QUROPE Quantum Information Processing and Communication in Europe

Quantum electronics is significantly involved in the development of the field of quantum information processing. In this domain, the growth of Blind Quantum Source Separation and Blind Quantum Process Tomography has led, within the formalism of the Hilbert space, to the introduction of the concept of a Random-Coefficient Pure State, or RCPS: the coefficients of its development in the chosen basis are random variables. This paper first describes an experimental situation necessitating its introduction. While the von Neumann approach to a statistical mixture considers statistical properties of an observable, in the presence of an RCPS one has to manipulate statistical properties of probabilities of measurement outcomes, these probabilities then being themselves random variables. It is recalled that, in the presence of a von Neumann statistical mixture, the consistency of the density operator \r{ho} formalism is based on a postulate. The interest of the RCPS concept is presented in the simple case of a spin 1/2, through two instances. The most frequent use of the \r{ho} formalism by users of quantum mechanics is a motivation for establishing some links between a given RCPS and the language of the density operator formalism, while keeping in mind that the situation described by an RCPS is different from the one which has led to the introduction of \r{ho}. It is established that the Landau - Feynman use of \r{ho} is mobilized in a situation differing from both the von Neumann statistical mixture and the RCPS. It is shown that the use of the higher-order moments of a well-chosen random variable helps solving a problem already identified by Zeh in 1970.

Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates that are geometrically local. Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with $k$-local gates, i.e. gates that act on no more than $k$ degrees of freedom, but are not restricted to be geometrically local. First, we construct explicit finite-depth circuits of symmetric $k$-local gates which create symmetry-protected topological (SPT) states from an initial a product state. Our construction applies both to SPT states protected by global symmetries and subsystem symmetries, but not to those with higher-form symmetries, which we conjecture remain nontrivial. Next, we show how to implement arbitrary translationally invariant quantum cellular automata (QCA) in any dimension using finite-depth circuits of $k$-local gates. These results imply that the topological classifications of SPT phases and QCA both collapse to a single trivial phase in the presence of $k$-local interactions. We furthermore argue that SPT phases are fragile to generic $k$-local symmetric perturbations. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the stability of phases and the feasibility of state preparation without the assumption of geometric locality.

NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such algorithms are heuristic in nature and aim to obtain an approximate solution. Significant improvements in computational time and/or the ability to treat large problems are some of the principal promises of quantum computing in this regard. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems. Moreover, the storage of qubits and introduction of entanglement require extreme physical conditions. An issue with quantum optimization algorithms such as QAOA is that they scale linearly with problem size. In this paper, we build upon a proprietary methodology which scales logarithmically with problem size - opening an avenue for treating optimization problems of unprecedented scale on gate-based quantum computers. In order to test the performance of the algorithm, we first find a way to apply it to a handful of NP-hard problems: Maximum Cut, Minimum Partition, Maximum Clique, Maximum Weighted Independent Set. Subsequently, these algorithms are tested on a quantum simulator with graph sizes of over a hundred nodes and on a real quantum computer up to graph sizes of 256. To our knowledge, these constitute the largest realistic combinatorial optimization problems ever run on a NISQ device, overcoming previous problem sizes by almost tenfold.

Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum-proof randomness extraction has also been widely studied, addressing the security issues in the presence of a quantum adversary. In contrast with conventional quantum-proof randomness extractors characterizing the input raw data as min-entropy sources, we find that the input raw data generated by a large class of trusted-device quantum random number generators can be characterized as the so-called reverse block source. This fact enables us to design improved extractors. Specifically, we propose two novel quantum-proof randomness extractors for reverse block sources that realize real-time block-wise extraction. In comparison with the general min-entropy randomness extractors, our designs achieve a significantly higher extraction speed and a longer output data length with the same seed length. In addition, they enjoy the property of online algorithms, which process the raw data on the fly without waiting for the entire input raw data to be available. These features make our design an adequate choice for the real-time post-processing of practical quantum random number generators. Applying our extractors to the raw data generated by a widely used quantum random number generator, we achieve a simulated extraction speed as high as $300$ Gbps.

Pseudo-unitary circuits are recurring in both S-matrix theory and analysis of No-Go theorems. We propose a matrix and diagrammatic representation for the operation that maps S-matrices to T-matrices and, consequently, a unitary group to a pseudo-unitary one. We call this operation ``partial inversion'' and show its diagrammatic representation in terms of permutations. We find the expressions for the deformed metrics and deformed dot products that preserve physical constraints after partial inversion. Subsequently, we define a special set that allows for the simplification of expressions containing infinities in matrix inversion. Finally, we propose a renormalized-growth algorithm for the T-matrix as a possible application. The outcomes of our study expand the methodological toolbox needed to build a family of pseudo-unitary and inter-pseudo-unitary circuits with full diagrammatic representation in three dimensions, so that they can be used to exploit pseudo-unitary flexibilization of unitary No-Go Theorems and renormalized circuits of large scattering lattices.

We present an experimental proposal for the rapid preparation of the center of mass of a levitated particle in a macroscopic quantum state, that is a state delocalized over a length scale much larger than its zero-point motion and that has no classical analog. This state is prepared by letting the particle evolve in a static double-well potential after a sudden switchoff of the harmonic trap, following initial center-of-mass cooling to a sufficiently pure quantum state. We provide a thorough analysis of the noise and decoherence that is relevant to current experiments with levitated nano- and microparticles. In this context, we highlight the possibility of using two particles, one evolving in each potential well, to mitigate the impact of collective sources of noise and decoherence. The generality and scalability of our proposal make it suitable for implementation with a wide range of systems, including single atoms, ions, and Bose-Einstein condensates. Our results have the potential to enable the generation of macroscopic quantum states at unprecedented scales of length and mass, thereby paving the way for experimental exploration of the gravitational field generated by a source mass in a delocalized quantum state.

In this proceedings we present Qibocal, an open-source software package for calibration and characterization of quantum processing units (QPUs) based on the Qibo framework. Qibocal is specifically designed for self-hosted QPUs and provides the groundwork to easily develop, deploy and distribute characterization and calibration routines for all levels of hardware abstraction. Qibocal is based on a modular QPU platform agnostic approach and it provides a general purpose toolkit for superconducting qubits with the possibility of extensions to other quantum technologies. After motivating the need for such a module, we explain the program's flow and show examples of actual use for QPU calibration. We also showcase additional features provided by the library including automatic report generation and live plotting.

There has been debate around applicability of exceptional points (EP) for quantum sensing. To resolve this, we first explore how to experimentally implement the nonhermitian non-diagonalizable Hamiltonians, that exhibit EPs, in quantum computers which run on unitary gates. We propose to use an ancilla-based method in this regard. Next, we show how such Hamiltonians can be used for parameter estimation using quantum computers and analyze its performance in terms of the Quantum Fisher Information ($QFI$) at EPs, both without noise and in presence of noise. It is well known that $QFI$ of a parameter to be estimated is inversely related to the variance of the parameter by the quantum Cramer-Rao bound. Therefore the divergence of the $QFI$ at EPs promise sensing advantages. We experimentally demonstrate in a cloud quantum architecture and theoretically show, using Puiseux series, that the $QFI$ indeed diverges in such EP systems which were earlier considered to be non-divergent.

The quantization of the two terminal conductance in 2D topological systems is justified by the Landauer-Buttiker (LB) theory that assumes perfect point contacts between the leads and the sample. We examine this assumption in a microscopic model of a Chern insulator connected to leads, using the nonequilibrium Greens function formalism. We find that the currents are localized both in the leads and in the insulator and enter and exit the insulator only near the corners. The contact details do not matter and a perfect point contact is emergent, thus justifying the LB theory. The quantized two-terminal conductance shows interesting finite-size effects and dependence on system-reservoir coupling.

Since its advent in 2011, boson-sampling has been a preferred candidate for demonstrating quantum advantage because of its simplicity and near-term requirements compared to other quantum algorithms. We propose to use a variant, called coarse-grained boson-sampling (CGBS), as a quantum Proof-of-Work (PoW) scheme for blockchain consensus. The users perform boson-sampling using input states that depend on the current block information, and commit their samples to the network. Afterward, CGBS strategies are determined which can be used to both validate samples and to reward successful miners. By combining rewards to miners committing honest samples together with penalties to miners committing dishonest samples, a Nash equilibrium is found that incentivizes honest nodes. The scheme works for both Fock state boson sampling and Gaussian boson sampling and provides dramatic speedup and energy savings relative to computation by classical hardware.

The variational quantum algorithms are crucial for the application of NISQ computers. Such algorithms require short quantum circuits, which are more amenable to implementation on near-term hardware, and many such methods have been developed. One of particular interest is the so-called variational quantum state diagonalization method, which constitutes an important algorithmic subroutine and can be used directly to work with data encoded in quantum states. In particular, it can be applied to discern the features of quantum states, such as entanglement properties of a system, or in quantum machine learning algorithms. In this work, we tackle the problem of designing a very shallow quantum circuit, required in the quantum state diagonalization task, by utilizing reinforcement learning (RL). We use a novel encoding method for the RL-state, a dense reward function, and an $\epsilon$-greedy policy to achieve this. We demonstrate that the circuits proposed by the reinforcement learning methods are shallower than the standard variational quantum state diagonalization algorithm and thus can be used in situations where hardware capabilities limit the depth of quantum circuits. The methods we propose in the paper can be readily adapted to address a wide range of variational quantum algorithms.

A restricted form of Landauer's Principle, independent of computational considerations, is shown to hold for thermal systems by reference to the joint entropy associated with conjugate observables. It is shown that the source of the compensating entropy for irreversible physical processes is due to the ontological uncertainty attending values of such mutually incompatible observables, rather than due to epistemic uncertainty as traditionally assumed in the information-theoretic approach. In particular, it is explicitly shown that erasure of logical (epistemic) information via reset operations is not equivalent to erasure of thermodynamic entropy, so that the traditional, information-theoretic form of Landauer's Principle is not supported by the physics. A further implication of the analysis is that, in principle, there can be no Maxwell's Demon in the real world.

We measure and model the combined relaxation of a qubit, a.k.a. central spin, coupled to a discrete two-level system (TLS) environment. If the TLSs are much longer lived than the qubit, non-exponential relaxation and non-Poissonian quantum jumps can be observed. In the limit of large numbers of TLSs the relaxation is likely to follow a power law, which we confirm with measurements on a superconducting fluxonium qubit. Moreover, the observed relaxation and quantum jump statistics are described by the Solomon equations, for which we present a derivation starting from the general Lindblad equation for an arbitrary number of TLSs. We also show how to reproduce the non-Poissonian quantum jump statistics using a diffusive stochastic Schr\"odinger equation. The fact that the measured quantum jump statistics can be reproduced by the Solomon equations, which ignore the quantum measurement back action, hints at a quantum-to-classical transition.

Quantum Key Distribution is a key distribution method that uses the qubits to safely distribute one-time use encryption keys between two or more authorised participants in a way that ensures the identification of any eavesdropper. In this paper, we have done a comparison between the BB84 and B92 protocols and BBM92 and E91 entanglement based protocols for satellite based uplink and downlink in low Earth orbit. The expressions for the quantum bit error rate and the keyrate are given for all four protocols. The results indicate that, when compared to the B92 protocol, the BB84 protocol guarantees the distribution of a higher secure keyrate for a specific distance. Similarly, it is observed that BBM92 ensures higher keyrate in comparison with E91 protocol.

The time-evolving matrix product operators (TEMPO) method, which makes full use of the Feynman-Vernon influence functional, is the state-of-the-art tensor network method for bosonic impurity problems. However, for fermionic impurity problems the Grassmann path integral prohibits application of this method. We develop Grassmann time-evolving matrix product operators, a full fermionic analog of TEMPO, that can directly manipulates Grassmann path integrals with similar numerical cost as the bosonic counterpart. We further propose a zipup algorithm to compute expectation values on the fly without explicitly building a single large augmented density tensor, which boosts our efficiency on top of the vanilla TEMPO. Our method has a favorable complexity scaling over existing tensor network methods, and we demonstrate its performance on the non-equilibrium dynamics of the single impurity Anderson models. Our method solves the long standing problem of turning Grassmann path integrals into efficient numerical algorithms, which could significantly change the application landscape of tensor network based impurity solvers, and could also be applied for broader problems in open quantum physics and condensed matter physics.

The transmission of strong laser light in nonlinear optical materials can generate output photons sources that carry quantum entanglement in multiple degrees of freedom, making this process a fundamentally important tool in optical quantum technology. However, the availability of efficient optical crystals for entangled light generation is severely limited in terms of diversity, thus reducing the prospects for the implementation of next-generation protocols in quantum sensing, communication and computing. To overcome this, we developed and implemented a multi-scale first-principles modeling technique for the computational discovery of novel nonlinear optical devices based on metal-organic framework (MOF) materials that can efficiently generate entangled light via spontaneous parametric down-conversion(SPDC). Using collinear degenerate type-I SPDC as a case study, we computationally screen a database of 114,373 synthesized MOF materials to establish correlations between the structure and chemical composition of MOFs with the brightness and coherence properties of entangled photon pairs. We identify a subset of 49 non-centrosymmetric mono-ligand MOF crystals with high chemical and optical stability that produce entangled photon pairs with intrinsic $G^{(2)}$ correlation times $\tau_c\sim 10-30$ fs and pair generation rates in the range $10^4-10^{8}$ s$^{-1}$mW$^{-1}$mm$^{-1}$ at 1064 nm. Conditions for optimal type-I phase matching are given for each MOF and relationships between pair brightness, crystal band gap and optical birefringence are discussed. Correlations between the optical properties of crystals and their constituent molecular ligands are also given. Our work paves the way for the computational design of MOF-based devices for optical quantum technology.

Here we investigate the role of quantum interference in the quantum homogenizer, whose convergence properties model a thermalization process. In the original quantum homogenizer protocol, a system qubit converges to the state of identical reservoir qubits through partial-swap interactions, that allow interference between reservoir qubits. We design an alternative, incoherent quantum homogenizer, where each system-reservoir interaction is moderated by a control qubit using a controlled-swap interaction. We show that our incoherent homogenizer satisfies the essential conditions for homogenization, being able to transform a qubit from any state to any other state to arbitrary accuracy, with negligible impact on the reservoir qubits' states. Our results show that the convergence properties of homogenization machines that are important for modelling thermalization are not dependent on coherence between qubits in the homogenization protocol. We then derive bounds on the resources required to re-use the homogenizers for performing state transformations. This demonstrates that both homogenizers are universal for any number of homogenizations, for an increased resource cost.

Quantum key distribution provides secure keys with information-theoretic security ensured by the principle of quantum mechanics. The continuous-variable version of quantum key distribution using coherent states offers the advantages of its compatibility with telecom industry, e.g., using commercial laser and homodyne detector, is now going through a booming period. In this review article, we describe the principle of continuous-variable quantum key distribution system, focus on protocols based on coherent states, whose systems are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. We start by reviewing the theoretical protocols and the current security status of these protocols. Then, we discuss the system structure, the key module, and the mainstream system implementations. The advanced progress for future applications are discussed, including the digital techniques, system on chip and point-to-multipoint system. Finally, we discuss the practical security of the system and conclude with promising perspectives in this research field.

We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-$\frac{1}{2}$ XYZ chain away from and at special lines with $U(1)$ symmetry and supersymmetry. We universally find that the average eigenstate entanglement entropy exhibits a volume-law coefficient that is smaller than that of quantum-chaotic interacting models. At the supersymmetric point, we resolve the effect that degeneracies have on the computed averages. We further find that the normalized standard deviation of the eigenstate entanglement entropy decays polynomially with increasing system size, which we contrast to the exponential decay in quantum-chaotic interacting models. Our results provide state-of-the art numerical evidence that integrability in spin-$\frac{1}{2}$ chains reduces the average, and increases the standard deviation, of the entanglement entropy of highly excited energy eigenstates when compared to those in quantum-chaotic interacting models.

We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. (IEEE Trans. IT, 67, 946 (2021)) to a function defined over a set of density matrices with linear constraints so that our algorithm can be applied to optimizations of quantum operations. This algorithm has wider applicability. Hence, we apply our algorithm to the quantum information bottleneck with three quantum systems, which can be used for quantum learning. We numerically compare our obtained algorithm with the existing algorithm by Grimsmo and Still (Phys. Rev. A, 94, 012338 (2016)). Our numerical analysis shows that our algorithm is better than their algorithm.