCCSD and $k$-UpCCGSD when $k$ is a constant suffer from BP. Contrary to previous perspectives, our results suggest that chemically inspired ansatz can also be susceptible to BP. Furthermore, our findings indicate that while the inclusion of double excitations in the ansatz is essential for improving accuracy, it may concurrently exacerbate the training difficulty.

A quantum measurement involves energy exchanges between the system to be measured and the measuring apparatus. Some of them involve energy losses, for example because energy is dissipated into the environment or is spent in recording the measurement outcome. Moreover, these processes take time. For this reason, these exchanges must be taken into account in the analysis of a quantum measurement engine, and set limits to its efficiency and power. We propose a quantum engine based on a spin 1/2 particle in a magnetic field and study its fundamental limitations due to the quantum nature of the evolution. The coupling with the electromagnetic vacuum is taken into account and plays the role of a measurement apparatus. We fully study its dynamics, work, power and efficiency.

Systems of interacting bosons in double-well potentials, modeled by two-site Bose-Hubbard models, are of significant theoretical and experimental interest and attracted intensive studies in contexts ranging from many-body physics and quantum dynamics to the onset of quantum chaos. In this work we systematically study a kicked two-site Bose-Hubbard model (Bose-Hubbard dimer) with the on-site potential difference being periodically modulated. Our model can be equivalently represented as a kicked Lipkin-Meshkov-Glick model and thus displays different dynamical behaviors from the kicked top model. By analyzing spectral statistics of Floquet operator, we unveil that the system undergoes a transition from regularity to chaos with increasing the interaction strength. Then based on semiclassical approximation and the analysis of R\'{e}nyi entropy of coherent states in the basis of Floquet operator eigenstates, we reveal the local chaotic features of our model, which indicate the existence of integrable islands even in the deep chaotic regime. The semiclassical analysis also suggests that the system in chaotic regime may display different dynamical behavior depending on the choice of initial states. Finally, we demonstrate that dynamical signatures of chaos can be manifested by studying dynamical evolution of local operators and out of time order correlation function as well as the entanglement entropy. Our numerical results exhibit the richness of dynamics of the kicked Bose-Hubbard dimer in both regular and chaotic regimes as the initial states are chosen as coherent spin states located in different locations of phase space.

We study the quantum metric in a driven Tavis-Cummings model, comprised of multiple qubits interacting with a quantized photonic field. The parametrical driving of the photonic field breaks the system's U(1) symmetry down to a ${\rm Z}_2$ symmetry, whose spontaneous breaking initiates a superradiant phase transition. We analytically solved the eigenenergies and eigenstates, and numerically simulated the system behaviors near the critical point. The critical behaviors near the superradiant phase transition are characterized by the quantum metric, defined in terms of the response of the quantum state to variation of the control parameter. In addition, a quantum metrological protocol based on the critical behaviors of the quantum metric near the superradiant phase transition is proposed, which enables greatly the achievable measurement precision.

A novel method has been devised to compute the Local Integrals of Motion (LIOMs) for a one-dimensional many-body localized system. In this approach, a class of optimal unitary transformations is deduced in a tensor-network formalism to diagonalize the Hamiltonian of the specified system. To construct the tensor network, we utilize the eigenstates of the subsystems Hamiltonian to attain the desired unitary transformations. Subsequently, we optimize the eigenstates and acquire appropriate unitary localized operators that will represent the LIOMs tensor network. The efficiency of the method was assessed and found to be both fast and almost accurate. In framework of the introduced tensor-network representation, we examine how the entanglement spreads along the considered many-body localized system and evaluate the outcomes of the approximations employed in this approach. The important and interesting result is that in the proposed tensor network approximation, if the length of the blocks is greater than the length of localization, then the entropy growth will be linear in terms of the logarithmic time. Also, it has been demonstrated that, the entanglement can be calculated by only considering two blocks next to each other, if the Hamiltonian has been diagonalized using the unitary transformation made by the provided tensor-network representation.

We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of effective sparsity among the matrix elements, such ensembles can serve as good models for a wide range of phase transitions e.g. localization to delocalization in non-Hermitian systems or Hermitian to non-Hermitian one. Our analysis reveals a rich behavior hidden beneath the spectral statistics e.g. a crossover of the spectral statistics from Poisson to Ginibre universality class with changing variances for finite matrix size, an abrupt transition for infinite matrix size and the role of complexity parameter, a single functional of all system parameters, as a criteria to determine critical point. We also confirm the theoretical predictions in \cite{psnh}, regarding the universality of the spectral statistics in non-equilibrium regime of non-Hermitian systems characterized by the complexity parameter.

Quantum computing has been widely applied in various fields, such as quantum physics simulations, quantum machine learning, and big data analysis. However, in the domains of data-driven paradigm, how to ensure the privacy of the database is becoming a vital problem. For classical computing, we can incorporate the concept of differential privacy (DP) to meet the standard of privacy preservation by manually adding the noise. In the quantum computing scenario, researchers have extended classic DP to quantum differential privacy (QDP) by considering the quantum noise. In this paper, we propose a novel approach to satisfy the QDP definition by considering the errors generated by the projection operator measurement, which is denoted as shot noises. Then, we discuss the amount of privacy budget that can be achieved with shot noises, which serves as a metric for the level of privacy protection. Furthermore, we provide the QDP of shot noise in quantum circuits with depolarizing noise. Through numerical simulations, we show that shot noise can effectively provide privacy protection in quantum computing.

The Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions are indispensable tools in quantum optics. However, although mathematical relations between them are well established, not much is known about their operational connection. In this paper, we prove that a single composition of finite-strength quantum limited amplifier and attenuator channels, known for their noise-adding properties, turns the Glauber-Sudarshan distribution of any input operator into its Wigner distribution, and its Wigner distribution into its Husimi distribution. As we dissect, the considered process, which can be performed in a quantum optical laboratory with relative ease, may be interpreted as realizing a quantum-to-classical transition.

We introduce a family of quantized field states that can perform exact (entanglement- and error-free) rotations of a two-level atom starting from a specific state on the Bloch sphere. We discuss the similarities and differences between these states and the recently-introduced "transcoherent states." Our field states have the property that they are left unchanged after the rotation, and we find they are the asymptotic states obtained when a field interacts with a succession of identically prepared ancillary atoms. Such a scheme was recently proposed [npj Quantum Information 3:17 (2017)] as a way to "restore" a field state after its interaction with a two-level atom, so as to reuse it afterwards, thus reducing the energy requirements for successive quantum logical operations. We generalize this scheme to find optimal pulses for arbitrary rotations, and also study analytically what happens if the ancillas are in a mixed, rather than a pure state. Consistent with the numerical results in the original proposal, we find that as long as the ancilla preparation error is small (of the order of $1/\bar n$, where $\bar n$ is the average number of atoms in the pulses considered) it will introduce only higher-order errors in the performance of the restored pulse.

We present the very first demonstration of a maser utilizing silicon vacancies (VSi) within 4H silicon carbide (SiC). Leveraging an innovative feedback-loop technique, we elevate the resonator's quality factor, enabling maser operation even above room temperature. The SiC maser's broad linewidth showcases its potential as an exceptional preamplifier, displaying measured gain surpassing 10dB and simulations indicating potential amplification exceeding 30dB. By exploiting the relatively small zero-field splitting (ZFS) of VSi in SiC, the amplifier can be switched into an optically-pumped microwave photon absorber, reducing the resonator's mode temperature by 35 K below operating conditions. This breakthrough holds promise for quantum computing advancements and fundamental studies in cavity quantum electrodynamics. Our findings highlight SiC's transformative potential in revolutionizing contemporary microwave technologies.

We consider a quantum junction described by a 1+1-dimensional boundary conformal field theory (BCFT). Our analysis focuses on correlations emerging at finite temperature, achieved through the computation of entanglement measures. Our approach relies on characterizing correlation functions of twist fields using BCFT techniques. We provide non-perturbative predictions for the crossover between low and high temperatures. An intriguing interplay between bulk and boundary effects, associated with the bulk/boundary scaling dimensions of the fields above, is found. In particular, the entanglement entropy is primarily influenced by bulk thermal fluctuations, exhibiting extensiveness for large system sizes with a prefactor independent of the scattering properties of the defect. In contrast, negativity is governed by fluctuations across the entangling points only, adhering to an area law; its value depends non-trivially on the defect, and it diverges logarithmically as the temperature is decreased. To validate our predictions, we numerically check them for free fermions on the lattice, finding good agreement.

We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the Magnus expansion is the appearance of a commutator term which leads to prohibitively long circuits. We present a technique for eliminating this commutator and find that a single time-step of the resulting algorithm is only marginally costlier than that required for time-stepping with a time-independent Hamiltonian, requiring only three additional single-qubit layers. For a large class of Hamiltonians appearing in liquid-state nuclear magnetic resonance (NMR) applications, we further exploit symmetries of the Hamiltonian and achieve a surprising reduction in the expansion, whereby a single time-step of our fourth-order method has a circuit structure and cost that is identical to that required for a fourth-order Trotterized time-stepping procedure for time-independent Hamiltonians. Moreover, our algorithms are able to take time-steps that are larger than the wavelength of oscillation of the time-dependent Hamiltonian, making them particularly suited for highly-oscillatory controls. The resulting quantum circuits have shorter depths for all levels of accuracy when compared to first and second-order Trotterized methods, as well as other fourth-order Trotterized methods, making the proposed algorithm a suitable candidate for simulation of time-dependent Hamiltonians on near-term quantum devices.

Quantum error correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain errors that arise during quantum computation. The latter technique is suitable to correct correlated errors with certain symmetries, whilst the former to correct independent errors. The concatenation of a QECC and DFS code results in a degenerate code that splits into actively and passively correcting parts, with the degeneracy impacting either part, leading to degenerate errors as well as degenerate stabilizers. The concatenation of the two types of code can aid universal fault-tolerant quantum computation when a mix of correlated and independent errors is encountered. In particular, we show that for sufficiently strongly correlated errors, the concatenation with the DFS as the inner code provides better entanglement fidelity, whereas for sufficiently independent errors, the concatenation with QECC as the inner code is preferable. As illustrative examples, we examine in detail the concatenation of a 2-qubit DFS code and a 3-qubit repetition code or 5-qubit Knill-Laflamme code, under independent and correlated errors.