Research

I was taught that the way of progress was neither swift nor easy. — Marie Curie

Overview

Improving our ability to accurately model, predict, and control the behavior of quantum-mechanical systems of increasing “complexity” is an outstanding challenge in quantum information science, whose implications encompass virtually all branches of contemporary physical and engineering sciences. Our efforts are driven by the long-term goal of developing better physical, mathematical, and information-theoretic tools to meet this challenge. To a large extent, this revolves around the central theme of understanding and harnessing quantum coherence and entanglement — and the multifaceted relations that ensue between the “parts and the whole” in the quantum world — in conjunction with different pathways by which “complexity” may emerge at both the kinematical and dynamical level:

  • Couplings between the system of interest and the uncontrollable surrounding environment, as well as controlled interactions with external classical or quantum auxiliary systems and/or measurement devices;
  • Increasing system size, supporting an arbitrarily large number of interconnected components and/or competing interactions, possibly in conjunction with quantum-statistical effects and “non-Hermiticity”;
  • Lack of “manifest” or “local” symmetries, underpinning quantum non-integrability and quantum randomness, as well as quantum phenomena of intrinsic topological nature.

Altogether, these factors are responsible for challenges not encountered in classical settings — along with a fascinating range of uniquely quantum phenomena — including quantum noise and decoherence, non-classical correlations, quantum chaos, topological quantum matter and light. Ultimately, these same factors also unlock novel frontiers in processing and sensing information with unparalleled efficiency compared to classical means, and call for a deeper understanding of the very foundations of quantum theory.

Selected research highlights

Within the above broad motivating context, our recent investigations have focused primarily on the following inter-related areas [please see Publications for a more complete and up-to-date account!]:

♦ Quantum characterization and control, noisy quantum metrology. As we transition from proof-of-principle demonstrations to the level of complexity and detailed engineering questions that must be addressed in order to bring scalable quantum information processing to experimental reality, new techniques are required to accurately characterize quantum systems and verify control performance. In parallel, detailed noise characterization is also instrumental to counter noise effects in quantum-enhanced metrology. In collaboration with both theory colleagues at Griffith U. (Gerardo  A. Paz-Silva) and experimental colleagues at U. Sydney (Michael Biercuk) and MIT (William Oliver), we have been working on a range of quantum characterization and control problems, including:

  • Control techniques for quantum noise spectroscopy in open quantum systems based on both multi-pulse and continuous-wave control as well as extension of classical multitaper methods to the quantum setting.
  • Improved schemes for mitigation of noise and decoherence — in particular, based on  dynamical decoupling and dynamically corrected gates — and implications for quantum fault-tolerance.
  • Model-reduction approaches for controlled open quantum dynamics — for instance, control-driven model reduction based on the use of frames.
  • Characterization of quantum vs. classical, and Gaussian vs. non-Gaussian noise environments — with implications for both semiclassical modeling and efficient simulation.
  • Quantum metrology and error-corrected quantum metrology in spatiotemporally correlated (non-Markovian) quantum (non-classical) noise environments.

Two-point correlation function of non-stationary noise from a diffusion process: Ideal vs. digitally reconstructed by control-adapted noise spectroscopy in a Walsh frame [Phys. Rev. X Quantum 2021

Simultaneous spectral estimation of dephasing and control noise by a trapped-ion sensor: Experimental data vs. theoretically predicted values [Phys. Rev. Applied 2020

Non-Gaussian “bispectrum” estimation by a superconducting qubit sensor: Experimental data vs. Monte Carlo simulation vs. ideal values [Nature Commun. 2019]

♦ Dissipative quantum control. Despite significant progress, a general understanding of the conditions under which stabilization to a desired target set may be attained in realistic open quantum systems – and, if so, how rapidly – is still lacking. One objective we are pursuing is to build a rigorous system-theoretic framework for controlled open-quantum system dynamics subject to resource constraints that limit the allowable dynamical models and manipulations, as inevitable in practical scenarios. In collaboration with control theorist Francesco Ticozzi at U. Padua, we are exploring quantum stabilization problems in various settings that have remained largely uncharted as yet, including:

  • Discrete-time Markovian dynamics under quasi-locality constraints — for which, unlike continuous-time dynamics, the possibility of exact dissipative state preparation and dissipative encoding in finite time arises.
  • Constrained continuous- and discrete-time Markovian dynamics under more general constraints than imposed by locality “in real space”– in particular, making contact with tools from both generalized entanglement theory and semidefinite programming.
  • Physical characterization of quantum states stabilizable under resource constraints– with emphasis on properties of their correlations and/or their parent Hamiltonians, and relationships to the quantum marginal problem.

Sequence of CPTP maps for finite-time dissipative encoding into Kitaev’s toric code [Quantum Inf. Comput. 2021]FTSAKLT3LV

Dissipative quantum circuit for finite-time generation of AKLT state on three spin-1 systems [Phys. Rev. A 2017]

♦ Open many-body quantum systems, topological quantum matter and light. Understanding and classifying topological phases of light and matter is an outstanding challenge in condensed-matter and AMO physics — with enormous fundamental and applied significance, including for fault-tolerant quantum information processing. We aim to uncover the role and the manifestations of topology for systems comprised of ‘quasi-free’ (mean-field) fermions and bosons in both natural and synthetic, at and away from equilibrium. On the fermionic side, working together with condensed-matter theorist Gerardo Ortiz at Indiana U., a major accomplishment has been a deeper and more rigorous understanding of the bulk-boundary correspondence for fermionic matter. In doing so, we have developed a method for exactly diagonalizating non-interacting fermionic models under arbitrary boundary conditions, that provides a powerful generalization of Bloch’s theorem for these systems. On the bosonic side, we have ruled out low-energy topological physics with a series of no-go theorems for stable bosonic matter, and focused our search on open bosonic systems subject to quadratic Markovian dissipation. This has led to the discovery of Majorana bosons which, remarkably, are tied to a distinctive topologically metastable dynamical phase. Some of the questions under investigation include:

  • Understanding the extent to which metastable dynamical phases of quadratic Markovian bosonic systems may be symmetry-protected and exist beyond one dimension.
  • Exploring the significance of Majorana bosons and topological metastability for  continuous-variable quantum information processing.
  • Assessing the potential for metastable dynamics and anomalous relaxation dynamics in more general many-body open quantum systems — for instance, quadratic Markovian fermionic models or discrete-time Markovian evolutions — with emphasis on the relevance of pseudo-spectral techniques.
  • Obtaining a deeper physical and mathematical understanding of symmetries and conservations, the breakdown of Noether’s theorem, and symmetry-breaking in open quantum systems.

Left: Topological dynamical stability of a dissipative bosonic Kitaev chain. Center and right: Signatures of topological metastability and Majorana bosons in steady-state power spectra  [Phys. Rev. Lett. 2021]

Stability phase diagram of a bosonic Kitaev chain by “Krein phase rigidity” [New J. Phys. 2020]