Spectral properties and thermalization with matrix product states
Dr Mari-Carmen Banuls, Max Planck Institute of Quantum Optics, Germany
Matrix product states, and operators, are powerful tools for the description of low energy eigenstates and thermal equilibrium states of quantum many-body systems in one spatial dimension. But in out-of-equilibrium scenarios, and for high energy eigenstates of generic systems, the scaling of entanglement with time and system size makes a direct application often impossible. However, beyond the standard algorithms, MPS and more general TNS techniques can still be used to explore some of the most interesting dynamical properties.
A particular case is a recently introduced method in which MPO techniques are combined with Chebyshev polynomial expansions to explore spectral properties of quantum many-body Hamiltonians. In particular, this method can be used to probe thermalization of large spin chains without explicitly simulating their time evolution, as well as to compute full and local densities of states.
Hydrodynamics and the Spectral Form Factor
Professor Brian Swingle, Brandeis University, USA
Ensembles of quantum chaotic systems are expected to exhibit random matrix universality in their energy spectrum. The presence of this universality can be diagnosed by looking for a linear in time 'ramp' in the spectral form factor, but for realistic systems this feature is typically only visible after a sufficiently long time. It is important to understand the emergence of this universality and how it connects to the larger body of phenomena associated with quantum chaos. This talk will present a hydrodynamic theory of the spectral form factor in systems with slow modes. The formalism predicts the linear ramp at sufficiently late time and gives a quantitative framework for computing the approach to ramp.
Quantum Algorithmic Measurement
Professor Xiao-Liang Qi, Stanford University, USA
Can quantum computational tools enhance the precision and efficiency of physical experiments? Promising examples are known, but a systematic treatment and comprehensive framework are missing. We introduce Quantum Algorithmic Measurements (QUALMs) to enable the study of quantum measurements and experiments from the perspective of computational complexity and communication complexity. The measurement process is described, in its utmost generality, by a many-round quantum interaction protocol between the experimental system and a full-fledged quantum computer. The QUALM complexity is quantified by the number of elementary operations performed by the quantum computer, including its coupling to the experimental system.
We study how the QUALM complexity depends on the type of allowed access the quantum computer has to the experimental system: coherent, incoherent, etc. We provide the first example of a measurement "task", which can be motivated by the study of Floquet systems, for which the coherent access QUALM complexity is exponentially better than the incoherent one, even if the latter is adaptive; this implies that using entanglement between different systems in experiments, as well as coherence between probes to the physical system at different times, may lead to exponential savings in resources. We extend our results to derive a similar exponential advantage for another physically motivated measurement task which determines the symmetry class of the time evolution operator for a quantum many-body system.
Many open questions are raised towards better understanding how quantum computational tools can be applied in experimental physics. A major question is whether an exponential advantage in QUALM complexity can be achieved in the NISQ era.
Panel Discussion 3
Dr Ulrich Schneider, University of Cambridge, UK
Professor Monika Aidelsburger, Ludwig-Maximilians-Universität (LMU) München & Munich Center for Quantum Science and Technology (MCQST), Germany
Professor Igor Lesanovsky, University of Tübingen, Germany
Dr Norman Yao, UC Berkeley, USA