arXiv subjects

J. Ignacio Cirac

Publications and source records attributed to J. Ignacio Cirac.

At least 73 records · Page 4Linked to original sources

arXiv2023

Efficient Adiabatic Preparation of Tensor Network States

We propose and study a specific adiabatic path to prepare those tensor network states that are unique ground states of few-body parent Hamiltonians in finite lattices, which include normal tensor network states, as well as other relevant nonnormal states. This path guarantees a gap for finite systems and allows for efficient numerical simulation. In one dimension, we numerically investigate the preparation of a family of states with varying correlation lengths and the one-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) state and show that adiabatic preparation can be much faster than standard methods based on sequential preparation. We also apply the method to the two-dimensional AKLT state on the hexagonal lattice, for which no method based on sequential preparation is known, and show that it can be prepared very efficiently for relatively large lattices.

quant-ph↗

arXiv2023

Fermionic matter-wave quantum optics with cold-atom impurity models

Motivated by recent cold-atom realisations of matter-wave waveguide QED, we study simple fermionic impurity models and discuss fermionic analogues of several paradigmatic phenomena in quantum optics, including formation of non-trivial bound states, (matter-wave) emission dynamics, and collective dissipation. For a single impurity, we highlight interesting ground-state features, focusing in particular on real-space signatures of an emergent length scale associated with an impurity screening cloud. We also present novel non-Markovian many-body effects in the quench dynamics of single- and multiple-impurity systems, including fractional decay around the Fermi level and multi-excitation population trapping due to bound states in the continuum.

quant-ph↗

arXiv2023

Exploiting the Photonic Non-linearity of Free Space Subwavelength Arrays of Atoms

Ordered ensembles of atoms, such as atomic arrays, exhibit distinctive features from their disordered counterpart. In particular, while collective modes in disordered ensembles show a linear optical response, collective subradiant excitations of subwavelength arrays are endowed with an intrinsic non-linearity. Such non-linearity has both a coherent and a dissipative component: two excitations propagating in the array scatter off each other leading to formation of correlations and to emission into free space modes. We show how to take advantage of such non-linearity to coherently prepare a single excitation in a subradiant (dark) collective state of a one dimensional array as well as to perform an entangling operation on dark states of parallel arrays. We discuss the main source of errors represented by disorder introduced by atomic center-of-mass fluctuations, and we propose a practical way to mitigate its effects.

quant-ph↗

arXiv2023

A variational Monte Carlo algorithm for lattice gauge theories with continuous gauge groups: a study of (2+1)-dimensional compact QED with dynamical fermions at finite density

Lattice gauge theories coupled to fermionic matter account for many interesting phenomena in both high energy physics and condensed matter physics. Certain regimes, e.g. at finite fermion density, are difficult to simulate with traditional Monte Carlo algorithms due to the so-called sign-problem. We present a variational, sign-problem-free Monte Carlo method for lattice gauge theories with continuous gauge groups and apply it to (2+1)-dimensional compact QED with dynamical fermions at finite density. The variational ansatz is formulated in the full gauge field basis, i.e. without having to resort to truncation schemes for the $U(1)$ gauge field Hilbert space. The ansatz consists of two parts: first, a pure gauge part based on Jastrow-type ansatz states (which can be connected to certain neural-network ansatz states) and secondly, on a fermionic part based on gauge-field dependent fermionic Gaussian states. These are designed in such a way that the gauge field integral over all fermionic Gaussian states is gauge-invariant and at the same time still efficiently tractable. To ensure the validity of the method we benchmark the pure gauge part of the ansatz against another variational method and the full ansatz against an existing Monte Carlo simulation where the sign-problem is absent. Moreover, in limiting cases where the exact ground state is known we show that our ansatz is able to capture this behavior. Finally, we study a sign-problem affected regime by probing density-induced phase transitions.

hep-lat↗

arXiv2023

Quantum Simulation of Z2 Lattice Gauge theory with minimal resources

The quantum simulation of fermionic gauge field theories is one of the anticipated uses of quantum computers in the NISQ era. Recently work has been done to simulate properties of the fermionic Z2 gauge field theory in (1+1) D and the pure gauge theory in (2+1) D. In this work, we investigate various options for simulating the fermionic Z2 gauge field theory in (2+1) D. To simulate the theory on a NISQ device it is vital to minimize both the number of qubits used and the circuit depth. In this work we propose ways to optimize both criteria for simulating time dynamics. In particular, we develop a new way to simulate this theory on a quantum computer, with minimal qubit requirements. We provide a quantum circuit, simulating a single first order Trotter step, that minimizes the number of 2-qubit gates needed and gives comparable results to methods requiring more qubits. Furthermore, variational approaches are investigated that allow to further decrease the circuit depth.

quant-ph↗

arXiv2023

Simulating prethermalization using near-term quantum computers

Quantum simulation is one of the most promising scientific applications of quantum computers. Due to decoherence and noise in current devices, it is however challenging to perform digital quantum simulation in a regime that is intractable with classical computers. In this work, we propose an experimental protocol for probing dynamics and equilibrium properties on near-term digital quantum computers. As a key ingredient of our work, we show that it is possible to study thermalization even with a relatively coarse Trotter decomposition of the Hamiltonian evolution of interest. Even though the step size is too large to permit a rigorous bound on the Trotter error, we observe that the system prethermalizes in accordance with previous results for Floquet systems. The dynamics closely resemble the thermalization of the model underlying the Trotterization up to long times. We extend the reach of our approach by developing an error mitigation scheme based on measurement and rescaling of survival probabilities. To demonstrate the effectiveness of the entire protocol, we apply it to the two-dimensional XY model and numerically verify its performance with realistic noise parameters for superconducting quantum devices. Our proposal thus provides a route to achieving quantum advantage for relevant problems in condensed matter physics.

quant-ph↗

arXiv2022

Cross-Platform Verification in Quantum Networks

Intermediate-scale quantum devices are becoming more reliable, and may soon be harnessed to solve useful computational tasks. At the same time, common classical methods used to verify their computational output become intractable due to a prohibitive scaling of required resources with system size. Inspired by recent experimental progress, here we describe and analyze efficient cross-platform verification protocols for quantum states and show how these can be used to verify computations. We focus on the pair-wise comparison between distant nodes of a quantum network, identify the most promising protocols and then discuss how they can be implemented in laboratory settings. As a proof of principle, we implement basic versions of these schemes on available quantum processors.

quant-ph↗

arXiv2022

Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases

We consider free fermions living on lattices in arbitrary dimensions, where hopping amplitudes follow a power-law decay with respect to the distance. We focus on the regime where this power is larger than the spatial dimension (i.e., where the single particle energies are guaranteed to be bounded) for which we provide a comprehensive series of fundamental constraints on their equilibrium and nonequilibrium properties. First we derive a Lieb-Robinson bound which is optimal in the spatial tail. This bound then implies a clustering property with essentially the same power law for the Green's function, whenever its variable lies outside the energy spectrum. The widely believed (but yet unproven in this regime) clustering property for the ground-state correlation function follows as a corollary among other implications. Finally, we discuss the impact of these results on topological phases in long-range free-fermion systems: they justify the equivalence between Hamiltonian and state-based definitions and the extension of the short-range phase classification to systems with decay power larger than the spatial dimension. Additionally, we argue that all the short-range topological phases are unified whenever this power is allowed to be smaller.

quant-ph↗

arXiv2022

Few-body analogue quantum simulation with Rydberg-dressed atoms in optical lattices

Most experiments with ultracold atoms in optical lattices have contact interactions, and therefore operate at high densities of around one atom per site to observe the effect of strong interactions. Strong ranged interactions can be generated via Rydberg dressing, which opens the path to explore the physics of few interacting particles. Rather than the unit cells of a crystal, the sites of the optical lattice can now be interpreted as discretized space. This allows studying completely new types of problems in a familiar architecture. We investigate the possibility of realizing problems akin to those found in quantum chemistry, although with a different scaling law in the interactions. Through numerical simulation, we show that simple pseudo-atoms and -molecules could be prepared with high fidelity in state-of-the-art experiments.

quant-ph↗

arXiv2022

A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model

We present an ansatz for the ground states of the Quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our ansatz, based on the concept of generalized coherent states, very well captures the fundamental aspects of the model, including the ground state energy and the position of the spin glass phase transition. It further enables us to study some previously unexplored features, such as the non-vanishing longitudinal field regime and the entanglement structure of the ground states. We find that the ground state entanglement can be captured by a simple ensemble of weighted graph states with normally distributed phase gates, leading to a volume law entanglement, contrasting with predictions based on entanglement monogamy.

quant-ph↗

arXiv2022

Simulability transitions in continuous-time dynamics of local open quantum systems

We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to sample from the state of the spins when the rate of noise is higher than a threshold determined by the strength of the local interactions. Furthermore, by encoding a 1D fault tolerant quantum computation into the dynamics of spin systems arranged on two or higher dimensional grids, we show that for several noise channels, the problem of weakly simulating the output state of both purely Hamiltonian and purely dissipative dynamics is expected to be hard in the low-noise regime.

quant-ph↗

arXiv2022

Topological Effects in Two-Dimensional Quantum Emitter Systems

In this work we discuss particular effects that take place in systems of quantum emitters coupled to two-dimensional bosonic topological insulators. For a single emitter coupled to the Haldane model, we find a "fragile" quasibound state that makes the emitter dynamics very sensitive to the model's parameters, and gives rise to effective long-range interactions that break time-reversal symmetry. We then discuss one-dimensional arrangements of emitters, emitter line defects, and how the topology of the bath affects the effective polariton models that appear in the weak-coupling regime when the emitters are spectrally tuned to a bandgap. In the Harper-Hofstadter model we link the non-monotonic character of the effective interactions to the Chern numbers of the surrounding energy bands, while in the Haldane model we show that the effective models are either gapless or not depending on the topology of the bath. Last, we discuss how the presence of emitters forming an ordered array, an emitter superlattice, can produce polariton models with non-trivial Chern numbers, and also modify the topology of the photonic states in the bath.

cond-mat.mes-hall↗

arXiv2022

Free-fermion Page Curve: Canonical Typicality and Dynamical Emergence

We provide further analytical insights into the newly established noninteracting (free-fermion) Page curve, focusing on both the kinematic and dynamical aspects. First, we unveil the underlying canonical typicality and atypicality for random free-fermion states. The former appears for a small subsystem and is exponentially weaker than the well-known result in the interacting case. The latter explains why the free-fermion Page curve differs remarkably from the interacting one when the subsystem is macroscopically large, i.e., comparable with the entire system. Second, we find that the free-fermion Page curve emerges with unexpectedly high accuracy in some simple tight binding models in long-time quench dynamics. This contributes a rare analytical result concerning quantum thermalization on a macroscopic scale, where conventional paradigms such as the generalized Gibbs ensemble and quasi-particle picture are not applicable.

quant-ph↗

arXiv2022

Symmetries and field tensor network states

We study the interplay between symmetry representations of the physical and virtual space on the class of tensor network states for critical spins systems known as field tensor network states (fTNS). These are by construction infinite dimensional tensor networks whose virtual space is described by a conformal field theory (CFT). We can represent a symmetry on the physical index as a commutator with the corresponding CFT current on the virtual space. By then studying this virtual space representation we can learn about the critical symmetry protected topological properties of the state, akin to the classification of symmetry protected topological order for matrix product states. We use this to analytically derive the critical symmetry protected topological properties of the two ground states of the Majumdar-Ghosh point with respect to the previously defined symmetries.

cond-mat.stat-mech↗

arXiv2022

Error propagation in NISQ devices for solving classical optimization problems

We propose a random circuit model to analyze the impact of noise on the performance of variational quantum circuits for classical optimization problems. Our model accounts for the propagation of arbitrary single qubit errors through the circuit. We find that even with a small noise rate, the quality of the obtained classical optima is low on average and a single-qubit error rate of $1 / nD$, where $n$ is the number of qubits and $D$ is the circuit depth, is needed for the possibility of a quantum advantage. We estimate that this translates to an error rate lower than $10^{-6}$ using QAOA for classical optimization problems with 2D circuits.

quant-ph↗

arXiv2022

Matrix product operator algebras I: representations of weak Hopf algebras and projected entangled pair states

Matrix Product Operators (MPOs) are tensor networks representing operators acting on 1D systems. They model a wide variety of situations, including communication channels with memory effects, quantum cellular automata, mixed states in 1D quantum systems, or holographic boundary models associated to 2D quantum systems. A scenario where MPOs have proven particularly useful is to represent algebras of non-trivial symmetries. Concretely, the boundary of both symmetry protected and topologically ordered phases in 2D quantum systems exhibit symmetries in the form of MPOs. In this paper, we develop a theory of MPOs as representations of algebraic structures. We establish a dictionary between algebra and MPO properties which allows to transfer results between both setups, covering the cases of pre-bialgebras, weak bialgebras, and weak Hopf algebras. We define the notion of pulling-through algebras, which abstracts the minimal requirements needed to define topologically ordered 2D tensor networks from MPO algebras. We show, as one of our main results, that any semisimple pivotal weak Hopf algebra is a pulling-trough algebra. We demonstrate the power of this framework by showing that they can be used to construct Kitaev's quantum double models for Hopf algebras solely from an MPO representation of the Hopf algebra, in the exact same way as MPO symmetries obtained from fusion categories can be used to construct Levin-Wen string-net models, and to explain all their topological features; it thus allows to describe both Kitaev and string-net models on the same formal footing.

quant-ph↗

arXiv2022

Preparation and verification of tensor network states

We consider a family of tensor network states defined on regular lattices that come with a natural definition of an adiabatic path to prepare them. This family comprises relevant classes of states, such as injective Matrix Product and Projected Entangled-Pair States, and some corresponding to classical spin models. We show how uniform lower bounds to the gap of the parent Hamiltonian along the adiabatic trajectory can be efficiently computed using semi-definite programming. This allows one to check whether the adiabatic preparation can be performed efficiently with a scalable effort. We also derive a set of observables whose expectation values can be easily determined and that form a complete set, in the sense that they uniquely characterize the state. We identify a subset of those observables which can be efficiently computed if one has access to the quantum state and local measurements, and analyze how they can be used in verification procedures.

quant-ph↗

arXiv2022

Classical algorithms for many-body quantum systems at finite energies

We investigate quantum inspired algorithms to compute physical observables of quantum many-body systems at finite energies. They are based on the quantum algorithms proposed in [Lu et al. PRX Quantum 2, 020321 (2021)], which use the quantum simulation of the dynamics of such systems, as well as classical filtering and sampling techniques. Here, we replace the quantum simulation by standard classical methods based on matrix product states and operators. As a result, we can address significantly larger systems than those reachable by exact diagonalization or by other algorithms. We demonstrate the performance with spin chains up to 80 sites.

quant-ph↗