Wednesday
Average-computation benchmarking for local expectation values in digital quantum devices
As quantum devices progress towards a quantum advantage regime, they become harder to benchmark. A particularly relevant challenge is to assess the quality of the whole computation, beyond testing the performance of each single operation. I will discuss a scheme for this task that combines the target computation with variants of it, which, when averaged, allow for classically solvable correlation functions. Importantly, the variants exactly preserve the circuit architecture and depth, without simplifying the gates into a classically-simulable set. The method is based on replacing each gate by an ensemble of similar gates, which when averaged together form space-time channels [P. Kos and G. Styliaris, Quantum 7, 1020 (2023)]. We introduce explicit constructions for ensembles producing such channels, all applicable to arbitrary brickwork circuits, and provide a general recipe to find new ones through semidefinite programming. The resulting average computation retains important information about the original circuit and is able to detect noise beyond a Clifford benchmarking regime. Moreover, we provide evidence that estimating average-computation expectation values requires running only a limited number of different circuit realizations.
Quantum Circuit Complexity of Tensor Network States and Unitaries
The preparation of quantum states is a fundamental task in quantum computing, error correction, and quantum simulation. Designing efficient preparation algorithms and understanding their gate complexity are therefore of central importance. In this talk, we focus on the preparation of many-body quantum states that obey an entanglement area law; such states are naturally represented by tensor networks. We present efficient preparation schemes in both one and two spatial dimensions. A key ingredient involves leveraging measurements and classical feedforward to generate long-range entanglement using only shallow quantum circuits. We then discuss one-dimensional unitaries that preserve the entanglement area law and present a polynomial-time algorithm for their implementation.
Complexity of injective PEPS
Projected-entangled pair states (PEPS) are a successful variational family of states with an area law that naturally capture ground states. Contracting such states is known to be postBQP-hard, but the existing hardness construction is highly pathological (non-injective). To make the physically realistic, PEPS ought to be injective, which makes them the unique ground state of a local Hamiltonian. Does this make contraction easier?
By embedding noisy postselected quantum circuits in them, we prove that injective PEPS undergo a complexity transition from postBQP-hard (constant weak injectivity) to classically easy (constant strong injectivity). These results also have implications on the type of correlations these states can support and whether the corresponding Hamiltonian is QMA-hard or not.
Universality and phase transition in the projected ensemble
In this talk I will discuss the projected ensemble, the collection of local post-measurement wavefunctions of a quantum many-body state. I will focus on states arising from evolution under generic isolated quantum dynamics, and describe the universal limiting distributions the projected ensemble attains, which depend on the interplay of conserved quantities and information obtained from the measurements. This amounts to a more refined version of quantum equilibration beyond standard thermalization of local observables, which has been dubbed “deep thermalization”. I will further explain how these limiting distributions are predicted by generalized maximum entropy principles rooted in quantum information theory. At the same time, I will also present a class of quantum dynamics where depending on the choice of measurements, the projected ensemble undergoes a phase transition from a maximally entropic one to a minimally entropic one, signatures of which are not detectable at the level of the density matrix. This constitutes a novel form of ergodicity-breaking, characterized not by the failure of the system to regularly thermalize, but rather by its failure to deep thermalize.
Classically Simulable Operator Scrambling
A fundamental aspect of quantum mechanics is the scrambling of quantum information - how information encoded in an initial state or operator gets spread out, scrambled, across many degrees of freedom under time evolution. For generic chaotic many-body quantum systems, numerically studying scrambling is exponentially hard in the number of qubits, and as such can only be done for small system size. I will describe a novel type of many-body quantum dynamics known as super-Clifford circuits, for which certain probes of operator scrambling can be efficiently simulated on a classical computer. In particular, I will show that in such circuits both operator entanglement and OTOCs can be efficiently computed for a large class of many-body operators. Furthermore, these super-Clifford circuits include examples of fast scramblers, in the sense that the operator entanglement of these many-body operators saturates as quickly as allowed by fundamental bounds.
Non-local Magic
There is nothing a quantum computer can do that a classical computer will not do without entanglement. There is also nothing that gives any quantum advantage without magic. For this reason, the onset of both quantum complex behavior and quantum advantage resides in the interplay between the two resources. A particularly strong form of such an interplay is that of the so-called non-local magic. This is the fraction of non-stabilizer resources that local unitary operations cannot erase. This quantity has also the operational meaning of the magic which is not accessible to be distilled using local operations. Non-local magic is also a hindrance to some genuine quantum behavior like violations of Bell's inequality. In a completely different setting, non-local magic is the holographic counterpart of back-reaction in the AdS-CFT correspondence, thus providing an additional intriguing connection between quantum advantage and holography. We also show the first experimental demonstration and measurement of non-local magic in a superconducting quantum computer.
Lieb-Robinson bounds with exponential-in-volume tails
We present Lieb-Robinson bounds for nested commutators, using the equivalence class framework of arXiv:1905.03682. These nested Lieb-Robinson bounds capture the enhanced suppression of extended operators in higher dimensions. We present two applications of these Lieb-Robinson bounds: (1) tighter bounds on disorder parameters and ground state splitting in spontaneous symmetry breaking states and (2) tight bounds on classical resources for simulation of quantum dynamics up to time with error in dimension . This talk is based on arXiv.2502.02652.
Thursday
Emergent random matrix universality in quantum operator dynamics
The memory function description of many-body quantum operator dynamics involves a carefully chosen split into ‘fast’ and ‘slow’ modes. An approximate model for the fast modes can then be used to solve for Green’s functions of the slow modes.
Using a formulation in operator Krylov space, we prove the emergence of a universal random matrix description of the fast mode dynamics. This emergent universality can occur in both chaotic and non-chaotic systems, provided their spectral functions are sufficiently smooth. Our proof is complex analytic in nature, involving a map to a Riemann-Hilbert problem which we solve using a nonlinear steepest-descent-type method. We further use these results to develop a new numerical approach for estimating spectral functions.
Operator dynamics and quantum Ruelle-Pollicott resonance
The decay of dynamical correlation functions encodes essential information about the system’s dynamics. In systems without conservation laws, the decay rate is governed by the (leading) Ruelle–Pollicott (RP) resonance. While the concept of RP resonances is well established for classical and single-particle quantum systems, its extension to quantum many-body systems has emerged only in the past two years. In this talk, I will introduce the notion of quantum RP resonances and present two complementary approaches to obtain them: weak dissipation and operator truncation. Both approaches, which turn out to be equivalent, necessarily introduce non-unitarity into the dynamics—an ingredient essential for defining RP resonances. I will illustrate these ideas using a prototypical Floquet circuit, the random phase model.
Classical Simulation of Non-Gaussian Quantum Circuits
We review recent progress on the problem of simulating the behavior of quantum circuits by classical algorithms, a key computational tool for the assessment of quantum-information-processing proposals. A cornerstone result here is the Gottesman-Knill theorem which provides a means for efficiently simulating the dynamics of a Clifford circuit applied to stabilizer states. By incorporating phase-sensitivity in the simulation, this approach has successfully been extended to apply to non-stabilizer states and non-Clifford operations. We argue that simulation algorithms for (fermionic and bosonic) Gaussian circuits can similarly be modified to study circuits with non-Gaussian elements. In addition, we present a new reduction from strong to weak simulation. This enables efficient sampling from output distributions of measurements having continuous outcomes and is particularly relevant for the simulation of quantum optics with non-linearities.
This is joint work with Beatriz Dias.
[1] Beatriz Diaz and Robert Koenig, Classical simulation of non-Gaussian bosonic circuits,
Phys. Rev. A 110, 042402 (2024)
[2] Beatriz Diaz and Robert Koenig, Classical simulation of non-Gaussian fermionic circuits,
Quantum 8, 1350 (2024)
[3] Beatriz Dias and Robert Koenig, On the sampling complexity of coherent superpositions,
arXiv:2501.17071
Classical simulation of parity-preserving quantum circuits and beyond
In this talk I will start by describing the main approaches to classically simulating fermionic systems and challenges associated with these methods. I will then present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a fermionic tensor network and introduce a novel decomposition of non-Matchgate gates into a Gaussian fermionic tensor and a residual quartic term, inspired by interacting fermionic systems. The quartic term is independent of the specific gate, which allows us to precompute intermediate results independently of the exact circuit structure and leads to significant speedups when compared to other methods. Our decomposition suggests a natural perturbative expansion which can be turned into an algorithm to compute measurement outcomes and observables to finite accuracy when truncating at some order of the expansion. For particle number conserving gates, our decomposition features a unique truncation cutoff reducing the computational effort for high precision calculations. Our algorithm significantly lowers resource requirements for simulating parity-preserving circuits while retaining high accuracy, making it suitable for simulations of interacting systems in quantum chemistry and material science. Lastly, we discuss how our algorithm compares to other classical simulation methods for fermionic quantum systems and ways of scaling our methods up further. This is joint work with Carolin Wille (https://arxiv.org/abs/2504.19317)
Full counting statistics after quantum quenches as hydrodynamic fluctuations
The statistics of fluctuations on large regions of space encodes universal properties of many-body systems. At equilibrium, it is described by thermodynamics. However, away from equilibrium such as after quantum quenches, the fundamental principles are more nebulous. In particular, although exact results have been conjectured in integrable models, a correct understanding of the physics is largely missing. In this talk, I will discuss these principles, taking the example of the number of particles within a large interval in one-dimensional interacting systems. These are based on simple hydrodynamic arguments from the theory of ballistically transported fluctuations, and in particular the Euler-scale transport of long-range correlations. This allows to obtain a formula for the full counting statistics in terms of thermodynamic and hydrodynamic quantities, whose validity though depends on the structure of hydrodynamic modes. In fermionic-statistics interacting integrable models with a continuum of hydrodynamic modes, such as the Lieb-Liniger model for cold atomic gases, the formula reproduces previous conjectures, but is in fact not exact: more specifically, it gives the correct cumulants up to, including, order 5, while long-range correlations modify higher cumulants.
Entanglement and symmetry dynamics in dual unitary circuits with impurities
The most common protocol for studying far-from-equilibrium quantum systems is the quantum quench. The system is prepared in a non-equilibrium state and then evolved unitarily. Typically, the time evolution operator is translationally invariant, and, in such cases, many universal results have been obtained concerning local relaxation, the growth of entanglement and lately, also, the dynamics of broken symmetries. In this talk, I will discuss some interesting phenomena which arise when translational invariance is broken by the presence of an impurity in the system. Concentrating on a specify example— dual unitary quantum circuits— I will show how the inclusion of an impurity gate which is not dual unitary can significantly impact the dynamics of entanglement and, in some cases, lead to non-monotonic behaviour. When the impurity breaks a symmetry of the bulk system, the physics is richer. A competition takes place between the bulk which restores the symmetry and the impurity which breaks it, thereby facilitating novel phenomena like the quantum Mpemba effect. If time permits, I will also discuss the case when the impurity is not unitary, and more specifically represents a projective measurement. In this case the entanglement growth shows a strong dependence on the placement of the impurity: in some cases, entanglement is suppressed, in others it is enhanced.
Entanglement and symmetry breaking in quantum spin systems
Friday
A Randomised East Model
Constrained quantum models are one of the pathways to breaking ergodicity without disorder. East models in particular are a type of model with irreducible dynamics (fully-connected Fock space representation). I will present some of our work on such models, including recent results on randomised versions of the East model, in the spirit of random matrix theory, which display the same behaviour. The conclusion is that it is the structure in Fock space, and not the details, that determine the qualitative impact of the constraints.
Finite-temperature quantum topological order in three dimensions
We identify a three-dimensional system that exhibits long-range entanglement at sufficiently small but nonzero temperature--it therefore constitutes a quantum topological order at finite temperature. The model of interest is known as the fermionic toric code, a variant of the usual 3D toric code, which admits emergent fermionic point-like excitations. The fermionic toric code, importantly, possesses an anomalous 2-form symmetry, associated with the space-like Wilson loops of the fermionic excitations. We argue that it is this symmetry that imbues low-temperature thermal states with a novel topological order and long-range entanglement. Based on the current classification of three-dimensional topological orders, we expect that the low-temperature thermal states of the fermionic toric code belong to an equilibrium phase of matter that only exists at nonzero temperatures. We conjecture that further examples of topological orders at nonzero temperatures are given by discrete gauge theories with anomalous 2-form symmetries. Our work therefore opens the door to studying quantum topological order at nonzero temperature in physically realistic dimensions.
Subexponential decay of local correlations from diffusion-limited dephasing
Chaotic quantum systems at finite energy density are expected to rapidly dephase local quantum superpositions. We argue this process is subexponential for generic chaotic dynamics with conservation laws (e.g., energy or magnetization) in one spatial dimension: all local correlation functions decay as stretched exponentials or slower. The stretched exponential bound is a quantum coherent effect, and could be saturated by operators which are orthogonal to all hydrodynamic modes. [arXiv: 2504.05380]
Measurement-induced phase transitions in quantum inference problems and quantum hidden Markov models
Author: Sun Woo Kim
Recently, there is interest in coincident 'sharpening' and 'learnability' transitions in monitored quantum systems. In the latter, an outside observer's ability to infer properties of a quantum system from measurements undergoes a phase transition. Such transitions appear to be related to the decodability transition in quantum error correction, but the precise connection is not clear. Here, we study these problems under one framework we call the general quantum inference problem. In cases as above where the system has a Markov structure, we say that the inference is on a quantum hidden Markov model. We show a formal connection to classical hidden Markov models and that they coincide for certain setups. For example, we prove this for those involving Haar-random unitaries and measurements. We introduce the notion of Bayes non-optimality, where parameters used for inference differs from true ones. This allows us to expand the phase diagrams of above models. At Bayes optimality, we obtain an explicit relation between 'sharpening' and 'learnability' order parameters, explicitly showing that the two transitions coincide. Next, we study concrete examples. We review quantum error correction on the toric and repetition code and their mapping to 2D random-bond Ising model (RBIM) through our framework. We study the Haar-random U(1)-symmetric monitored quantum circuit and tree, mapping each to inference models that we call the planted SSEP and planted XOR, respectively, and expanding the phase diagram to Bayes non-optimality. For the circuit, we deduce the phase boundary numerically and analytically argue that it is of a single universality class. For the tree, we present an exact solution of the entire phase boundary, which displays re-entrance as does the 2D RBIM. We discuss these phase diagrams, with their interpretations for quantum inference problems and rigorous arguments on their shapes.
