Published on January 7, 2008
Quantum computation: Shifting the computational paradigm: Quantum computation: Shifting the computational paradigm Juan Pablo Paz Theoretical Division Los Alamos National Laboratory Slide2: What is a computer? Abacus (China, XIII): Add, substract, multiply, divide,.. : The King: Kiyoshu Matzukai, 1946!) Blaise Pascal (France, 1642). Charles Babbage, England 1830. Multipurpose computer (differerence engine, analytical engine: two failures of XIX century technology!) Slide3: Turing machine: Could do anything... Initial use: code breaking (Enigma, etc) Slide4: Microelectronics: Computers are getting smaller and smaller.. Moore’s law: Number of transistors per chip doubles every 18 months. Quantum technology Slide5: So: What is a computer? Physical system that stores and process information. Computer behavior: consistent with laws of physics! Information is physics: no information without representation! Slide6: HOW DO THEY WORK? Require quantum hardware: quantum bits (qubits). Then: Prepares an initial state. Executes a program (sequence of physical actions on the qubits). Make a final measurement. The key: During the execution of the program the quantum computer explores many classical computations (quantum paralelism) Quantum computers WHAT ARE THEY GOOD FOR? They could do everything a classical computer can do..(not very interesting) A FEW quantum algorithms are much more efficient than their classical counterparts: find prime factors of integer numbers (Shor). perform simulations of natural systems (physics simulations) search databases (Grover) …? Slide7: A physical system can tepresent a “Classical Bit” if it can exist in two distinct states The basic ingredient for quantum hardware: Quantum Bits (qubits) In the microscopic world “balls” do not follow definite trajectories. A quantum particle (a photon) can be used to represent a “quantum bit”: something that can exist in more than two states… Slide8: Shine light on a half silvered mirror (50% reflected, 50% transmitted) Clasical case: intense beam (laser pointer) 50% of the light intensity goes to each detector Quantum case: attenuated beam: light comes in “packets” (photons) Quantum Physics: The strange properties of photons Slide9: Photons arrive “one by one” to the detectors. But what trajectory do they follow? Quiz: How many photons in each detector? Hint 1: Consider the photons following the “down” path (50%). Half of them end up on each detector. Hint 2: The same should happen with the photons that follow the “up” path (50%). Therefore: we should get 50% in each detector Empirical fact (hard to swallow): All photons end up in one detector!! This CANNOT be explained unless we accept that photons follow both trajectories while unobserved. During the experiment, the state of the photon is a superposition of both alternatives (corresponding to the “up” and “down” trajectories) Slide10: Photon is a quantum bit (qubit) Slide11: And, similarly, (very) strange effects are observed with electrons, atoms, … Electrons, and all spin 1/2 particles Atoms can act, under some circumstances as two level systems Photons (polarization degrees of freedom) Composite systems: superconductors, quantum dots, etc Slide12: Evolution of a classical computer Initial state First step Second step The computer follows a sequence of computational states (computational trajectory) Slide13: Evolution of a quantum computer New paradigm: quantum parallelism (magic version...) Slide14: How to use quantum parallelism to do something useful? Find prime factors of integer numbers: Peter Shor (1994) Challenge ($ 10,000): RSA-576 (172 digits), find P and Q such that P x Q =188198812920607963838697239461650439807163563379417382700763356422988859715234 665485319060606504743045317388011303396716199692321205734031879550656996221305168759 307650257059 (details in www.rsa.com) Building a quantum computer: Status of the race… (2003): Building a quantum computer: Status of the race… (2003) Slide16: Cold trapped ions for quantum information processing Idea: I. Cirac and P. Zoller (1995). Experiments: Wineland @ Boulder, Blatt @ Innsbruck Qubits: Internal states of electron in a cold trapped ion (laser cooled). Interaction: Use coupling of ions with vibrational states of “cristal” (phonons). Operations: Shine lasers on ions to make them interact. 2003: c-not gate between two ions What is the main obstacle?: What is the main obstacle? Extreme sensitivity to interaction with outside environment: Decoherence: Due to interaction with environment, quantum computer “colapses” into a classical one (loosing all its advantadges). This is a soluble problem (in principle, at least) Quantum error correcting codes (1996-98) Fault tolerant quantum computation (1997-2000) Perspectives on Quantum computation (or why is this interesting?): Perspectives on Quantum computation (or why is this interesting?) Shift in computational paradigm: A new way to compute (inspired by physics). New algorithms? (other than factoring). Use most counterintuitive aspects of quantum physics. Experiments probe the boundary between quantum and classical worlds as never before. Experiments require amazing control over individual quantum systems (single atoms, etc). Quantum Technology. Is it realistic? A big effort is under way (100M$/year from govt agencies). Motivation? Factoring: Code breaking… Timescale: 10-20 years? Slide23: Cuán dificil es encontrar los factores primos de un número entero?