Photonic Quantum Information, Computation Experimental & Simulation BosonSampling qt Andrew White lab University of Queensland quantum.info CENTRE FOR ENGINEERED QUANTUM SYSTEMS : AUSTRALIAN RESEARCH COUNCIL CENTRE OF EXCELLENCE 15,470 km Quantum simulation Quantum foundations & emulation 0.4 0.2 Probability -8 -6 -4 1 -2 0 2 Nature Physics 11, 249 (2015) 2 4 3 6 4 Scientific Reports 4, 06955 (2014) 8 Physical Review Letters 112, 143603 (2014) Nature Communications 5, 04145 (2014) Physical Review Letters 112, 020401 (2014) Science 339, 794 (2013) Nature Communications 3, 625 (2012) Nature Communications 3, 882 (2012) Physical Review Letters 106, 200402 (2011) New Journal of Physics 13, 075003 (2011) New Journal of Physics 13, 053038 (2011) Physical Review Letters 104, 153602 (2010) Proceedings of the National Nature Chemistry 2, 106 (2010) Academy of Sciences 108, 1256 (2011) Quantum computation Quantum photonics Physical Review Letters 114, 173603 (2015) Physical Review Letters 114, 090402 (2015) Physical Review Letters 112, 143603 (2014) Physical Review A 89, 042323 (2014) Physical Review Letters 110, 250501 (2013) Physical Review Letters 111, 230504 (2013) Physical Review A 88, 013819 (2013) Physical Review Letters 106, 100401 (2011) Optics Express 21, 13450 (2013) New Journal of Physics 12 083027 (2010) Optics Express 19, 22698 (2011) Nature Physics 5, 134 (2009) Journal of Modern Optics 58, 276 (2011) Physical Review Letters 101, 200501 (2008) Optics Express 19, 55 (2011) Christina Geoff Juan Aleksandrina Markus Martin Azwa The Giarmatzi Gillett Loredo Nikolova Rambach Ringbauer Zakaria Team from July Marcelo Ivan Jacqui Till Almeida Kassal Romero Weinhold & you ? Professor, Senior Postdoc, Heriot-Watt University Oxford University Industry, Scotland England Australia + £1.5M Fellowship Alessandro Michael Devon Fedrizzi Vanner Biggerstaff Part 1: Quantum Information: What is it? Why do it? What is information? Classical: bits ≡ binary digits information that can be stored in a 3-bit register can store 0 1 system is proportional to logb N one number, from 0–7 b is the number of states that can be stored in the unit N is the number of possible states of that system for three bits, log2 8 = 3 Hartley, Bell System Tech. J. 7, 535–563 (1928) Shannon, Bell System Tech. J. 7, 379–423 (1948) What is information? Classical: bits ≡ binary digits 3-bit register can store 0 1 one number, from 0–7 N bits: one N-bit number Quantum: qubits 0 qubit sphere also known as Poincaré sphere 1 Bloch sphere Poincaré, Leçons sur la théorie Mathématique de la lumière II,(1897) Hartley, Bell System Tech. J. 7, 535–563 (1928) Bloch, Phys. Rev. 70, 460 (1946) Shannon, Bell System Tech. J. 7, 379–423 (1948) Qubit Sphere 0 also known as Poincaré sphere Bloch sphere 0+1 0+i1 1 Qubit Sphere 0 also known as Poincaré sphere Bloch sphere 0+1 0+i1 1 Pure states are a collective delusion of theorists Qubit Sphere 0 also known as Poincaré sphere Bloch sphere 0+1 0+i1 1 Hermitean non-negative eigenvalues unity trace population Qubit Sphere 0 also known as Poincaré sphere Bloch sphere 0+1 0+i1 1 Hermitean non-negative eigenvalues unity trace population coherence Qubit Sphere 0 also known as Poincaré sphere Bloch sphere 0+1 0+i1 1 purity Density Matrix qutrit ququart or two qubits quoct or three qubits What is information? Classical: bits ≡ binary digits Classical gates 3-bit register can store NAND Toffoli 0 1 one number, from 0–7 INPUT OUTPUT INPUT OUTPUT N bits: one N-bit number A B A and B A B C A B C 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 Quantum: qubits 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 3-qubit register can 0 1 0 0 1 0 0 irreversible 1 0 1 1 0 1 store eight numbers 1 1 0 1 1 1 1 1 1 1 1 0 a |000+ b |001 reversible + c |010+ d |011 0+1 0+i1 + e |100+ f |101 1 Quantum gates INPUT OUTPUT + g |110+ h |111 A B A B CNOT 0 0 0 0 0 1 0 1 N N qubits: all possible 2 numbers 1 0 1 1 1 1 1 0 0+1 0 00+11 must be reversible 300-qubit register can store more information than number of atoms in universe Important problems benefit from factoring Physical Review Letters 99, 250505 (2007) this exponential scaling: simulation Nature Chemistry 2, 106 (2010) What is classical computing? quantum.info insoluble soluble What is classical computing? quantum.info insoluble insoluble hard factoring soluble travelling sales- easy man Nomenclature easy = “tractable” = “efficiently computable” hard = “intractable” = “not efficiently computable” What is quantum computing? quantum.info insoluble insoluble hard factoring soluble travelling sales- easy man Nomenclature easy = “tractable” = “efficiently computable” hard = “intractable” = “not efficiently computable” What is quantum computing? quantum.info insoluble insoluble hard factoring soluble travelling sales- easy man Nomenclature easy = “tractable” = “efficiently computable” hard = “intractable” = “not efficiently computable” In a world of quantum computers then we would need to abandon most of the algorithms that are in use today. —Robin Balean, VeriSign Australia, 2008 Software updates, email, online banking, and the entire realm of public-key cryptography and digital signatures rely on just two cryptography schemes to keep them secure—RSA and elliptic-curve cryptography (ECC). They are exceedingly impractical for today’s computers to crack, but if a quantum computer is ever built it would be powerful enough to break both codes. Cryptographers are starting to take the threat seriously, and last fall many of them gathered at the PQCrypto conference, in Cincinnati, to examine the alternatives. —IEEE Spectrum, January 2009 Why do quantum computing? quantum.info Aaronson’s Trilemma Shor’s factoring algorithm → Why do quantum computing? quantum.info Aaronson’s • Extended Church-Turing Thesis—foundation of theoretical Trilemma computer science for decades—is wrong Shor’s factoring algorithm → The assertion of the Church-Turing thesis might be compared, for example, to Galileo and Newton’s achievement in putting physics on a mathematical basis. By mathematically defining the computable functions they enabled people to reason precisely about those functions in a mathematical manner, opening up a whole new world of investigation. —Michael Nielsen, UQ, 2004 Statement: “All computational problems that are efficiently solvable by realistic physical devices, are efficiently solvable by a probabilistic Turing machine” Why do quantum computing? quantum.info Aaronson’s • Extended Church-Turing Thesis—foundation of theoretical Trilemma computer science for decades—is wrong • Quantum mechanics is wrong Shor’s factoring algorithm → It’s entirely conceivable that quantum computing will turn out to be impossible for a fundamental reason. This would be much more interesting than if it’s possible, since it would overturn our most basic ideas about the physical world. The only real way to find out is to try to build a quantum computer. Such an effort seems to me at least as scientifically important as (say) the search for supersymmetry or the Higgs boson. I have no idea— none—how far it will get in my lifetime. —Scott Aaronson, MIT, 2006 “All computational problems that are efficiently solvable by realistic physical devices, are efficiently solvable by a probabilistic Turing machine” Why do quantum computing? quantum.info Aaronson’s • Extended Church-Turing Thesis—foundation of theoretical Trilemma computer science for decades—is wrong • Quantum mechanics is wrong Shor’s factoring • A fast classical factoring algorithm exists algorithm → I love Shor’s algorithm because it proves to me that a fast classical factoring algorithm must exist. – Peter Sarnak, Princeton, 2012 I believe that there is a polynomial-cost answer to the strong correlation problem. We just haven't found it yet. – Gus Scuseria, Nature Chemistry, 2015 Why do quantum computing? quantum.info Aaronson’s • Extended Church-Turing Thesis—foundation of theoretical Trilemma computer science for decades—is wrong • Quantum mechanics is wrong Shor’s factoring • A fast classical factoring algorithm exists algorithm → All three seem crazy. At least one is true! Which of these do you think is the case? a. The Extended Church-Turing thesis is wrong b. Quantum mechanics is wrong c. Fast factoring exists & QC’s are not necessary d. Two of the above e. All of the above f. Shhh, I’m sleeping. How do we experimentally test this trilemma? Why do quantum computing? quantum.info Aaronson’s • Extended Church-Turing Thesis—foundation of theoretical Trilemma computer science for decades—is wrong • Quantum mechanics is wrong Shor’s factoring • A fast classical factoring algorithm exists algorithm → All three seem crazy. At least one is true! Which of these do you think is the case? a. The Extended Church-Turing thesis is wrong b. Quantum mechanics is wrong c. Fast factoring exists & QC’s are not necessary d. Two of the above e. All of the above f. Shhh, I’m sleeping. Computer scientists and / or Theoretical physicists and /or Mathematicians & chemists will be badly upset How do we experimentally test this trilemma? Why do quantum computing? quantum.info Aaronson’s • Extended Church-Turing Thesis—foundation of theoretical Trilemma computer science for decades—is wrong • Quantum mechanics is wrong Shor’s factoring • A fast classical factoring algorithm exists algorithm → All three seem crazy. At least one is true! Church-Turing-Deutsch principle: Any physical process can be efficiently simulated on a quantum computer Why do quantum computing? quantum.info Aaronson’s • Extended Church-Turing Thesis—foundation of theoretical Trilemma computer science for decades—is wrong • Quantum mechanics is wrong Shor’s factoring • A fast classical factoring algorithm exists algorithm → All three seem crazy.