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This is a collection of statements gathered on the occasion of the Quantum Physics of Nature meeting in Vienna.
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For the last few years, the NASA Quantum Artificial Intelligence Laboratory (QuAIL) has been performing research to assess the potential impact of quantum computers on challenging computational problems relevant to future NASA missions. A key aspect of this research is devising methods to most effectively utilize emerging quantum computing hardware. Research questions include what experiments on early quantum hardware would give the most insight into the potential impact of quantum computing, the design of algorithms to explore on such hardware, and the development of tools to minimize the quantum resource requirements. We survey work relevant to these questions, with a particular emphasis on our recent work in quantum algorithms and applications, in elucidating mechanisms of quantum mechanics and their uses for quantum computational purposes, and in simulation, compilation, and physics-inspired classical algorithms. To our early application thrusts in planning and scheduling, fault diagnosis, and machine learning, we add thrusts related to robustness of communication networks and the simulation of many-body systems for material science and chemistry. We provide a brief update on quantum annealing work, but concentrate on gate-model quantum computing research advances within the last couple of years.
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its invariance properties under variations of the action. These relations determine a dynamical algebra of bounded operators which encodes all properties of the corresponding quantum theory. This novel approach is applied to non-relativistic particles, where quantum mechanics emerges from it. The method works also in interacting quantum field theories and sheds new light on the foundations of quantum physics.
In Phys. Rev. A 101 (2020) 022117 it was argued that Bell inequalities are based on classical, not quantum, physics, and hence their violation in experiments provides no support for the claimed existence of peculiar nonlocal and superluminal influences in the real (quantum) world. Following a brief review of some aspects of the Consistent Histories approach used in that work, the objections raised in Lambares Comment, arXiv:2102.075243v3, are examined and shown to rest on serious misunderstandings, and as a result fail to identify any errors in, or problems with, the work being criticized.
The mathematical apparatus of quantum--mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinational aspects. SU(2) recoupling theory, involving Wigners 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, play nowadays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory -and of its extension to other Lie and quantum group- by using the collective term of `spin networks. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey Scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper we list and discuss some aspects of these developments -such as for instance the hyperquantization algorithm- as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.
We uncover a new quantum paradox, where a simple question about two identical quantum systems reveals unsettlingly paradoxical answers when weak measurements are considered. Our resolution of the paradox, from within the weak measurement framework, amounts to a proof of counterfactuality for our generalised protocol (2014)---the first to do so---for sending an unknown qubit without any particles travelling between the communicating parties, i.e. counterfactually. The paradox and its resolution are reproduced from a consistent-histories viewpoint. We go on to propose a novel, experimentally feasible implementation of this counterfactual disembodied transport that we call counterportation, based on cavity quantum electrodynamics, estimating resources for beating the no-cloning fidelity limit---except that unlike teleportation no previously-shared entanglement nor classical communication are required. Our approach is up to several orders of magnitude more efficient in terms of physical resources than previously proposed techniques and is remarkably tolerant to device imperfections. Surprisingly, while counterfactual communication is intuitively explained in terms of interaction-free measurement and the Zeno effect, we show based on our proposed scheme that neither is necessary, with implications in support of an underlying physical reality.
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