Threshold for Life Prof. Isaac Chuang MIT Media Laboratory.

Slides:

Advertisements

Similar presentations

Survey on the Bounds of the Threshold For Quantum Decoherence Chris Graves December 12, 2012.

Advertisements

Computing with adversarial noise Aram Harrow (UW -> MIT) Matt Hastings (Duke/MSR) Anup Rao (UW)

Models of Computation Prepared by John Reif, Ph.D. Distinguished Professor of Computer Science Duke University Analysis of Algorithms Week 1, Lecture 2.

The Threshold for Fault-Tolerant Quantum Computation Daniel Gottesman Perimeter Institute.

1 SODA January 23, 2011 Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D Matthew CookUniversity of Zurich and.

The Recursion Theorem Sipser – pages Self replication Living things are machines Living things can self-reproduce Machines cannot self reproduce.

F AULT T OLERANT Q UANTUM C OMPUTATION December 21 st, 2009 Mirmojtaba Gharibi.

Umesh V. Vazirani U. C. Berkeley Quantum Algorithms: a survey.

Finite Automata and Non Determinism

A Universal Operator Theoretic Framework for Quantum Fault Tolerance Yaakov S. Weinstein MITRE Quantum Information Science Group MITRE Quantum Error Correction.

1 Introduction to Computability Theory Lecture2: Non Deterministic Finite Automata (cont.) Prof. Amos Israeli.

Quantum Error Correction SOURCES: Michele Mosca Daniel Gottesman Richard Spillman Andrew Landahl.

Phase in Quantum Computing. Main concepts of computing illustrated with simple examples.

Quantum Computation and Error Correction Ali Soleimani.

Local Fault-tolerant Quantum Computation Krysta Svore Columbia University FTQC 29 August 2005 Collaborators: Barbara Terhal and David DiVincenzo, IBM quant-ph/

Beyond the DiVincenzo Criteria: Requirements and Desiderata for Fault-Tolerance Daniel Gottesman.

Quantum Algorithms I Andrew Chi-Chih Yao Tsinghua University & Chinese U. of Hong Kong.

Automata & Formal Languages, Feodor F. Dragan, Kent State University 1 CHAPTER 5 Reducibility Contents Undecidable Problems from Language Theory.

In Search of a Magic Bottle of Error-Be-Gone Dave Bacon Caltech Department of Physics Institute for Quantum Information Decoherence errosol.

Von Neumann’s Automaton and Viruses Most slides taken from Weizmann Institute of Science and Rensselaer Polytechnic Institute.

Threshold for Life MIT Media Laboratory Prof. Isaac Chuang.

Cellular Automata Avi Swartz 2015 UNC Awards Ceremony.

Introduction At the heart of the growth of a multi-cellular organism is the process of cellular division… … aka (in computing) self-replication.

MAS.S62 FAB The Threshold for Life

Software faults & reliability Presented by: Presented by: Pooja Jain Pooja Jain.

Requirements and Desiderata for Fault-Tolerant Quantum Computing Daniel Gottesman Perimeter Institute for Theoretical Physics Beyond the DiVincenzo Criteria.

Quantum Error Correction Jian-Wei Pan Lecture Note 9.

MAS.S62 FAB Error Correcting Systems n MAJ p p p p p p p p p k.

CSCI 4325 / 6339 Theory of Computation Zhixiang Chen.

Ketan Patel, Igor Markov, John Hayes {knpatel, imarkov, University of Michigan Abstract Circuit reliability is an increasingly important.

Computer Viruses, Artificial Life & the Origin of Life Robert C Newman Abstracts of Powerpoint Talks - newmanlib.ibri.org -newmanlib.ibri.org.

Theory of Computing Lecture 15 MAS 714 Hartmut Klauck.

Computer Science Dept, San Jose State University, CA Self Reproducing CA’s and Programs Shruti Parihar May 06, 2003.

Course material – G. Tempesti Course material will generally be available the day before the lecture Includes.

FAB 2 MAS 960 Special Topics: How To Make Something That Makes (almost) Anything 1.Air inlets 2.Crushers 3.Ganglion 4.Multiple Visual.

Cellular Automata & DNA Computing 우정철. Definition Of Cellular Automata Von Von Neuman’s Neuman’s Definition Wolfram’s Wolfram’s Definition Lyman.

1 New Coins from old: Computing with unknown bias Elchanan Mossel, U.C. Berkeley

Quantum Computing Reversibility & Quantum Computing.

Why synthsize genes and genomes? minimal life -genome rewrite -genetic circuits -metabolic pathways -vaccines -gene therapy -individual.

Cybernetics and American Youth Subculture From Wikipedia In 1947, Wiener decided to introduce the neologism cybernetics into his scientific theory. The.

Physics of Information Technology MIT – Spring 2006 PART II Avogadro Scale Engineering ‘COMPLEXITY’

Capabilities and limitations of quantum computers Michele Mosca 1 November 1999 ECC ’99.

An Introduction to Quantum Computation Sandy Irani Department of Computer Science University of California, Irvine.

Quantum Computation Stephen Jordan. Church-Turing Thesis ● Weak Form: Anything we would regard as “computable” can be computed by a Turing machine. ●

Physics of Information Technology MIT – Spring 2006 Avogadro Scale Engineering ‘COMPLEXITY’

Attendance Syllabus Textbook (hardcopy or electronics) Groups s First-time meeting.

Quantum Bits (qubit) 1 qubit probabilistically represents 2 states

From bacteria to artificial cells. The problem of self reproduction

Formal Foundations-II [Theory of Automata]

Fabricational Capacity

Linear Quantum Error Correction

A low cost quantum factoring algorithm

OTHER MODELS OF TURING MACHINES

Presentation Title Greg Snider QSR, Hewlett-Packard Laboratories

CSE322 The Chomsky Hierarchy

Non-Deterministic Finite Automata

Bio, Nano and Quantum Computing

Reliability is a Fungible Resource

A Ridiculously Brief Overview

Genetic Algorithms Artificial Life

CSE838 Lecture notes copy right: Moon Jung Chung

Chap 4 Quantum Circuits: p

Avogadro Scale Engineering & Fabricational Complexity

Undecidable problems:

Towards Neuromorphic Complexity Analysis

Improving Quantum Circuit Dependability

G5BAIM Artificial Intelligence Methods

Von Neumann’s Automaton and Viruses

Cellular Automata (CA) Overview

The Chomsky Hierarchy Costas Busch - LSU.

Presentation transcript:

Threshold for Life Prof. Isaac Chuang MIT Media Laboratory

Objective Claim: Life can be constructed from faulty components Question: How Faulty?

Reliable computers can be constructed from faulty components An Amazing Theorem Reliable computers can be constructed from faulty components A circuit containing N (error-free) gates can be simulated with probability of error at most e, using N log(N/e) faulty gates, which fail with probability p, so long as p<pth. von Neumann (1956) Quantum version: Preskill, Shor, Aharonov, Ben-Or, Gottesman, Chuang*,… * D. Gottesman and I. Chuang, Nature, vol. 402, p. 390, 1999

Fault-Tolerant Circuits

Fault-Tolerant Circuits

The Fault-Tolerance Threshold A circuit containing N (error-free) gates can be simulated with probability of error < e, using cdN faulty gates, which fail with probability p, if p<pth. Proof: Assume 3-input gates. N=1 easy. MAJ Fails with probability < 3(4e)2 + p < 49e2 If p<e2 and 49e2 < e p<0.0004 Fault-Tolerant Non-Fault-Tolerant Circuit 1: e Circuit 2: e Circuit 3: e p Fails with probability 3e+p < 4e

Efficient Fault Tolerance A circuit containing N (error-free) gates can be simulated with prob. of error < e, using O(N log N) faulty gates, which fail with prob. p, if p<pth. Key concept: concatenation (encoding at multiple levels) Status: pth ¼ 1/6 (Hajek & Weller ’91)

Fault-Tolerant Life Nature does not seem to use such constructions How can life be made fault-tolerant?

What is Life? Desirable characteristics: Self repair Self reproduction Growth Evolution Schrodinger von Neumann (1966) Theory of Self-Reproducing Automata: elementary machine capable of reproduction and universal computation

Von Neumann’s Automaton Model based on 29 state Cellular Automaton Langton’s 8-state replicator (not universal) (simulation from H-H Chou) Universal Turing machine Universal constructor

Visions of Fault-Tolerant Life Two interesting questions: What is the fault-tolerance threshold for Life? What would fault-tolerant creatures be like? Rad-hard biology Immortal Biosystems …Reproduction?