Gauge theories represent a fierce challenge and an amazing opportunity for quantum simulation. Up to date, proof-of-principle experiments have been limited to gauge theories in one spatial dimension. In this talk, I will focus on three key problems encountered in simulating gauge theories beyond one spatial dimension: I) the realization of magnetic interactions, II) the ability to “take the...
I discuss the implementation of a two-dimensional $Z_2$ lattice gauge theory on a shallow quantum circuit, suitable for near-term quantum computers.
The ground state preparation of this model is numerically analyzed on a small lattice with a variational quantum algorithm, the quantum approximate optimization algorithm, which requires a small number of parameters to reach high fidelities and...
Non-abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. In this talk, I will present an approach where gauge fields, discretized in spacetime, are represented by qudits and are time-evolved in Trotter steps with...
I review the introduction of the gauge invariant Ising model and my motivation based on my 1971 paper "Duality in generalized Ising Models and Phase Transitions without Local Order Parameter". I start with the exact determination of the critical temperature of the two-dimensional Ising model on the square lattice by Kramers and Wannier 1941 before Onsager gave the exact solution for this model...
The fermion sign problem tends to stymie exploration of highly entangled phases of matter such as interacting fermions at finite density. In this talk, I will present recent progress in simulating Fermi and non-Fermi liquids in the context of Kondo lattice systems. I will also discuss analytical results on quantum criticality in related models, and a few ideas on diagnosing Kondo breakdown.
I will present review of recent progress on theory of quantum simulators of gauge theories in the Quantum Optic Group at ICFO. In particular, I will talk about the following papers: 1) Titas Chanda, Maciej Lewenstein, Jakub Zakrzewski, and Luca Tagliacozzo, On the phase diagram of 1+1D Abelian-Higgs model and its critical point, Phys. Rev. Lett. 128, 090601 (2022); 2) Adith Sai Aramthottil,...
I will review some of the recent results we have obtained by performing MPS simulations of Abelian gauge theories in 1D
In recent years, exotic far-from-equilibrium phenomena have been discovered that lead to novel paradigms in condensed matter and particle physics, with salient examples ranging from string breaking to quantum many-body scarred dynamics and disorder-free localization. Underlying many of these phenomena are gauge symmetries, which endow their host models with rich dynamical behavior arising from...
Quantum computation of quantum field theories requires one to regularize the local lattice Hilbert space. We define this type of regularization as Qubit Regularization. This naturally leads to the concept of a Qubit Embedding Algebra (QEA) which replaces the traditional symmetry algebra. We derive some QEAs for lattice spin models and gauge theories. We discover a simple qubit regularization...
I will discuss a theory of topological insulators with topological order. The topological field theory exhibits oblique confinement with a universal "magneto-electric" response to background two-form probe fields. I will discuss the relation of this system with a lattice gauge theory of Z_N gauge fields with a 𝜃 term.
Digital quantum simulators provide a table-top platform for addressing salient questions in lattice gauge theories (LGTs). In this talk, I will present a recent work where we implemented a Z2 lattice gauge theory on the Google Sycamore chips within the Google Early Access Program. We synthesize the charge--gauge-field interaction using only 6 native two-qubit gates, enabling us to reach...
When quantum fluctuations meet an extensive classical degeneracy, exotic strongly correlated states can arise. Paradigmatic examples are resonating valence bond (RVB) states of hard dimers. They are defined as equal weight quantum superpositions of all dimer coverings with one dimer entering each vertex of a lattice. In this work, we consider RVB states of hard trimers (tRVB), which are...
Topologically ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Thus, their preparation requires a precise fine-tunning of the system’s parameters, a very challenging task in most experimental setups. In this talk, I will present a model of spinless fermions interacting with dynamical Z2 gauge fields on...
Pumped Rydberg atoms trapped in arrays of optical tweezers realize systems of individually controllable qubits with strong interactions.
I will describe recent theory and experiments on Z2 spin liquids, which are deconfined phases of Z2 gauge theory in 2+1 dimensions
Gauge theories play an interdisciplinary, fundamental role in physics, ranging from the study of elementary particles all the way to strongly correlated and topological quantum matter. While their equilibrium properties have been explored extensively for decades, their nonequilibrium quantum real-time dynamics has attracted significant attention rather recently, driven particularly by strong...
One of the main challenges for the simulation of lattice gauge theories with cold atoms in optical lattices is to find resource-efficient implementations of the required local symmetries. Despite the recent experimental progress, there is no clear path towards implementations of lattice gauge theories in extended systems beyond one dimension or with non-Abelian symmetries. Here, I report on...
We present an exact full symmetry analysis of the 0-π superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofold degeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus...
