P versus NP and geometry

I describe three geometric approaches to resolving variants of P v. NP, present several results that illustrate the role of group actions in complexity theory, and make a first step towards completely geometric definitions of complexity classes.Comment: 20 pages, to appear in special issue of J. Symbolic. Comp. dedicated to MEGA 200

Aspects of The First Law of Complexity

We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed, in more detail. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit. We apply the first law to gain new insights into the quantum circuits and complexity models underlying holographic complexity. In particular, we examine the variation of the holographic complexity for both the complexity=action and complexity=volume conjectures in perturbing the AdS vacuum with coherent state excitations of a free scalar field. We also examine the variations of circuit complexity produced by the same excitations for the free scalar field theory in a fixed AdS background. In this case, our work extends the existing treatment of Gaussian coherent states to properly include the time dependence of the complexity variation. We comment on the similarities and differences of the holographic and QFT results.Comment: 108 pages, 15 figures; v2: references adde

The Chronicle [January 22, 2004]

The Chronicle, January 22, 2004https://repository.stcloudstate.edu/chron/4590/thumbnail.jp

The Quantum Hologram Theory of Consciousness as a Framework for Altered States of Consciousness Research

We can learn more about how our reality is made and what non-ordinary states of consciousness are by studying the Quantum Hologram Theory of Physics and Consciousness (QHTC). The QHTC says that consciousness is not local and that altered states of consciousness can help us understand how our minds work in more than one way. That's what Schrödinger thought. He thought that the quantum mechanical wave function was a field of consciousness. QHTC is based on holographic theories for human consciousness. These theories say that the brain works like a hologram and that it processes images into interference patterns that are then turned into virtual images, just like a laser hologram. These quantum waves can store a lot of information, which our brains use to make our three-dimensional world. This article says that this last theory should be the main framework for research on altered states of consciousness, and it talks about how to get data for analysis and how to get into an altered state for possible experiments