QUROPE Quantum Information Processing and Communication in Europe

We further investigate novel features of the $T-$vacuum state, originally defined in the context of quantum field theory in a (1+1) dimensional radiation dominated universe [Modak, JHEP 12, 031 (2020)]. Here we extend the previous work to a realistic (3+1) dimensional set up and show that $T-$vacuum causes an \emph{anisotropic particle creation} in the radiation dominated early universe. Unlike the Hawking or Unruh effect, where the particle content is thermal and asymptotically defined, here it is non-thermal and time dependent. This novel example of particle creation is interesting because these particles are detected in the frame of physical/cosmological observers, who envision the $T-$vacuum as a particle excited state, and therefore may eventually be compared with observations.

One promising application of near-term quantum devices is to prepare trial wavefunctions using short circuits for solving different problems via variational algorithms. For this purpose, we introduce a new circuit design that combines graph-based diagonalization circuits with arbitrary single-qubit rotation gates to get Hamiltonian-based graph states ans\"atze (H-GSA). We test the accuracy of the proposed ansatz in estimating ground state energies of various molecules of size up to 12-qubits. Additionally, we compare the gate count and parameter number complexity of the proposed ansatz against previously proposed schemes and find an order magnitude reduction in gate count complexity with slight increase in the number of parameters. Our work represents a significant step towards constructing compact quantum circuits with good trainability and convergence properties and applications in solving chemistry and physics problems.

The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and anti-correlation. A numerical simulation of the fluctuations requires a knowledge of both the probability distribution and the correlation function. Although there are widely used methods to generate a sequence of random numbers which obey a given probability distribution, the imposition of a given correlation function can be more difficult. Here we propose a simple method in which the outcome of a given measurement determines a shift in the peak of the probability distribution, to be used for the next measurement. We illustrate this method for three examples of quantum field correlation functions, and show that the resulting simulated function agree well with the original, analytically derived function. We then discuss the application of this method to numerical studies of the effects of correlations on the random walks of test particles coupled to the fluctuating field.

Lindbladian formalism, as tuned to dissipative and open systems, has been all-pervasive to interpret non-equilibrium steady states of quantum many-body systems. We study the fate of free fermionic and superconducting phases in a dissipative one-dimensional Kitaev model - where the bath acts both as a source and a sink of fermionic particles with different coupling rates. As a function of these two couplings, we investigate the steady state, its entanglement content, and its approach from varying initial states. Interestingly, we find that the steady state phase diagram retains decipherable signatures of ground state critical physics. We also show that early-time fidelity is a useful marker to find a subclass of phase transitions in such situations. Moreover, we show that the survival of critical signatures at late-times, strongly depend on the thermal nature of the steady state. This connection hints at a correspondence between quantum observables and classical magnetism in the steady state of such systems. Our work uncovers interesting connections between dissipative quantum many-body systems, thermalization of a classical spin and many-body quantum critical phenomena.

Symmetry Topological Field Theory (SymTFT) is a framework to capture universal features of quantum many-body systems by viewing them as a boundary of topological order in one higher dimension. This yielded numerous insights in static low-energy settings. Here we study what SymTFT can tell about nonequilibrium, focusing on one-dimensional (1D) driven systems and their 2D SymTFT. In driven settings, boundary conditions (BCs) can be dynamical and can apply both spatially and temporally. We show how this enters SymTFT via topological operators, which we then use to uncover several new results for 1D dynamics. These include revealing time crystals (TCs) as systems with symmetry-twisted temporal BCs, finding robust bulk TC features in phases thought to be only boundary TCs, Floquet dualities, or identifying Floquet codes as space-time duals to systems with duality-twisted spatial BCs. We also show how, by making duality-twisted BCs dynamical, non-Abelian braiding of duality defects can enter SymTFT, leading to effects such as the exact pumping of symmetry charges between a system and its BCs. We illustrate our ideas for $\mathbb{Z}_2$-symmetric 1D systems, but our construction applies for any finite Abelian symmetry.

Noise is an important concept and its measurement and characterization has been a flourishing area of research in contemporary mesoscopic physics. Here we propose interaction-free measurements as a noise-detection technique, exploring two conceptually different schemes: the coherent and the projective realizations. These detectors consist of a qutrit whose second transition is coupled to a resonant oscillatory field that may have noise in amplitude or phase. For comparison, we consider a more standard detector previously discussed in this context - a qubit coupled in a similar way to the noise source. We find that the qutrit scheme offers clear advantages, allowing precise detection and characterization of the noise, while the qubit does not. Finally, we study the signature of noise correlations in the detector's signal.

We review recent suggestions to quantum simulate scalar electrodynamics (the lattice Abelian Higgs model) in $1+1$ dimensions with rectangular arrays of Rydberg atoms. We show that platforms made publicly available recently allow empirical explorations of the critical behavior of quantum simulators. We discuss recent progress regarding the phase diagram of two-leg ladders, effective Hamiltonian approaches and the construction of hybrid quantum algorithms targeting hadronization in collider physics event generators.

The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then utilized to compute the expectation value of a given Hamiltonian. Designing efficient PQCs is crucial for improving convergence speed. In this study, we introduce problem-specific PQCs tailored for optimization problems by dynamically generating PQCs that incorporate problem constraints. This approach reduces a search space by focusing on unitary transformations that benefit the VQE algorithm, and accelerate convergence. Our experimental results demonstrate that the convergence speed of our proposed PQCs outperforms state-of-the-art PQCs, highlighting the potential of problem-specific PQCs in optimization problems.

In recent years, fermionic topological phases of quantum matter has attracted a lot of attention. In a pioneer work by Gu, Wang and Wen, the concept of equivalence classes of fermionic local unitary(FLU) transformations was proposed to systematically understand non-chiral topological phases in 2D fermion systems and an incomplete classification was obtained. On the other hand, the physical picture of fermion condensation and its corresponding super pivotal categories give rise to a generic mathematical framework to describe fermionic topological phases of quantum matter. In particular, it has been pointed out that in certain fermionic topological phases, there exists the so-called q-type anyon excitations, which have no analogues in bosonic theories. In this paper, we generalize the Gu, Wang and Wen construction to include those fermionic topological phases with q-type anyon excitations. We argue that all non-chiral fermionic topological phases in 2+1D are characterized by a set of tensors $(N^{ij}_{k},F^{ij}_{k},F^{ijm,\alpha\beta}_{kln,\chi\delta},n_{i},d_{i})$, which satisfy a set of nonlinear algebraic equations parameterized by phase factors $\Xi^{ijm,\alpha\beta}_{kl}$, $\Xi^{ij}_{kln,\chi\delta}$, $\Omega^{kim,\alpha\beta}_{jl}$ and $\Omega^{ki}_{jln,\chi\delta}$. Moreover, consistency conditions among algebraic equations give rise to additional constraints on these phase factors which allow us to construct a topological invariant partition for an arbitrary triangulation of 3D spin manifold. Finally, several examples with q-type anyon excitations are discussed, including the Fermionic topological phase from Tambara-Yamagami category for $\mathbb{Z}_{2N}$, which can be regarded as the $\mathbb{Z}_{2N}$ parafermion generalization of Ising fermionic topological phase.

Transition metal dichalcogenides layered nano-crystals are emerging as promising candidates for next-generation optoelectronic and quantum devices. In such systems, the interaction between excitonic states and atomic vibrations is crucial for many fundamental properties, such as carrier mobilities, quantum coherence loss, and heat dissipation. In particular, to fully exploit their valley-selective excitations, one has to understand the many-body exciton physics of zone-edge states. So far, theoretical and experimental studies have mainly focused on the exciton-phonon dynamics in high-energy direct excitons involving zone-center phonons. Here, we use ultrafast electron diffraction and ab initio calculations to investigate the many-body structural dynamics following nearly-resonant excitation of low-energy indirect excitons in MoS2. By exploiting the large momentum carried by scattered electrons, we identify the excitation of in-plane K- and Q-phonon modes with E^' symmetry as key for the stabilization of indirect excitons generated via near-infrared light at 1.55 eV, and we shed light on the role of phonon anharmonicity and the ensuing structural evolution of the MoS2 crystal lattice. Our results highlight the strong selectivity of phononic excitations directly associated with the specific indirect-exciton nature of the wavelength-dependent electronic transitions triggered in the system.

In the literature of calculating atomic and molecular structures, most Schrodinger equations are described by Coulomb potential. However, there are also a few literatures that discuss some magnetic correction methods, such as Pauli and Shortley's early work. But in fact, the calculation accuracy of these Schrodinger equations is not consistent with Lamb shift. Therefore, in the traditional ab initio calculation of quantum mechanics, it is common and necessary to use Dirac theory or quantum electrodynamics (QED) to correct the energy level of Schrodinger equation. However, the calculation of Feynman diagram is a daunting problem, including the application of self-consistent field in relativity and density functional theory. So recently, we have noticed the simplicity of the modified Newtonian mechanics, and we think that quantum mechanics will have similar properties. Here, we state this and improve the correction function in our previous action potential. In addition, through the demonstration of hydrogen-like and helium-like systems here, it can be proved that this conclusion is a potential application, that is, the energy level structure of our modified Schrodinger equation is consistent with Lamb shift.

Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. We demonstrate that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance probabilities of our algorithms. We execute one of our symmetry-testing algorithms on existing quantum computers for simple examples of both symmetric and asymmetric cases.

Causality can be defined in terms of space-time or based on information-theoretic structures, which correspond to very different notions of causation. Yet, in physical experiments, these notions play together in a compatible manner. The process matrix framework is useful for modelling indefinite causal structures (ICS) in an information-theoretic sense, but there remain important open questions regarding the physicality of such processes. In particular, there are several experiments that claim to implement ICS processes in Minkowski space-time, which presents an apparent theoretical paradox: how can an indefinite information-theoretic causal structure be compatible with a definite space-time structure? To address this, we develop a general framework that disentangles the two causality notions and formalises their relations. The framework describes a composition of quantum operations through feedback loops, and the embedding of the resulting (possibly cyclic) information-theoretic structure in an acyclic space-time structure. Relativistic causality is formalised as an operational compatibility condition between the two structures. Reformulating the process matrix framework here, we establish no-go results which imply that it is impossible to physically realise ICS in a fixed space-time with space-time localised quantum systems. Further, we prove that physical realisations of any ICS process, even those involving space-time non-localised systems, will ultimately admit an explanation in terms of a definite (and acyclic) causal order process, at a more fine-grained level. These results fully resolve the apparent paradox and we discuss their implications for the interpretation of the above-mentioned experiments. Moreover, our work offers concrete insights on the operational meaning of indefinite causality, both within and beyond the context of a fixed space-time.

A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This paper establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. We give a complete classification of the open boundary point-gap topology with symmetry and show that the non-trivial open boundary topology results in robust and exotic surface states.

We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${\sf RwBQP}$, ${\sf CBQP}$, and ${\sf AdPostBQP}$ as sets of decision problems solvable by polynomial-size quantum circuits with a polynomial number of rewinding operators, cloning operators, and adaptive postselections, respectively. Our main result is that ${\sf BPP}^{\sf PP}\subseteq{\sf RwBQP}={\sf CBQP}={\sf AdPostBQP}\subseteq{\sf PSPACE}$. As a byproduct of this result, we show that any problem in ${\sf PostBQP}$ can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that ${\sf BQP}\nsupseteq{\sf SZK}$, or the shortest independent vectors problem cannot be efficiently solved with quantum computers, we also show that a single rewinding operator is sufficient to achieve tasks that are intractable for quantum computation. In addition, we consider rewindable Clifford and instantaneous quantum polynomial time circuits.

Born machines are quantum-inspired generative models that leverage the probabilistic nature of quantum states. Here, we present a new architecture called many-body localized (MBL) hidden Born machine that utilizes both MBL dynamics and hidden units as learning resources. We show that the hidden units act as an effective thermal bath that enhances the trainability of the system, while the MBL dynamics stabilize the training trajectories. We numerically demonstrate that the MBL hidden Born machine is capable of learning a variety of tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and non-local parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources, and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems.

Quantum-enhanced (i.e., less query complexity compared to any classical method) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum computing algorithms. Notably, the quantum estimation theory identifies the ultimate precision of such estimator, which is referred to as the quantum Cram\'{e}r-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. Because the estimation precision directly determines the performance of those quantum technological systems, it is highly demanded to develop a generic and practically implementable estimation method that achieves the QCR bound. Under imperfect conditions, however, such an ultimate and implementable estimator for quantum mean values has not been developed. In this paper, we propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that asymptotically achieves the QCR bound in the limit of a large number of qubits. To approach the QCR bound in a practical setting, the method adaptively optimizes the amplitude amplification and a specific measurement that can be implemented without any knowledge of state preparation. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimator such as consistency and asymptotic normality. Furthermore, several numerical simulations are provided to demonstrate the effectiveness of the method, particularly showing that the estimator needs only a modest number of measurements to almost saturate the QCR bound.

Hilbert space fragmentation (HSF) is a phenomenon that the Hilbert space of an isolated quantum system splits into exponentially many disconnected subsectors. The fragmented systems do not thermalize after long-time evolution because the dynamics are restricted to a small subsector. Inspired by recent developments of the HSF, we construct the Hamiltonian that exhibits the HSF in the momentum space. We show that persistent-current (PC) states emerge due to the HSF in the momentum space. We also investigate the stability of the PC states against the random potential, which breaks the structure of the HSF, and find that the decay rate of the PC is almost independent of the current velocity.

Quantum computing has entered fast development track since Shor's algorithm was proposed in 1994. Multi-cloud services of quantum computing farms are currently available. One of which, IBM quantum computing, presented a road map showing their Kookaburra system with over 4158 qubits will be available in 2025. For the standardization of Post-Quantum Cryptography or PQC, the National Institute of Standards and Technology or NIST recently announced the first candidates for standardization with one algorithm for key encapsulation mechanism (KEM), Kyber, and three algorithms for digital signatures. NIST has also issued a new call for quantum-safe digital signature algorithms due June 1, 2023. This timeline shows that FIPS-certified quantum-safe TLS protocol would take a predictably long time. However, "steal now, crack later" tactic requires protecting data against future quantum threat actors today. NIST recommended the use of a hybrid mode of TLS 1.3 with its extensions to support PQC. The hybrid mode works for certain cases but FIPS certification for the hybridized cryptomodule might still be required. This paper proposes to take a nested mode to enable TLS 1.3 protocol with quantum-safe data, which can be made available today and is FIPS compliant. We discussed the performance impacts of the handshaking phase of the nested TLS 1.3 with PQC and the symmetric encryption phase. The major impact on performance using the nested mode is in the data symmetric encryption with AES. To overcome this performance reduction, we suggest using quantum encryption with a quantum permutation pad for the data encryption with a minor performance reduction of less than 10 percent.

Non-Hermitian (NH) Hamiltonians have been shown to exhibit unique signatures, including the NH skin effect and an exponential spectral sensitivity with respect to boundary conditions. Here, we investigate as to what extent these remarkable phenomena, recently predicted and observed in a broad range of settings, may also occur in closed correlated fermionic systems that are governed by a Hermitian many-body Hamiltonian. There, an effectively NH quasiparticle description naturally arises in the Green's function formalism due to inter-particle scattering that represents an inherent source of dissipation. As a concrete platform we construct an extended interacting Su-Schrieffer-Heeger (SSH) model subject to varying boundary conditions, which we analyze using exact diagonalization and non-equilibrium Green's function methods. That way, we clearly identify the presence of the aforementioned NH phenomena in the quasi-particle properties of this Hermitian model system.