Jordan Cotler

Abstract 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: local-local, incoherent, coherent, adaptive, etc. We provide the first example of a measurement "task" for which the coherent 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 may lead to exponential savings in resources. We extend our results to derive a similar exponential advantage for a 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; an equally important one is to design new, efficient quantum algorithmic measurements based on our framework, perhaps relying on ideas from quantum algorithms.

We demonstrate that in quantum many-body systems, local arrows of time can differ from the global time $t$ induced by Hamiltonian evolution. That is, within a quantum many-body system, the flow of time can be relative to each observer or by proxy each local subsystem. We provide a definition of local arrows of time in quantum many-body systems, and explain their relation to spacetime quantum entropies. Then we give a variety of numerical and analytical examples which explore different ways in which local arrows of time can manifest in quantum many-body dynamics, including exotic arrows of time arising from quantum thermalization and quantum error correction. We find that even in standard Hamiltonian dynamics, the arrow of time is not strictly temporal; it develops spatial components that deviate from the local entropy gradient.