Correlated volumes for metallic wavefunctions on a random-regular graph

We study the metallic phase of the Anderson model in a random-regular graph, specifically the
degree of ergodicity of the high-energy wavefunctions. We use the multifractal formalism to analyze numerical data for unprecedented large system sizes, obtaining a set of correlated volumes which control finite-size effects. Those volumes grow very fast with disorder strength but show no tendency to diverge, at least in an intermediate metallic regime. Close to the Anderson transitions, we characterize the crossover to system sizes much smaller than the first correlated volume. Once this crossover has taken place, we obtain evidence of a scaling in which the derivative of the first fractal dimension behaves critically with an exponent ν = 1.

The talk is based on the following works:

-  Correlated volumes for extended wavefunctions on a random-regular graph.

M Pino, JE Roman arXiv preprint. ArXiv:2311.07690 (2023)

-  Scaling up the Anderson transition in random-regular graphs.

M Pino. Physical Review Research 2 (4), 042031 (2020)

- From ergodic to non-ergodic chaos in Rosenzweig–Porter model.

M Pino, J Tabanera, P Serna Journal of Physics A: Mathematical and Theoretical 52 (47), 475101 (2019)

Quantum spin liquids and tensor networks

Quantum spin liquids are strongly-correlated systems of spins that do not order at zero temperature. As a result, they exhibit exciting collective many-body effects such as topological order, quantum criticality and quasiparticle fractionalization. In this talk, I will explain how we can model these systems naturally using the language of tensor networks. I will show that this gives us insight into the nature of a spin liquid wavefunction, and allows us to perform numerical simulations of candidate models for realizing spin liquid physics.

Criticality, computing, and chaos in open quantum systems.

Quantum technologies represent a frontier of both fundamental and applied research, with global efforts aimed at developing quantum computers and simulation platforms that address practical challenges. However, the current era, known as the Noisy Intermediate-Scale Quantum (NISQ) era [1], presents a unique set of challenges. In NISQ systems, quantum devices are open, interacting with their environment and experiencing dissipation. This dissipation poses a significant obstacle to the large-scale fabrication of quantum hardware, potentially limiting quantum advantages by degrading crucial properties like entanglement.

NISQ devices consist of numerous interacting particles undergoing both local and non-local unitary processes. They are also subject to non-unitary effects from the environment, active measurements, and feedback operations. As such, they can only be modeled within the framework of many-body open quantum systems. In these systems, the interplay between dissipative and Hamiltonian evolution leads to states and phenomena distinct from those observed in equilibrium condensed matter physics. In this presentation, I will delve into the understanding and investigation of these emergent properties in open quantum systems. The focus will particularly be on critical phenomena like phase transitions [2] and chaos [3], highlighting their unique features. I will also showcase the recent experimental demonstrations of our theoretical predictions [4,5].

While in many applications dissipation is a barrier to overcome, given appropriate engineering of the system-environment coupling, dissipation can be a resource. Indeed, dissipative processes can be used to steer the dynamics of NISQ systems, bypassing the hardware limitation determined by design and fabrication, such as energy, couplings, connectivity, etc. I will discuss how leveraging the distinctive features of open quantum systems and its emergent phenomena significantly boost the performance of quantum hardware, with a specific focus on their applications in quantum information encoding [6] and precision metrology [7].

[1] J. Preskill, Quantum Computing in the NISQ era and beyond, Quantum 2, 79 (2018).
[2] FM, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of Liouvillians for dissipative phase transitions, Phys. Rev. A 98, 042118 (2018).
[3] F. Ferrari, L. Gravina, D. Eeltink, P. Scarlino, V. Savona, and FM, Transient and steady-state quantum chaos in driven-dissipative bosonic systems, arXiv 2305.15479 (2023).
[4] G. Beaulieu, FM, S. Frasca, V. Savona, S. Felicetti, R. D. Candia, and P. Scarlino, Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator, arXiv 2310.13636 (2023).
[5] L. P. Peyruchat, F. Ferrari, FM, and P. Scarlino, Signature of dissipative quantum chaos in coupled nonlinear driven resonators, in preparation.
[6] L. Gravina, FM, and V. Savona, Critical Schrödinger Cat Qubit, PRX Quantum 4, 020337 (2023).
[7] R. Di Candia, FM, K. V. Petrovnin, G. S. Paraoanu, and S. Felicetti, Critical parametric quantum sensing, npj Quantum Information 9, 23 (2023).

Advantages of Digital Qubit-Boson Hardware for Quantum Simulation

Finding a straightforward, scalable and universal framework for quantum simulation of strongly correlated fermions and bosons is important from material science to high-energy physics. Here, we develop hybrid qubit-oscillator operations for microwave cavities coupled to transmon qubits required for implementing dynamics of bosonic matter, fermionic matter, and Abelian gauge fields in (2+1)D. We then expand the method to ground state preparation and propose measurement of various long-range correlation functions required for the study of phase transitions. We implement numerical proof of principle experiments for a (1+1)D Z2 Bose Hubbard (BH) gauge theory and the U(1) Schwinger model. We include the main sources of hardware noise, which we mitigate through post-selection based on Gauss' law. This new approach motivates us to uncover the phase diagram of the Z2 BH model, relevant to the Higgs sector. We discover a new phase of matter which exhibits strong density fluctuations which we dub the `clump' phase. Finally, we perform a complexity analysis and find that for one Trotter step of these example models, qubit systems require higher gate counts than our proposal by three orders of magnitude. Our correspondingly higher circuit fidelities may help us to successfully capture the essential physics of these theories in the near-term.

Ion transport at the nanoscale: from ion-electron coupling to artificial ion channels