Learning and certifying time-dependent quantum dynamics under realistic noise is key to trustworthy quantum simulation. I will present an efficient protocol that reconstructs the generators Hamiltonian and Markovian noise generators of multi-qubit devices from derivatives of expectation values of few-qubit observables via stable polynomial interpolation and semidefinite programming. To the best of our knowledge, this is the first scheme to efficiently learn local time-dependent Hamiltonians and Markovian noise at scale. The scheme is experimentally light, requiring only product-state preparation, single-qubit measurements, and post-processing polynomial in the qubit number, while the number of samples needed to identify all parameters grows only logarithmically with the qubit count. Our protocol thus enables a-posteriori certification of various crucial routines on quantum simulators such as adiabatic state preparation, and yield confidence guarantees for estimated expectation values along the schedule. Thus, together, these results provide a scalable route to diagnosing and certifying controlled time-dependent many-body dynamics. If time permits, we will also discuss recent experimental implementations of related protocols.
I will present recent analytical and numerical results on quantum complexity and anticoncentration in many-body wave functions, using random tensor-network ensembles as a powerful, tractable testbed for non-equilibrium dynamics. I will then introduce new algorithms for the classical simulation of quantum time evolution: (i) hybrid tensor-network methods enhanced by Clifford unitaries, and (ii) Monte Carlo sampling of spatially contracted networks. Together, these approaches extend the reach of tensor network simulations, showing how less resources suffice to capture key quantum features.
Tensor Network States, like matrix product or projected entangled pair states play an important role in both, quantum information theory and many-body physics. They offer a compact and efficient representation, enabling accelerated numerical computations and providing intuitive insights into many-body phenomena. In this talk, I will discuss how certain states can be efficiently prepared and manipulated using quantum devices, highlighting the use of local operations and classical communication.
A many-body Green's function $G(z)$ has a well-known continued fraction representation involving a so-called Krylov operator basis $\{O_{m}\}_{m \geq 0}$. The content of the continued fraction at depth $n$ is denoted by $G_{n}(z)$, and can be thought of as the Green's function for the operator dynamics restricted to the 'fast space' $\{O_{m}\}_{m \geq n}$. In this work we prove that $G_{n}(z)$ can exhibit universality in the $n \to \infty$ limit, approaching different universal scaling forms in different sections of the complex $z$-plane. At finite $z$, we show that $G_{n}(z)$ approaches the Wigner semicircle law from random matrix theory (RMT), the same as the average resolvent in the bulk of the spectrum for the Gaussian Unitary Ensemble with an appropriately rescaled bandwidth. With hydrodynamics in mind, we also study the signatures of power-law decaying autocorrelation functions, showing that at low frequencies $G_{n}(z)$ is instead governed by the Bessel universality class from RMT.
As an application we give a new numerical method, the spectral bootstrap, for approximating spectral functions, including hydrodynamic transport data, from a finite number of Lanczos coefficients. Our proof is complex analytic in nature, involving a map to a Riemann-Hilbert problem which we solve using a steepest-descent-type method, rigorously controlled in the $n\to\infty$ limit. This proof technique requires we make some analyticity and regularity assumptions on the spectral function, and we comment on their possible connections to the eigenstate thermalization hypothesis. We also discuss how a recent conjecture from quantum chaos, the 'Operator Growth Hypothesis', implies that chaotic operator dynamics can generically be identified with the critical point of a confinement transition in a classical Coulomb gas. We then elucidate how this criticality has implications for the computational resources required to reconstruct transport coefficients to a given precision.
We analyze the entanglement structures of states produced in 1D monitored circuits where local Clifford unitaries are interspersed with single-site measurements. In the volume law phase, the average entanglement depth scales linearly with system size. Curiously, we continue to see long-range entanglement within the area law phase as well. At the critical point and in the area law phase, the entanglement depth scales with system size as a power law with an exponent between 0 and 1. We further calculate the fractal dimension of the largest cluster of entangled qubits within the state. We find that there is self similarity and the largest clusters have fractal dimensions between 0 and 1 in the area law phase.
This fractal dimension continuously goes to zero as the measurement probability approaches 1. Within the volume law phase, the fractal dimension of such clusters is 1.
We investigate the effects of a static impurity, modeled by a localized barrier, in a one-dimensional mesoscopic system comprised of strongly correlated repulsive SU(N)-symmetric fermions. For a mesoscopic sized ring under the effect of an artificial gauge field, we analyze the particle density and the current flowing through the impurity at varying interaction strength, barrier height and number of components. We find a non-monotonic behaviour of the persistent current, due to the competition between the screening of the impurity, quantum fluctuations, and the phenomenon of fractionalization, a signature trait of SU(N) fermionic matter-waves in mesoscopic ring potentials. This is also highlighted in the particle density at the impurity site. We show that the impurity opens a gap in the energy spectrum selectively, constrained by the total effective spin and interaction. Our findings hold significance for the fundamental understanding of the localized impurity problem and its potential applications for sensing and interferometry in quantum technology.
Quantum error correction (QEC) protects quantum information by adding redundancies that help detect and correct errors. Understanding the limitations of QEC under different noise sources is crucial for the development of fault-tolerant quantum computers. In this talk, I will address the challenge of determining the fundamental (optimal) error correction thresholds of QEC codes using the coherent information (CI) of the mixed-state density matrix associated with these codes. This new approach allows us to obtain accurate optimal thresholds from small-sized codes (PRR L042014, 2024), uncover new connections between decoding phase transitions and fermionic topological phases of matter (arXiv:2412.12279), and study optimal thresholds under erasure errors and computational errors together in a rigorous manner (arXiv:2412.16727). I will also discuss how this approach to fundamental thresholds has led to new insights at the interface of quantum information, condensed matter physics, and statistical mechanics.
Links:
Direct fidelity estimation is a protocol that estimates the fidelity between an experimental quantum state and a target pure state. By measuring the expectation values of Pauli operators selected through importance sampling, the method is exponentially faster than full quantum state tomography. We propose an enhanced direct fidelity estimation protocol that uses fewer copies of the experimental state by grouping Pauli operators before the sampling process. We derive analytical bounds on the measurement cost and estimator variance, showing improvements over the standard method. Numerical simulations validate our approach, demonstrating that for 8-qubit Haar-random states, our method achieves a one-third reduction in the required number of copies and reduces variance by an order of magnitude using only local measurements. These results underscore the potential of our protocol to enhance the efficiency of fidelity estimation in current quantum devices.
Quantum simulation has emerged as an interdisciplinary research field that enables microscopic access to quantum matter, both in and out of equilibrium, across various physical platforms. As an example, we analyze the emergence of the pseudogap phase in the fermionic Hubbard model. We identify a universal behavior of magnetic correlations upon entering the pseudogap phase, observed in both spin-spin and higher-order spin-charge correlations.
In addition to analog approaches, gate-based fermionic quantum computing offers distinct advantages for quantum simulations. We demonstrate the elementary operations required to manipulate orbital degrees of freedom, which form the basis of a fermionic quantum computer. We show high-fidelity gate operations and the generation of long-lived entangled states. Such gate-based operations can also be used to read out relevant order parameters and pairing correlations in analog quantum simulations.
In 1982, Streda and Widom established a thermodynamic relation that connects the quantized Hall conductivity of insulating phases to the magnetic response of particle density. This presentation examines how this fundamental relation can be harnessed and generalized to shed light on key properties of topological quantum matter, with particular emphasis on strongly correlated phases and out-of-equilibrium settings.
We propose a cooling algorithm, which can be utilized for state preparation. We analyze its properties in noiseless and noisy settings and show that in various scenarios the cooling algorithm outperforms the dissipative state preparation method.
We analyze the role of entanglement in particle physics
The precise quantification of the ultimate efficiency in manipulating quantum resources lies at the core of quantum information theory. However, purely information-theoretic measures fail to capture the actual computational complexity involved in performing certain tasks. In this work, we rigorously address this issue within the realm of entanglement theory, a cornerstone of quantum information science. We consider two key figures of merit: the computational distillable entanglement and the computational entanglement cost, quantifying the optimal rate of entangled bits (ebits) that can be extracted from or used to dilute many identical copies of n-qubit bipartite pure states, using computationally efficient local operations and classical communication (LOCC). We demonstrate that computational entanglement measures diverge significantly from their information-theoretic counterparts. While the von Neumann entropy captures information-theoretic rates for pure-state transformations, we show that under computational constraints, the min-entropy instead governs optimal entanglement distillation. Meanwhile, efficient entanglement dilution incurs a major cost, requiring maximal (order n) ebits even for nearly unentangled states. Surprisingly, in the worst-case scenario, even if an efficient description of the state exists and is fully known, one gains no advantage over state-agnostic protocols. Our results reveal a stark, maximal separation between computational and information-theoretic entanglement measures. Finally, our findings yield new sample-complexity bounds for measuring and testing the von Neumann entropy, fundamental limits on efficient state compression, and efficient LOCC tomography protocols. https://arxiv.org/abs/2502.12284
Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement [1]. It refutes Einstein's belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning.
While the few-body case is well-explored, the detection of nonlocality especially in quantum many-body systems, is notoriously challenging.
In this talk, I first motivate the usage of energy as a detector for many-body Bell nonlocality [2,3] and the certification of Bell correlation depth [4]. If an appropriate Hamiltonian is chosen, it can be used as a Bell correlation witness and by variationally decreasing the energy of a many-body system across a hierarchy of thresholds, we certify an increasing Bell correlation depth from experimental data.
In a recent work [5], we show that this theoretical concept is experimentally viable. We report an experimental certification of genuine multipartite Bell correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor.
As an illustrating example, we variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations.
Our results establish a viable approach for preparing and certifying multipartite Bell correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide towards exploiting multipartite Bell correlation in a wide spectrum of practical applications.
References
[1] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell Nonlocality, Rev. Mod. Phys. 86, 419 (2014).
[2] Tura, J., De las Cuevas, G., Augusiak, R., Lewenstein, M., Acín, A., & Cirac, J. I. Physical Review X, 7(2), 021005. (2017).
[3] P. Emonts, M. Hu, A. Aloy, and J. Tura, Effects of Topological Boundary Conditions on Bell Nonlocality, arXiv:2405.14587.
[4] G. Svetlichny, Distinguishing Three-Body from Two-Body Nonseparability by a Bell-Type Inequality, Phys. Rev. D 35, 3066 (1987).
[5] K. Wang et al., Probing Many-Body Bell Correlation Depth with Superconducting Qubits, Phys. Rev. X 15, 021024 (2025).
For years, an answer to the question of whether the triangle network with no inputs and binary outcomes supports quantum network nonlocality has remained elusive. By post-processing known higher-outcome quantum nonlocal distributions, quantum nonlocality was found when two of the parties have ternary outcomes. In addition to this, it is known that this scenario admits PR-box-type correlations. Yet, all efforts to prove, either, that all quantum realizations admit an alternative classical one, or that quantum nonlocality exists, have not fulfilled their goal.
In this talk I will give the first demonstration of a quantum nonlocal distribution in the no-input-two-outcome triangle network, thus demonstrating the existence of quantum advantage in the scenario. In order to find it, it was necessary to combine a recent complete characterization of the corresponding local set [arXiv:2503.16654] and novel methods of exploring the set of quantum realizations in networks, based on higher-order quantum transformations.
Understanding the confinement mechanism in gauge theories and the universality of effective string-like descriptions of gauge flux tubes remains a fundamental challenge in modern physics. We probe string modes of motion with dynamical matter in a digital quantum simulation of a (2+1) dimensional gauge theory using a superconducting quantum processor with up to 144 qubits, stretching the hardware capabilities with quantum-circuit depths comprising up to 192 two-qubit layers. We realize the Z2-Higgs model (Z2HM) through an optimized embedding into a heavy-hex superconducting qubit architecture, directly mapping matter and gauge fields to vertex and link superconducting qubits, respectively. Using the structure of local gauge symmetries, we implement a comprehensive suite of error suppression, mitigation, and correction strategies to enable real-time observation and manipulation of electric strings connecting dynamical charges. Our results resolve a dynamical hierarchy of longitudinal oscillations and transverse bending at the end points of the string, which are precursors to hadronization and rotational spectra of mesons. We further explore multi-string processes, observing the fragmentation and recombination of strings. The experimental design supports 300,000 measurement shots per circuit, totaling 600,000 shots per time step, enabling high-fidelity statistics. We employ extensive tensor network simulations using the basis update and Galerkin method to predict large-scale real-time dynamics and validate our error-aware protocols. This work establishes a milestone for probing non-perturbative gauge dynamics via superconducting quantum simulation and elucidates the real-time behavior of confining strings.
TNS provide efficient approximations of thermal equilibrium states. The most common algorithm constructs a purification of the thermal state starting from infinite temperature and evolving the state in imaginary time towards lower temperature. At very low temperatures, this has the practical drawback of trying to approximate a low rank density operator via a full rank one. We present a complementary ansatz, constructed from the zero-temperature limit, the ground state, which can be found with a standard tensor network approach. Motivated by properties of the ground state for conformal field theories, our ansatz is especially well-suited near criticality. Moreover, it allows an efficient computation of thermodynamic quantities and entanglement properties. We demonstrate the performance of our approach with a tree tensor network ansatz, although it can be extended to other tensor networks, and present results illustrating its effectiveness in capturing the finite-temperature properties in one- and two-dimensional scenarios. In particular, in the critical 1D case we show how the ansatz reproduces the finite temperature scaling of entanglement in a CFT.
Open system dynamics, in continuous time, remains largely understood within the Born-Markov approximation where a closed form master equation can be obtained to describe the system dynamics. However, many-body systems arising in quantum optics and condensed matter physics often interact with environments that have memory and cannot be described by a Lindblad master equation. While both theoretical and algorithmic tools are available for understanding many-body Markovian open systems, their counterparts for non-Markovian systems remain less well understood.
In this talk I will present some of our attempts to develop a mathematically rigorous theory of non-Markovian open quantum systems with Gaussian environments. I will show that, for a broad class of environments which strictly generalize the Markovian environment, a system-environment unitary group can be rigorously defined and, in many cases, can also be shown to be strongly-continuous two-parameter group. I will then go onto consider many-body lattice models with non-Markovian environment and establish a Lieb-Robinson bounds for these models. Finally, I will describe our recent work on developing quantum algorithms for simulating the dynamics of these models with near-optimal scaling on the system size and evolution time.
References:
[1] R. T, arXiv:2204.0963 (2022).
[2] R. T, M. Rudner, arXiv:2410.15481 (2024).
[3] X. Yu et al R. T, arXiv:2509.02268 (2025).
Topology is one of the latest branches in the history of mathematics and has entered fully into the most modern aspects of theoretical physics: quantum computation. This talk presents an overview of topological color codes as a solution for fault-tolerant quantum computing. Topology helps address the fundamental challenge of quantum computation: overcoming its inherent fragility to harness its enormous potential. After demonstrating the experimental realization of color codes across three quantum computing platforms—trapped ions with high-fidelity operations, cold atoms offering scalable architectures, and superconducting circuits providing fast gate times—we address the remaining challenges toward realizing fault-tolerant quantum computers capable of executing practical quantum algorithms.
https://www.museothyssen.org/actividades/100-anos-fisica-cuantica
Metastability —the persistence of a system in a long-lived, non-equilibrium state— is a ubiquitous phenomenon in physics, underlying behaviors from supercooled liquids, glasses, and magnetic materials to the false vacuum in cosmology. In this talk, I will explore how metastability arises in quantum many-body dynamics. I will present rigorous results on the lifetimes of metastable states in quantum many-body systems and discuss how these effects can be probed and controlled in state-of-the-art quantum simulators.
In this talk I will discuss recent results on long time dynamics of strongly interacting many body quantum systems, focusing on two settings: local random quantum circuits and time dynamics of closed quantum systems . For random quantum circuitsI will show that circuit complexity of states and unitaries saturate in exponential time and undergo recurrence after double exponential time (in system size). For unitary quantum dynamics I will present a general doubly exponential upper bound on recurrence time of and show examples of Hamiltonians and states that saturate it.
In this talk, we will review and compare two methods to efficiently prepare the Gibbs state of the 2D toric code at any positive temperature. We will first show that the Davies generator associated to the 2D toric code satisfies a modified logarithmic Sobolev inequality at any positive temperature, and hence mixes rapidly towards the Gibbs state. This allows for efficient Gibbs sampling via dissipation. Secondly, we will show that the 2D toric code can be mapped with a circuit of polynomial depth to two decoupled Ising chains, and thus can be efficiently sampled by sampling the Ising chains and conjugating with the circuit. Both methods are extended to larger families of CSS codes.
The last two decades have witnessed an increasingly growing interest in the study and characterisation of the entanglement structure of many-body quantum systems, also due to the development of related experiments. In this framework, a central object is the so-called entanglement Hamiltonian (EH), defined as the logarithm of the reduced density matrix, that provides a full description of the entanglement of a quantum state. In this seminar, I will present some recent results on the EH of inhomogeneous free fermionic systems. First, I will consider the two paradigmatic cases of the hopping chain with a linear potential, and the Fermi gas with a quadratic chemical potential. For both systems, we find that the EH is given by a deformed version of the physical Hamiltonian, with local inverse temperatures increasing linearly from the entanglement cut, in agreement with CFT predictions. Moreover, we show that the structure predicted by CFT is inherited by a tridiagonal matrix and a differential operator that commute exactly with the EH in the lattice and continuum cases, respectively. This result allows to obtain a very good approximation of the entanglement spectrum and entropy, using the properly rescaled eigenvalues of the commuting operator. Second, I will present the results for the EH of free-fermion chains with a particular form of inhomogeneity, namely the hopping amplitudes and chemical potentials are chosen such that the single particle eigenstates are related to discrete orthogonal polynomials of the Askey scheme. The bispectral properties of these functions allows the construction of an operator which commutes exactly with the EH. We show that also for these systems the commuting operators have the form of a spatial deformation of the physical Hamiltonian, with a deformation term identified as the local inverse temperature derived from a CFT treatment of the problem in the continuum limit. As in the previous cases, rescaling the eigenvalues of the commuting operators provides an excellent approximation of the entanglement spectrum.
We present a framework that leverages Clifford-enhanced matrix product state (MPS) techniques to tackle the challenges of simulating quantum many-body dynamics. By integrating stabilizer-based disentangling strategies into MPS algorithms, we enable efficient simulations of both circuit-based and Hamiltonian-driven evolutions. Our approach begins with a hybrid method combining tensor networks and random Clifford circuits, demonstrating reduced entanglement growth and improved simulation capabilities in circuit dynamics. Building on this foundation, we develop a Clifford-dressed time-dependent variational principle (TDVP) algorithm that actively suppresses entanglement during Hamiltonian evolution, significantly extending accessible simulation times and improving accuracy in local observables. Finally, we extend this framework to compute quantities beyond standard expectation values—such as Loschmidt echoes—by exploiting overlaps between MPS and stabilizer states. This suite of techniques opens new pathways for scalable simulations of quantum systems, bridging computational efficiency with the richness of many-body physics.
References:
Hybrid Stabilizer Matrix Product Operator. AFM, A. Santini, M. Collura. PRL. (2024)
Clifford dressed time-dependent variational principle. AFM, A. Santini, G. Lami, J. De Nardis, M. Collura. PRL. (2025)
Clifford-dressed variational principles for precise Loschmidt echoes. AFM, A. Santini, M. Collura. Accepted in PRA. (2025)
Understanding the emergence of computational complexity in quantum many-body systems is a central challenge in quantum information and condensed matter physics. While fermionic Gaussian states and operations define a class of classically simulable dynamics, non-Gaussianity plays an analogous role to magic in the qubit Clifford/non-Clifford framework—serving as the key resource that enables universal quantum computation and classical intractability. In this talk, I will introduce the fermionic antiflatness (FAF), a novel, efficiently computable measure of fermionic non-Gaussianity based on two-point Majorana correlators. The FAF vanishes only for fermionic Gaussian states and remains invariant under Gaussian operations.
I will demonstrate how this framework captures essential features of quantum complexity, from the structure of typical Haar-random states to critical phenomena in equilibrium systems and the dynamical buildup of non-Gaussianity in out-of-equilibrium settings.
The thermalization dynamics of quantum spin systems, in certain regimes, is described by an ergodic quantum Markov semigroup, whose mixing time can be controlled by estimating the spectral gap of its generator. In the case of semigroups which satisfy a strong quantum detailed balance condition, I will show how to estimate the spectral gap of the generator via a correlation decay measure on the invariant state. Examples of models for which the correlation decay can be explicitly computed are every 1D model and the 2D quantum double models by Kitaev.
Based on a joint work with D. Pérez-García and A. Pérez-Hernández (arXiv:2505.08991).
Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued by collections of both environmental influence and temporal instabilities. These induce noisy quantum and classical correlations at the level of the circuit. The relevant spatiotemporal effects are difficult enough to understand, let alone combat. There is presently a lack of either scalable or complete methods to address the phenomena responsible for scrambling and loss of quantum information. Here, we make deep strides to remedy this problem. We establish a theoretical framework that uniformly incorporates and classifies all non-Markovian phenomena. Our framework is universal, assumes no parameters values, and is written entirely in terms of experimentally accessible circuit-level quantities. We formulate an efficient reconstruction using tensor network learning, allowing also for easy modularization and simplification based on the expected physics of the system. This is then demonstrated through both extensive numerical studies and implementations on IBM Quantum devices, estimating a comprehensive set of spacetime correlations. Finally, we conclude our analysis with applications thereof to the efficacy of control techniques to counteract these effects—including noise-aware circuit compilation and optimized dynamical decoupling. We find significant improvements are possible in the diamond norm and average gate fidelity of arbitrary SU(4) operations, as well as related decoupling improvements in contrast to off-the-shelf schemes.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings.
We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. This is achieved by applying single-qubit π or π/2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by solving an efficient linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite pulse time errors and various control errors. Finally, we demonstrate the performance of our scheme with numerical simulations for various examples, including systems Hamiltonians with all-to-all connectivity motivated by ion traps and with a 2D square lattice connectivity.
Quantum-gas microscopes allow one to image synthetic quantum materials made of ultracold atoms trapped in optical lattices at the single-site and single-atom level, and have opened a new era in the field of quantum simulation. A prime example is the study of the Fermi-Hubbard model and its many-body phase diagram, where the investigation of antiferromagnetic order was enabled by the achievement of spin-resolved imaging of fermionic alkali atoms. Alkaline-earth elements, like strontium, offer novel tools for the study of Hubbard quantum many-body systems. These include large-spin fermionic isotopes with SU(N) symmetry as well as narrow and ultranarrow transitions. In my talk, I will present our very recent realization of a quantum-gas microscope for fermionic strontium-87 atoms. With its nuclear spin of I = 9/2, this atom realizes the SU(N) Fermi-Hubbard model with N = 10 spin states. Building on our previous results with bosonic strontium [1], we have developed an imaging scheme that exploits strontium's narrow intercombination line and allows us to consecutively image the site occupation of the 10 spin states in each single experimental sequence. Thanks to its single-atom resolved images and full spin-resolution, our system provides unparalleled access to the exotic quantum-magnetic phases of the SU(N) Fermi-Hubbard model.
[1] S. Buob, J. Höschele, V. Makhalov, A. Rubio-Abadal, L. Tarruell, A strontium quantum-gas microscope, PRX Quantum 5, 020316 (2024).
The framework of process tensors, also known as quantum combs, is a powerful tool to characterize non-Markovian processes in terms of only system-level quantities. However, these analyses are limited in generality due to the common digitisation of processes. Currently, there is an absence of a complete framework for arbitrary open quantum processes at continuous intervals. Therefore, despite the practical success of the traditional process tensor framework, there is a lack of operational understanding of continuous time, non-Markovian open quantum systems. This is a problem at the practical level (devices take finite time to implement control) as well as dissatisfying at the foundational level (we should be able to treat fully general stochastic processes and phenomena such as multi-time correlations in way that is commensurate with Schrödinger evolution — without resorting to digitisation).
In this work, we propose a continuous generalization of the process tensor framework using continuous matrix product states (cMPS) to extend it into the continuous-time domain. Here, we encode the time process into the spatial structure of a 1D field theory state which is naturally continuous. We demonstrate how the interplay of control and environment can be expressed as the overlap of two cMPS states. Any multi-time experiment, including analog control and continuous measurements with feedback, is describable under this picture. In other words, the effects of continuous non-Markovian phenomena can be made precise. Importantly, we show how families of discrete process tensors emerge from this formalism, thereby completing the Kolmogorov picture of quantum stochastic processes in a constructive sense.
In addition to providing insight into the nature of all device noise, from the physical to the logical level, our framework presents a new way to understand continuous multi-time phenomena by offering a compact yet fully general approach to characterize non-Markovianity in continuous settings.
Lattice gauge theories (LGTs) describe a broad range of phenomena in condensed matter and particle physics. A prominent example is confinement, responsible for bounding quarks inside hadrons such as protons or neutrons. When quark-antiquark pairs are separated, the energy stored in the string of gluon fields connecting them grows linearly with their distance, until there is enough energy to create new pairs from the vacuum and break the string. While such phenomena are ubiquitous in LGTs, simulating the resulting dynamics is a challenging task. In this talk, I will report the observation of string breaking in synthetic quantum matter using a programmable quantum simulator based on neutral atom arrays [1]. I will first show how a (2+1)D LGT with dynamical matter can be efficiently implemented when the atoms are placed on a Kagome geometry, with a local U(1) symmetry emerging from the Rydberg blockade, while long-range Rydberg interactions naturally give rise to a linear confining potential between pairs of charges. In the experiment, we probe string breaking in equilibrium by adiabatically preparing the ground state of the atom array in the presence of defects, distinguishing regions within the confined phase dominated by fluctuating strings or by broken string configurations. Finally, by harnessing local control over the atomic detuning, we quench string states and observe string breaking dynamics exhibiting a many-body resonance phenomenon. As an outlook, I will present a roadmap to further explore phenomena in high-energy physics using programmable quantum simulators.
[1] arXiv:2410.16558 (2024) (accepted in Nature)
Quantum Information Theory, the standard formalism used to represent information contained in quantum systems, is based on complex Hilbert spaces (CQT). It was recently shown that it predicts correlations in quantum networks which cannot be explained by Real Quantum Theory (RQT), a quantum theory with real Hilbert spaces instead of complex ones, when three parties are involved in a quantum network with non-trivial locality constraints. In this work, we study a scenario with N+1 parties sharing quantum systems in a star network. Here, we construct a "conditional" multipartite Bell inequality that exhibits a gap between RQT and CQT, which linearly increases with N and is thus arbitrarily large in the asymptotic limit. This implies, that, as the number of parties grows, Hilbert space formalism based on real numbers becomes exceedingly worse at describing complex networks of quantum systems. Furthermore, we also compute the tolerance of this gap to experimental errors.
In this talk I will describe our work on quantum networks of quantum emitters [1]. From the point of view of Quantum Optics, these are setups of quantum emitters (i.e. qubits or cavities that talk to qubits) connected by waveguides that transport photons among those nodes. This leads to a paradigm of quantum systems interacting through the exchange of retarded photons, creating what we call a non-local quantum many-body system. I will discuss the theoretical tools we have developed and how these tools can already provide insight in topics ranging from quantum state transfer among quantum processors to a new type of collective emission, called cascaded superradiance, that takes place in these networks.[1] Time-delayed collective dynamics in waveguide QED and bosonic quantum networks, Carlos Barahona-Pascual, Hong Jiang, Alan C. Santos, Juan José García-Ripoll, arXiv:2505.02642