This is what led Brown et al. âI regard what they did as one of the more remarkable syntheses of physics and computer science that I've seen in my career,â he says. According to general relativity, Susskind and Maldacena noted, two black holes can be many light years apart yet still have their interiors connected by a space-time tunnel known as a wormhole. But if the approach works, says Susskind, it could resolve one of the most baffling theoretical conundrums to hit his field in recent years: the black-hole firewall paradox, which seems to imply that either quantum mechanics or general relativity must be wrong. correspondence Holographic complexity of the electromagnetic black hole. Working off-campus? Investigating the complexity-equals-action conjecture in regular magnetic black holes. Complexity of the Einstein-Born-Infeld-massive black holes. Gravitational thermodynamics of causal diamonds in (A)dS. & Sully, J. J. Rev. Circuit complexity for free fermion with a mass quench. Harlow, D. & Hayden, P. J. Interior volume and entropy of higher-dimensional charged black holes. Because this is AdS, he said, the object can be described by some configuration of particles and fields on the boundary. Surface/state correspondence and Computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. Simulating lattice gauge theories within quantum technologies. . Maldacena, J. Holographic subregion complexity of boosted black brane and Fisher information. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. Thermodynamic information geometry and complexity growth of a warped AdS black hole and the warped Leonard Susskind, a co-author of the new study, proposed that the continued growth in the interior reflects growing complexity of the quantum state, beyond the complexity captured by entanglement entropy . Recently, Aaronson and Susskind have showed that the complexity really does become superpolynomial, assuming (1) the unitary implements a computationally universal cellular automaton, and (2) the complexity class PSPACE is not contained in PP/poly. AGORA, HINARI, OARE, INASP, CrossRef and COUNTER. Holographic complexity from Crofton’s formula in Lorentzian AdS 4, Fig. Introduction and Motivations Susskind et al. In place of the heart is a Mandelbrot set, a fractal pattern widely recognized as a symbol for complexity at its most beautiful. Action growth for black holes in modified gravity. 5 – Fig. . This article inadvertently underplayed the role of Daniel Harlow in bringing computational complexity to fundamental physics â he worked with Patrick Hayden from the start of their project. Meanwhile, David Brown asked me about the 2017 paper Computational complexity of the landscape II - Cosmological considerations by Denef, Douglas, Greene, and Zukowski. All Rights Reserved. The quest for the elusive unified theory has led him to advocate counter-intuitive ideas, such as superstring theory or the concept that our three-dimensional Universe is actually a two-dimensional hologram. If AMPS's theory is true, says Raphael Bousso, a theoretical physicist at the University of California, Berkeley, âthis is a terrible blow to general relativityâ. âThe black hole's interior is protected by an armour of computational complexity.â, Hayden was sceptical of the result at first. Unlike our Universe, however, it has a boundary â a domain where there is no gravity, just elementary particles and fields governed by quantum physics. ... Daniel A. Roberts, Leonard Susskind, Brian Swingle, and Ying Zhao. Rev. Black hole entropy in canonical quantum gravity and superstring theory. Computational complexity is essential to understanding the properties of black hole horizons. It is possible that gravity will provide tools to study problems of complexity; especially the range of complexity between scrambling and exponential complexity. Enter your email address below and we will send you your username, If the address matches an existing account you will receive an email with instructions to retrieve your username, I have read and accept the Wiley Online Library Terms and Conditions of Use. What matters in science â and why â free in your inbox every weekday. . A computational problem is a task solved by a computer. Lecture two reviews the connection between the second law of complexity and the interior of black holes. Quantum Complexity and Chaos in Young Black Holes. 4 shows results for the circuit complexity, while Fig. On the other hand if the radiation is bottled up then after an exponentially long period of time firewalls may be common. Fundamental physics has been in an uproar ever since, as practitioners have struggled to find a resolution to this paradox. Given at PiTP 2018 summer program entitled "From Qubits to Spacetime." Consequently, their complexity continuously grows. Entanglement entropy and complexity of singular subregions in deformed CFT. deformation Homepage of the Electronic Colloquium on Computational Complexity located at the Weizmann Institute of Science, Israel. Under the auspices of the Computational ... Yosi Atia, Leonard Susskind Publication: 24th September 2020 01:45 Downloads: 234 . Learn about our remote access options, Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA, 94305‐4060 USA. Effect of the dilaton on holographic complexity growth. When physicist Leonard Susskind gives talks these days, he often wears a black T-shirt proclaiming âI â¥ Complexityâ. © 2019 Macmillan Publishers Limited, part of Springer Nature. These are scribed notes from a graduate courses on Computational Complexity oﬁered at the University of California at Berkeley in the Fall of 2002, based on notes scribed by students in Spring 2001 and on additional notes scribed in Fall 2002. âI don't know where all of this will lead,â says Susskind. Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. The full text of this article hosted at iucr.org is unavailable due to technical difficulties. Susskind, L. Preprint available at http://arxiv.org/abs/1402.5674 (2014). Computational complexity is essential to understanding the properties of black hole horizons. Susskind decided to look at a black hole sitting at the centre of an AdS universe, and to use the boundary description to explore what happens inside a black hole's event horizon. The problem of Alice creating a firewall behind the horizon of Bob's black hole is a problem of computational complexity. Steady States, Thermal Physics, and Holography. The Black Hole Paradoxes and Possible Solutions. Lowe, D. A., Polchinski, J., Susskind, L., Thorlacius, L. & Uglum, J. Phys. 5 shows results from the Fubini-Study line element; in both figures, panel (a) shows quenches from the massive phases to the QCP, while panel (b) shows quenches to a massive phase. Our first paper is Computational Complexity and Black Hole Horizons, by Lenny Susskind. His research interests include string theory, quantum field theory, quantum … And more than that, he says, computational complexity could give theorists a whole new way to unify the two branches of their science â using ideas based fundamentally on information. But not everyone is convinced. Computational Complexity and Black Hole Horizons Computational complexity may lie at the heart of a number of black hole paradoxes collectively called the firewall paradox. But now he is part of a small group of researchers arguing for a new and equally odd idea: that the key to this mysterious theory of everything is to be found in the branch of computer science known as computational complexity. & Susskind, L. Fortschr. Physical Review D: Particles and Fields . Complexity growth, butterfly velocity and black hole thermodynamics. AMPS concluded that nature prevents this abomination by creating a blazing firewall just inside the horizon that will incinerate any observer â or indeed, any particle â trying to pass through. Evolutions of entanglement and complexity after a thermal quench in massive gravity theory. No conceivable computer could finish the calculations until long after the black hole had radiated all of its energy and vanished, along with the forbidden information clones. Black holes, complexity and quantum chaos. Computational complexity is grounded in practical matters, such as how many logical steps are required to execute an algorithm. With his latest work, Susskind says, it turns out that the growth of complexity on the boundary of AdS shows up as an increase in the wormhole's length. Computational Complexity meets Quantum Gravity Speaker Schedule Monday 3/20 Tuesday 3/21 Wednesday 3/22 8:45 to 9:00 Welcome - Leonard Susskind 9:00 to 9:45 Scott Aaronson Douglas Stanford John Preskill 9:45 to 10:30 Beni Yoshida/Dan Roberts Charlie Bennett Don Page 10:30 to 11:00 Refreshments Refreshments Refreshments 11:00 to 12:00 Adam Brown Rob Myers Juan Maldacena The text has been corrected to reflect this. Switchback effect of holographic complexity in multiple-horizon black holes. Our earlier paper “Complexity Equals Action” conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the “Wheeler-DeWitt” patch). Using toy models that represent black holes as holograms, Susskind and his collaborators have shown that the complexity and volume of black holes both grow at the same rate, supporting the idea that the one might underlie the other. Harlow and Hayden (see also chapter 6 of Aaronson’s notes and this overview of Susskind) proposed a way to resolve this paradox using computational complexity. Holographic complexity of subregions in the hyperscaling violating theories. Interior volume of Banados–Teitelboim–Zanelli black hole. In this addendum to [arXiv:1402.5674] two points are discussed. Phys. Furthermore, Susskind noticed, the computational complexity tends to grow with time. and you may need to create a new Wiley Online Library account. But in 2012, four physicists at the University of California, Santa Barbara â Ahmed Almheiri, Donald Marolf, Joseph Polchinski and James Sully, known collectively as AMPS â spotted a dangerous exception to this rule2. This describes a cosmos that is like our own Universe in the sense that everything in it, including black holes, is governed by gravity. Post-quench evolution of complexity and entanglement in a topological system. deformation Their ﬁndings are particularly interesting in the case of black holes (BH) and the horizons which are formed in spacetime. Holographic complexity and thermodynamics of AdS black holes. He captured that idea in a slogan4: âThings fall because there is a tendency toward complexity.â. Fidelity susceptibility for Lifshitz geometries via Lifshitz holography. D 52, 6997 (1995). The first people to bring computational complexity into the debate were Stanfordâs Patrick Hayden, a physicist who also happens to be a computer scientist, and Daniel Harlow, a physicist at Princeton University in New Jersey. They found a scenario in which an observer could decode the information in the radiation, jump into the black hole and then compare that information with its forbidden duplicate on the way down. Holographic complexity in general quadratic curvature theory of gravity. Operator approach to complexity: Excited states. Action growth rate for a higher curvature gravitational theory. (e.g., [1–3]) in a series of papers have approached the complexity of quantum systems. International Journal of Modern Physics D. Holographic complexity in Vaidya spacetimes. Thermodynamic and holographic information dual to volume. The evolution of the complexity is shown in Fig. Multiscale structural complexity of natural patterns. Hopefully someone in Tselil’s and my upcoming seminar will present this in more detail and also write a blog post about it. âIt did seem to be a robust principle,â says Hayden: âa conspiracy of nature preventing you from performing this decoding before the black hole had disappeared on you.â. Holographic complexity in FRW spacetimes. Download PDF Abstract: Computational complexity is essential to understanding the properties of black hole horizons. High Energy Phys. 61, 781–811 (2013). Computational complexity is essential to understanding the properties of black hole horizons. Complexity and scaling in quantum quench in 1 + 1 dimensional fermionic field theories. Smart Network Field Theory: The Technophysics of Blockchain and Deep Learning. • Computational complexity and black hole horizons FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS Susskind, L. 2016; 64 (1): 24-43 • Localized shocks JOURNAL OF HIGH ENERGY PHYSICS Roberts, D. A., Stanford, D., Susskind, L. 2015 • Complexity and shock wave geometries PHYSICAL REVIEW D Stanford, D., Susskind, L. 2014; 90 (12) Happily, as Susskind and his colleagues observed1 in 1995, nature seemed to sidestep any such violation by making it impossible to see both copies at once: an observer who remains outside the horizon cannot communicate with one who has fallen in. PMID 10017902 DOI: 10.1103/PhysRevD.50.2700 The HarlowâHayden argument made a big impression on Scott Aaronson, who works on computational complexity and the limits of quantum computation at the Massachusetts Institute of Technology in Cambridge. International Journal of Geometric Methods in Modern Physics. Holographic complexity in charged Vaidya black hole. Recently a certain conceptual puzzle in the AdS/CFT correspondence, concerning the growth of quantum circuit complexity and the wormhole volume, has been identified by Bouland-Fefferman-Vazirani and Susskind. Part II. It all began 40 years ago, when physicist Stephen Hawking at the University of Cambridge, UK, realized that quantum effects would cause a black hole to radiate photons and other particles until it completely evaporates away. Time dependence of holographic complexity in Gauss-Bonnet gravity. If complexity does underlie spatial volume in black holes, Susskind envisions consequences for our understanding of cosmology in general. The 74-year-old Susskind, a theorist at Stanford University in California, has long been a leader in efforts to unify quantum mechanics with the general theory of relativity â Albert Einstein's framework for gravity. Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization. Number of times cited according to CrossRef: Path integral optimization for But according to quantum theory, these widely separated black holes can also be connected by having their states 'entangled', meaning that information about their quantum states is shared between them in a way that is independent of distance. In this note, we propose a resolution of the puzzle and save the quantum Extended Church-Turing thesis by arguing that there is no computational shortcut in … There is a widespread belief in the field that the laws of nature must somehow be based on information. Holographic entanglement entropy, complexity, fidelity susceptibility and hierarchical UV/IR mixing problem in AdS All Rights Reserved. © 2019 Macmillan Publishers Limited, part of Springer Nature. But then he and Harlow found much the same answer for many types of black hole3. Computational complexity and black hole horizons FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS Susskind, L. 2016; 64 (1): 24-43 View details for DOI 10.1002/prop.201500092 View details for Web of Science ID 000370142400003

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