QUROPE Quantum Information Processing and Communication in Europe

We theoretically investigate the pure dephasing dynamics of two static impurity qubits embedded within a common environment of ultracold fermionic atoms, which are confined to one spatial dimension. Our goal is to understand how bath-mediated interactions between impurities affect their performance as nonequilibrium quantum thermometers. By solving the dynamics exactly using a functional determinant approach, we show that the impurities become correlated via retarded interactions of the Ruderman-Kittel-Kasuya-Yosida type. Moreover, we demonstrate that these correlations can provide a metrological advantage, enhancing the sensitivity of the two-qubit thermometer beyond that of two independent impurities. This enhancement is most prominent in the limit of low temperature and weak collisional coupling between the impurities and the gas. We show that this precision advantage can be exploited using standard Ramsey interferometry, with no need to prepare correlated initial states nor to individually manipulate or measure the impurities. We also quantitatively assess the impact of ignoring these correlations when constructing a temperature estimate, finding that acceptable precision can still be achieved from a simplified model of independent impurities. Our results demonstrate the rich nonequilibrium physics of impurities dephasing in a common Fermi gas, and may help to provide better temperature estimates at ultralow temperatures.

Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.

In the noisy intermediate-scale quantum era, variational algorithms have become a standard approach to solving quantum many-body problems. Here, we present variational quantum eigensolver (VQE) results of selected oxygen isotopes within the shell model description. The aim of the present work is to locate the neutron drip line of the oxygen chain using unitary coupled cluster (UCC) type ansatze with different microscopic interactions (DJ16, JISP16, and N3LO), in addition to a phenomenological USDB interaction. While initially infeasible to execute on contemporary quantum hardware, the size of the problem is reduced significantly using qubit tapering techniques in conjunction with custom circuit design and optimization. The optimal values of ansatz parameters from classical simulation are taken for the DJ16 interaction, and the tapered circuits are run on IonQ's Aria, a trapped-ion quantum computer. After applying gate error mitigation for three isotopes, we reproduced exact ground state energies within a few percent error. The post-processed results from hardware also clearly show $^{24}$O as the drip line nucleus of the oxygen chain. Future improvements in quantum hardware could make it possible to locate drip lines of heavier nuclei.

Chain-mapping techniques combined with the time-dependent density matrix renormalization group are powerful tools for simulating the dynamics of open quantum systems interacting with structured bosonic environments. Most interestingly, they leave the degrees of freedom of the environment open to inspection. In this work, we fully exploit the access to environmental observables to illustrate how the evolution of the open quantum system can be related to the detailed evolution of the environment it interacts with. In particular, we give a precise description of the fundamental physics that enables the finite temperature chain-mapping formalism to express dynamical equilibrium states. Furthermore, we analyze a two-level system strongly interacting with a super-Ohmic environment, where we discover a change in the spin-boson ground state that can be traced to the formation of polaronic states.

In the context of partial entanglement entropy (PEE), we study the entanglement structure of the island phases realized in several 2-dimensional holographic set-ups. The self-encoding property of the island phase changes the way we evaluate the PEE. With the contributions from islands taken into account, we give a generalized prescription to construct PEE and balanced partial entanglement entropy (BPE). Here the ownerless island region, which lies inside the island $\text{Is}(AB)$ of $A\cup B$ but outside $\text{Is}(A)\cup \text{Is}(B)$, plays a crucial role. Remarkably, we find that under different assignments for the ownerless island, we get different BPEs, which exactly correspond to different saddles of the entanglement wedge cross-section (EWCS) in the entanglement wedge of $A\cup B$. The assignments can be settled by choosing the one that minimizes the BPE. Furthermore, under this assignment we study the PEE and give a geometric picture for the PEE in holography, which is consistent with the geometric picture in the no-island phases.

We investigate the effect of symmetry breaking on chaos in one-dimensional quantum mechanical models using the numerical chaos diagnostic tool, Out-of-Time-Order Correlator(OTOC). Previous research has primarily shown that OTOC shows exponential growth in the neighbourhood of a local maximum. If this is true, the exponential growth should disappear once the local maximum is removed from the system. However, we find that removing the local maximum by a small symmetry-breaking(perturbation) term to the Hamiltonian does not drastically affect the behaviour of OTOC. Instead, with the increase of perturbation strength, the broken symmetric region expands, causing the exponential growth of OTOC to spread over a broader range of eigenstates. We adopt various potentials and find this behaviour universal. We also use other chaos diagnostic tools, such as Loschmidt Echo(LE) and spectral form factor(SFF), to confirm this. This study confirms that a broken symmetric region is responsible for the exponential growth of the microcanonical and thermal OTOC rather than the local maximum. In other words, OTOC is sensitive to symmetry breaking in the Hamiltonian, which is often synonymous with the butterfly effect.

Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as the inputs and description of the unitary to be run are not too large. We then prove a bound on quantum processors which shows many unitaries cannot be implemented inside the black hole, and further show some of these have short descriptions and act on small systems. These unitaries with short descriptions must be computationally forbidden from happening inside the black hole.

In some quantum many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [arXiv:2007.00845] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (it is not a symmetry of the Hamiltonian). The quantum many-body scars are invariant under this group, while all other states are not. Here we apply this idea to lattice systems containing $M$ Majorana fermions per site. The Hilbert space for $N$ sites may be decomposed under the action of the O$(N)\times$O$(M)$ group, and the scars are the SO$(N)$ singlets. For any even $M$ there are two families of scars. One of them, which we call the $\eta$ states, is symmetric under the group O$(N)$. The other, the $\zeta$ states, has the SO$(N)$ invariance. For $M=4$, where our construction reduces to spin-$1/2$ fermions on a lattice with local interactions, the former family are the $N+1$ $\eta$-pairing states, while the latter are the $N+1$ states of maximum spin. We generalize this construction to $M>4$. For $M=6$ we exhibit explicit formulae for the scar states and use them to calculate the bipartite entanglement entropy analytically. For large $N$, it grows logarithmically with the sub-system size. We present a general argument that any group-invariant scars should have the entanglement entropy that is parametrically smaller than that of typical states. The energies of the scars we find are not equidistant in general but can be made so by choosing Hamiltonian parameters. For $M>6$ we find that with local Hamiltonians the scars typically have certain degeneracies. The scar spectrum can be made ergodic by adding a non-local interaction term. We derive the dimension of each scar family and show the scars could have a large contribution to the density of states for small $N$.

A recently proposed fully passive QKD removes all source modulator side channels. In this work, we combine the fully passive sources with MDI-QKD to remove simultaneously side channels from source modulators and detectors. We show a numerical simulation of the passive MDI-QKD, and we obtain an acceptable key rate while getting much better implementation security, as well as ease of implementation, compared with a recently proposed fully passive TF-QKD, paving the way towards more secure and practical QKD systems. We have proved that a fully passive protocol is compatible with MDI-QKD and we also proposed a novel idea that could potentially improve the sifting efficiency.

In this paper, we lay down the foundation of a quantum computational framework for algebraic topology based on simplicial set theory. This extends previous work, which was limited to simplicial complexes and aimed mostly to topological data analysis. Our set--up applies to any parafinite simplicial set and proceeds by associating with it a finite dimensional simplicial Hilbert space, whose simplicial operator structure we study in depth. We show in particular how the problem of determining the simplicial set's homology can be solved within the simplicial Hilbert framework. We examine further the conditions under which simplicial set theoretic algorithms can be implemented in a quantum computational setting taking into account a quantum computer's finite resources. We outline finally a quantum algorithmic scheme capable to compute the simplicial homology spaces and Betti numbers of a simplicial set combining a number of basic quantum algorithms.

A theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. The critical point separates a gapless phase with $\ell^{d-1} \ln \ell$ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with $\ell^{d-1}$ scaling, where $\ell$ is a size of the subsystem. The problem is mapped onto an SU($R$) replica non-linear sigma model in $d+1$ dimensions, with $R\to 1$. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for $d = 1+ \epsilon$ with $\epsilon \ll 1$. Further, we carry out a numerical study of the transition for a $d=2$ model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, $\nu \approx 1.4$.

Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a "super-Hamiltonian". We demonstrate this for conventional symmetries such as $Z_2$, $U(1)$, and $SU(2)$, where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity breaking phenomena of Hilbert space fragmentation and quantum many-body scars. In addition, we show that this super-Hamiltonian is exactly the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits. This physical interpretation provides a novel interpretation for Mazur bounds for autocorrelation functions, and relates the low-energy excitations of the super-Hamiltonian to approximate symmetries that determine slowly relaxing modes in symmetric systems. We find examples of gapped/gapless super-Hamiltonians indicating the absence/presence of slow-modes, which happens in the presence of discrete/continuous symmetries. In the gapless cases, we recover slow-modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of $U(1)$ symmetry, Hilbert space fragmentation, and a tower of quantum scars respectively. In all, this demonstrates the power of the commutant algebra framework in obtaining a comprehensive understanding of symmetries and their dynamical consequences in systems with locality.

Quantum estimation of parameters defining open-system dynamics may be enhanced by using ancillas that are entangled with the probe but are not submitted to the dynamics. Here we consider the important problem of estimation of transmission of light by a sample, with losses due to absorption and scattering. We show, through the determination of the quantum Fisher information, that the ancilla strategy leads to the best possible precision in single-mode estimation, the one obtained for a Fock state input, through joint photon-counting of probe and ancilla, which are modes of a bimodal squeezed state produced by an optical parametric amplifier. This proposal overcomes the challenge of producing and detecting high photon-number Fock states, and it is quite robust against additional noise: we show that it is immune to phase noise and the precision does not change if the incoming state gets disentangled. Furthermore, the quantum gain is still present under moderate photon losses of the input beams. We also discuss an alternative to joint photon counting, which is readily implementable with present technology, and approaches the quantum Fisher information result for weak absorption, even with moderate photons losses of the input beams before the sample is probed: a time-reversal procedure, placing the sample between two optical parametric amplifiers, with the second undoing the squeezing produced by the first one. The precision of estimation of the loss parameter is obtained from the average outgoing total photon number and its variance. In both procedures, the state of the probe and the detection procedure are independent of the value of the parameter.

In the framework of the hybrid quantum-classical variational cluster approach (VCA) to strongly correlated fermion systems one of the goals of a quantum subroutine is to find single-particle correlation functions of lattice fermions in polynomial time. Previous works suggested to use variants of the Hadamard test for this purpose. However, it requires an implementation of controlled unitaries specifying the full dynamics of the simulated model. In this work, we propose a new quantum algorithm, which uses an analog of the Kubo formula within linear response theory adapted to a quantum circuit simulating the Hubbard model. It allows to access the Green's function of a cluster directly and thereby circumvents the usage of the Hadamard test. We find a drastic reduction in gate count of two-qubits gates and limitations on hardware design as compared to previous approaches.

Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their potential for a quantum advantage. To do so, earlier works developed the geometric difference, which can be understood as a closeness measure between two kernel-based machine learning approaches, most importantly between a quantum kernel and classical kernel. This metric links the quantum and classical model complexities. Therefore, it raises the question of whether the geometric difference, based on its relation to model complexity, can be a useful tool in evaluations other than for the potential for quantum advantage. In this work, we investigate the effects of hyperparameter choice on the model performance and the generalization gap between classical and quantum kernels. The importance of hyperparameter optimization is well known also for classical machine learning. Especially for the quantum Hamiltonian evolution feature map, the scaling of the input data has been shown to be crucial. However, there are additional parameters left to be optimized, like the best number of qubits to trace out before computing a projected quantum kernel. We investigate the influence of these hyperparameters and compare the classically reliable method of cross validation with the method of choosing based on the geometric difference. Based on the thorough investigation of the hyperparameters across 11 datasets we identified commodities that can be exploited when examining a new dataset. In addition, our findings contribute to better understanding of the applicability of the geometric difference.

The interest in the Werner-Holevo channel has been mainly due to its abstract mathematical properties. We show that in three dimensions and with a slight modification, this channel can be realized as rotation of qutrit states in random directions by random angles. Therefore and in view of the potential use of qutrits in quantum processing tasks and their realization in many different platforms, the modifed Werner-Holevo channel can be used as a very simple and realistic noise model, in the same way that the depolarizing channel is for qubits. We will make a detailed study of this channel and derive its various properties. In particular we will use the recently proposed flag extension and other techniques to derive analytical expressions and bounds for different capacities of this channel. The role of symmetry is revealed in these derivations.

We show how to capture both the non-unitary Page curve and replica wormhole-like contributions that restore unitarity in a toy quantum system with random dynamics. The motivation is to find the simplest dynamical model that captures this aspect of gravitational physics. In our model, we evolve with an ensemble of Hamiltonians with GUE statistics within microcanonical windows. The entropy of the averaged state gives the non-unitary curve, the averaged entropy gives the unitary curve, and the difference comes from matrix index contractions in the Haar averaging that connect the density matrices in a replica wormhole-like manner.

Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be highly desirable. In this paper, we initiate the study of program synthesis for quantum unitary programs that recursively define a family of unitary circuits for different input sizes, which are widely used in existing quantum programming languages. Specifically, we present QSynth, the first quantum program synthesis framework, including a new inductive quantum programming language, its specification, a sound logic for reasoning, and an encoding of the reasoning procedure into SMT instances. By leveraging existing SMT solvers, QSynth successfully synthesizes ten quantum unitary programs including quantum adder circuits, quantum eigenvalue inversion circuits and Quantum Fourier Transformation, which can be readily transpiled to executable programs on major quantum platforms, e.g., Q#, IBM Qiskit, and AWS Braket.

The identification, description, and classification of topological features is an engine of discovery and innovation in several fields of physics. This research encompasses a broad variety of systems, from the integer and fractional Chern insulators in condensed matter, to protected states in complex photonic lattices in optics, and the structure of the QCD vacuum. Here, we introduce another playground for topology: the dissipative dynamics of the Sachdev-Ye-Kitaev (SYK) model, $N$ fermions in zero dimensions with strong $q$-body interactions coupled to a Markovian bath. For $q = 4, 8, \ldots$ and certain choices of $N$ and bath details, involving pseudo-Hermiticity, we find a rectangular block representation of the vectorized Liouvillian that is directly related to the existence of an anomalous trace of the unitary operator implementing fermionic exchange. As a consequence of this rectangularization, the Liouvillian has purely real modes for any coupling to the bath. Some of them are demonstrated to be topological by an explicit calculation of the spectral flow, leading to a symmetry-dependent topological index $\nu$. Topological properties have universal features: they are robust to changes in the Liouvillian provided that the symmetries are respected and they are also observed if the SYK model is replaced by a quantum chaotic dephasing spin chain in the same symmetry class. Moreover, the topological symmetry class can be robustly characterized by the level statistics of the corresponding random matrix ensemble. In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium, which may enable a direct path for experimental confirmation of topology in dissipative many-body quantum chaotic systems.

Row-column multiplexing has proven to be an effective strategy in scaling single-photon detector arrays to kilopixel and megapixel spatial resolutions. However, with this readout mechanism, multiphoton coincidences on the array cannot be easily resolved due to ambiguities concerning their spatial locations of incidence. In this work, we propose a method to resolve up to 4-photon coincidences in single-photon detector arrays with row-column readouts. By utilizing unambiguous single-photon measurements to estimate probabilities of detection at each pixel, we redistribute the ambiguous multiphoton counts among candidate pixel locations such that the peak signal-to-noise-ratio of the reconstruction is increased between 3 and 4 dB compared to conventional methods at optimal operating conditions. We also show that our method allows the operation of these arrays at higher incident photon fluxes as compared to previous methods. The application of this technique to imaging natural scenes is demonstrated using Monte Carlo experiments.