QUROPE Quantum Information Processing and Communication in Europe

We present the asymptotic analysis of the quantum two-port interferometer in the $n \rightarrow \infty$ limit of $n$ partially indistinguishable photons. Using the unitary-unitary duality between port and inner-mode degrees of freedom, the probability distribution of output port counts can be decomposed as a sum of contributions from independent channels, each associated to a spin-$j$ representation of $SU(2)$ and, in this context, to $2 j$ effectively indistinguishable photons in the channel. Our main result is that the asymptotic output distribution is dominated by the $O(\sqrt{n})$ channels around a certain $j^*$ that depends on the degree of indistinguishability. The asymptotic form is essentially the doubly-humped semi-classical envelope of the distribution that would arise from $2 j^*$ indistinguishable photons, and which reproduces the corresponding classical intensity distribution.

We consider the double scaling limit of a model of Pauli spin operators recently studied in Hanada et al. [1] and evaluate the moments of the Hamiltonian by the chord diagrams. We find that they coincide with those of the double scaled SYK model, which makes it more likely that this model may play an important role in the study of holography. We compare the model with another previously studied model. We also speculate on the form of the Hamiltonian in the double scaling limit.

The bosonic Josephson junction, one of the maximally simple models for periodic-driven many-body systems, has been intensively studied in the past two decades. Here, we revisit this problem with five different methods, all of which have solid theoretical reasoning. We find that to the order of $\omega^{-2}$ ($\omega$ is the modulating frequency), these approaches will yield slightly different Floquet Hamiltonians. In particular, the parameters in the Floquet Hamiltonians may be unchanged, increased, or decreased, depending on the approximations used. Especially, some of the methods generate new interactions, which still preserve the total number of particles; and the others do not. The validity of these five effective models is verified using dynamics of population imbalance and self-trapping phase transition. In all results, we find the method by first performing a unitary rotation to the Hamiltonian will have the highest accuracy. The difference between them will become significate when the modulating frequency is comparable with the driving amplitude. The results presented in this work indicate that the analysis of the Floquet Hamiltonian has some kind of subjectivity, which will become an important issue in future experiments with the increasing of precision. We demonstrate this physics using a Bose-Josephson junction, and it is to be hoped that the validity of these methods and their tiny differences put forward in this work can be verified in realistic experiments in future using quantum simulating platforms, including but not limited to ultracold atoms.

Typical fermion algorithms require the computation (or sampling) of the fermion determinant. We focus instead on cluster algorithms which do not involve the determinant and involve a more physically relevant sampling of the configuration space. We develop new cluster algorithms and design classes of models for fermions coupled to $\mathbb{Z}_2$ and $U(1)$ gauge fields that are amenable to being simulated by these cluster algorithms in a sign-problem free way. Such simulations should contain rich phase diagrams and are particularly relevant for quantum simulator experiments.

Nonlinear action of the group of spatial rotations on commuting components of a position operator of a massless particle (Hawton operator) is studied. Using Callan, Coleman, Wess and Zumino method it is shown that coordinates which linearize this action correspond to the Pryce operator with non-commuting components.

In this work, we present a quantum circuit for a binary classification prediction algorithm using a random forest model. The quantum prediction algorithm is presented in our previous works. We construct a circuit and implement it using qiskit tools (python module for quantum programming). One of our goals is reducing the number of basic quantum gates (elementary gates). The set of basic quantum gates which we use in this work consists of single-qubit gates and a controlled NOT gate. The number of CNOT gates in our circuit is estimated by $O(2^{n+2h+1})$ , when trivial circuit decomposition techniques give $O(4^{|X|+n+h+2})$ CNOT gates, where $n$ is the number of trees in a random forest model, $h$ is a tree height and $|X|$ is the length of attributes of an input object $X$. The prediction process returns an index of the corresponding class for the input $X$.

This study investigates the dynamic behavior of polaritons in an optical cavity containing one million molecules, emphasizing the influence of molecular rotation and level disorder on the coupling between molecules and photons. Through rigorous theoretical simulations and numerical analyses, we systematically explore the formation and spectral characteristics of polaritons in this complex environment. Our findings reveal that the rotational motion of molecules significantly affects the electromagnetic field distribution within the cavity, leading to distinct alterations in polariton properties. Simultaneously, the presence of level disorder induces diverse energy level structures, influencing the energy distribution of polaritons. The comprehensive examination of these factors provides valuable insights into the intricate interplay between molecules and photons in large-scale cavity systems. This research not only advances the fundamental understanding of molecular-photon coupling but also offers theoretical guidance for practical applications in the design and exploration of optical cavities.

In the paper, we investigate Two Sets Intersection problem. Assume that we have two sets that are subsets of n objects. Sets are presented by two predicates that show which of n objects belong to these sets. We present a quantum algorithm that finds an element from the two sets intersection. It is a modification of the well-known Grover's search algorithm that uses two Oracles with access to the predicates. The algorithm is faster than the naive application of Grover's search.

We perform an experimental investigation of Quantum Discord with Spin-Orbit X-states. These states are prepared through the incoherent superposition of different laser beans, where a two-level system is encoded in polarization and the first-order Hermitian-Gaussian modes, as proposed in Phys. Rev. A 103,0022411 (2022). We characterize different classes of spin-orbit X-states by performing an all-optical tomography for polarization and first-order transverse mode degrees of freedom. We also perform a study on the dependence of Discord with respect to the Fidelity of spin-orbit modes, revealing that Discord is very sensitive to incoherent noise. Our experimental results align with the theoretical predictions of Quantum Discord when accounting for the effect of fidelity. These results reinforce the spin-orbit modes as an important platform for quantum information processing. On the other hand, the need of astigmatic optical elements to implement unitary operations required by quantum information protocols implies in a loss of fidelity and quantum correlations. Alternative methods to manipulate spin-orbit modes are welcome.

Quantum sensors offer control flexibility during estimation by allowing manipulation by the experimenter across various parameters. For each sensing platform, pinpointing the optimal controls to enhance the sensor's precision remains a challenging task. While an analytical solution might be out of reach, machine learning offers a promising avenue for many systems of interest, especially given the capabilities of contemporary hardware. We have introduced a versatile procedure capable of optimizing a wide range of problems in quantum metrology, estimation, and hypothesis testing by combining model-aware reinforcement learning (RL) with Bayesian estimation based on particle filtering. To achieve this, we had to address the challenge of incorporating the many non-differentiable steps of the estimation in the training process, such as measurements and the resampling of the particle filter. Model-aware RL is a gradient-based method, where the derivatives of the sensor's precision are obtained through automatic differentiation (AD) in the simulation of the experiment. Our approach is suitable for optimizing both non-adaptive and adaptive strategies, using neural networks or other agents. We provide an implementation of this technique in the form of a Python library called qsensoropt, alongside several pre-made applications for relevant physical platforms, namely NV centers, photonic circuits, and optical cavities. This library will be released soon on PyPI. Leveraging our method, we've achieved results for many examples that surpass the current state-of-the-art in experimental design. In addition to Bayesian estimation, leveraging model-aware RL, it is also possible to find optimal controls for the minimization of the Cram\'er-Rao bound, based on Fisher information.

To control and measure the state of a quantum system it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement back-action, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multi-mode element -- an artificial molecule -- with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential non-linear modes, one of which is flux-insensitive and used as the protected qubit mode. The second mode is flux-tunable and serves via a cross-Kerr type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed.

The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if the logical error rate diminishes with system size. Here we unravel their relations and propose a unified framework to extract an intrinsic error threshold from the approximate QEC condition, which could upper bound other decoder-dependent error thresholds. Our proof establishes that relative entropy, effectively measuring deviations from exact QEC conditions, serves as the order parameter delineating the transition from asymptotic recoverability to unrecoverability. Consequently, we establish a unified framework for determining the error threshold across both exact and approximate QEC codes, addressing errors originating from noise channels as well as those from code space imperfections. This result sharpens our comprehension of error thresholds across diverse QEC codes and error models.

We analyze the time-dependent free energy functionals of the semiclassical one-dimensional Bose-Hubbard chain. We first review the weakly chaotic dynamics and the consequent early-time anomalous diffusion in the system. The anomalous diffusion is robust, appears with strictly quantized coefficients, and persists even for very long chains (more than hundred sites), crossing over to normal diffusion at late times. We identify fast (angle) and slow (action) variables and thus consider annealed and quenched partition functions, corresponding to fixing the actions and integrating over the actions, respectively. We observe the leading quantum effects in the annealed free energy, whereas the quenched energy is undefined in the thermodynamic limit, signaling the absence of thermodynamic equilibrium in the quenched regime. But already the leading correction away from the quenched regime reproduces the annealed partition function exactly. This encapsulates the fact that in both slow- and fast-chaos regime both the anomalous and the normal diffusion can be seen (though at different times).

Random numbers play a crucial role in numerous scientific applications. Source-independent quantum random number generators (SI-QRNGs) can offer true randomness by leveraging the fundamental principles of quantum mechanics, eliminating the need for a trusted source. Silicon photonics shows great promise for QRNG due to its benefits in miniaturization, cost-effective device manufacturing, and compatibility with CMOS microelectronics. In this study, we experimentally demonstrate a silicon-based discrete variable SI-QRNG. Using a well-calibrated chip and an optimized parameter strategy, we achieve a record-breaking random number generation rate of 7.9 Mbits/s. Our research paves the way for integrated SI-QRNGs.

In this work, we consider a fundamental task in quantum many-body physics - finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value of sums of geometrically local observables by learning from data. For short-range gapped Hamiltonians, a sample complexity that is logarithmic in the number of qubits and quasipolynomial in the error was obtained. Here we extend these results beyond the local requirements on both Hamiltonians and observables, motivated by the relevance of long-range interactions in molecular and atomic systems. For interactions decaying as a power law with exponent greater than twice the dimension of the system, we recover the same efficient logarithmic scaling with respect to the number of qubits, but the dependence on the error worsens to exponential. Further, we show that learning algorithms equivariant under the automorphism group of the interaction hypergraph achieve a sample complexity reduction, leading in particular to a constant number of samples for learning sums of local observables in systems with periodic boundary conditions. We demonstrate the efficient scaling in practice by learning from DMRG simulations of $1$D long-range and disordered systems with up to $128$ qubits. Finally, we provide an analysis of the concentration of expectation values of global observables stemming from central limit theorem, resulting in increased prediction accuracy.

In this work, we analyze the local certification of unitary quantum channels and von Neumann measurements, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel and von Neumann measurement, operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement. We introduce a new mathematical structure q-product numerical range, which is a natural generalization of the q-numerical range, used to obtain result, when dealing with one system. In our findings, we employ the q-product numerical range as a pivotal tool, leveraging its properties to derive our results and minimize the probability of type II error under the constraint of type I error probability. We show a fundamental dependency: for local certification, the tensor product structure inherently manifests, necessitating the transition from q-numerical range to q-product numerical range.

Surface codes are versatile quantum error-correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used Pauli $X$ or Pauli $Z$ operators in a square structure, these codes can be improved by rotating the lattice or incorporating a mix of generators in the XZZX variant. However, a comprehensive theoretical analysis of the logical error rate for these variants has been lacking. To address this gap, we present theoretical formulas based on recent advancements in understanding the weight distribution of stabilizer codes. For example, over an asymmetric channel with asymmetry $A=10$ and a physical error rate $p \to 0$, we observe that the logical error rate asymptotically approaches $p_\mathrm{L} \to 10 p^2$ for the rotated $[[9,1,3]]$ XZZX code and $p_\mathrm{L} \to 18.3 p^2$ for the $[[13,1,3]]$ surface code. Additionally, we observe a particular behavior regarding rectangular lattices in the presence of asymmetric channels. Our findings demonstrate that implementing both rotation and XZZX modifications simultaneously can lead to suboptimal performance. Thus, in scenarios involving a rectangular lattice, it is advisable to avoid using both modifications simultaneously. This research enhances our theoretical understanding of the logical error rates for XZZX and rotated surface codes, providing valuable insights into their performance under different conditions.

We propose a time-crystal model based on a disordered interacting long-range spin chain where the periodic swapping of nearby spin couples is applied. This protocol can be applied to systems with any local spin magnitude $s$ and in principle also to systems with nonspin (fermionic or bosonic) local Hilbert space. We explicitly consider the cases $s = 1/2$ and $s = 1$, using analytical and numerical methods to show that the time-crystal behavior appears in a range of parameters. In particular, we study the persistence of period-doubling oscillations in time, the properties of the Floquet spectrum ($\pi$-spectral pairing and correlations of the Floquet states), and introduce a quantity (the local imbalance) to assess what initial states give rise to a period-doubling dynamics. We also use a probe of quantum integrability/ergodicity to understand the interval of parameters where the system does not thermalize, and a nontrivial persistent period-doubling behavior is possible.

We study entanglement distillation and dilution of states and channels in the single-shot regime. With the help of a recently introduced conversion distance, we provide compact closed-form expressions for the dilution and distillation of pure states and show how this can be used to efficiently calculate these quantities on multiple copies of pure states. These closed-form expressions also allow us to obtain second-order asymptotics. We then prove that the epsilon-single-shot entanglement cost of mixed states is given exactly in terms of an expression containing a suitably smoothed version of the conditional max-entropy. For pure states, this expression reduces to the smoothed max-entropy of the reduced state. Based on these results, we bound the single-shot entanglement cost of channels. We then turn to the one-way entanglement distillation of states and channels and provide bounds in terms of a quantity we denote coherent information of entanglement.

The evolution of molecular quantum states is central to many research areas, including chemical reaction dynamics, precision measurement, and molecule based quantum technology. Details of the evolution is often obscured, however, when measurements are performed on an ensemble of molecules, or when the molecules are subjected to environmental perturbations. Here, we report real-time observations of quantum jumps between rotational states of a single molecule driven by thermal radiation, and present techniques to maintain the molecule in a chosen state over a timescale of tens of seconds. Molecular state detection is achieved nondestructively through quantum-logic spectroscopy, in which information on the state of the molecule is transferred to a co-trapped "logic" atomic ion for readout. Our approaches for state detection and manipulation are applicable to a wide range of molecular ion species, thereby facilitating their use in many fields of study including quantum science, molecular physics, and ion-neutral chemistry. The measured rotational transition rates show anisotropy in the background thermal radiation, which points to the possibility of using a single molecular ion as an in-situ probe for the strengths of ambient fields at the relevant transition frequencies.