Quantum Computers presented by Siva Desaraju Bindu Katragadda

Quantum Computers presented by Siva Desaraju Bindu Katragadda Manusri Edupuganti

Outline Introduction Quantum computation Implementation Quantum compiler Error correction Architecture Classification Fabrication Challenges Advantages over classical computers Applications Recent advances Timeline Conclusion

Introduction Quantum Mechanics n Why? – Moore’s law n Study of matter at atomic level (The power of atoms) n Classical physics laws do not apply [2] Superposition n Simultaneously possess two or more values Entanglement n Quantum states of two atoms correlated even though spatially separated!!! n Albert Einstein baffled “spooky action at a distance”

Bits n Qubits Classical computers 0 or 1 (bits) n High/low voltage Quantum computers 0 or 1 or 0 & 1 (Qubits) n Nuclear spin up/down 0 or 1 n Isolated atom spin up & down 0 & 1 Represent more with less (n bits 2 n states) ” To be or not to be. That is the question” – William Shakespeare The classic answers: ”to be” or ”not to be” [2] The quantum answers: ”to be” or ”not to be” or a x (to be) + b x (not to be)

Quantum Computation Prime factorization (Cryptography) n n n Peter Shor’s algorithm Hard classical computation becomes easy quantum computation Factor n bit integer in O(n 3) Search an unordered list n n n Lov Grover’s algorithm Hard classical computation becomes less hard quantum computation n elements in n 1/2 queries

Implementation model Early quantum computation - Circuit model(ASIC) Quantum unitary transforms (gates) Quantum measurements Quantum program Instruction stream Quantum compiler Classical bit instruction stream Classical computation Classical control flow decisions

Quantum Compiler Static precompiler n End-to-end error probability Dynamic compiler n Accepts the precompiled binary code & produces an instruction stream

Error Correction Localized errors on a few qubits can have global impact Hamming code Difficulty of error correcting quantum states n Classical computers – bit flip n Quantum computers – bit flip + phase flip n Difficulty in measurement (collapses superposition) Quantum error correction code n [n, k] code uses n qubits to encode k qubits of data n Extra bits (n-k) are called ancilla bits n Ancilla bits are in initial state

Architecture Aims of efficient architecture n n n Minimize error correction overhead Support different algorithms & data sizes Reliable data paths & efficient quantum memory Major components n n n Quantum ALU Quantum memory Dynamic scheduler

Architecture contd… [1]

Quantum ALU Sequence of transforms n n n n n the Hadamard (a radix-2, 1 -qubit Fourier transform) identity (I, a quantum NOP) bit flip (X, a quantum NOT) phase flip (Z, which changes the signs of amplitudes) bit and phase flip (Y) rotation by π/4 (S) rotation by π/8 (T) controlled NOT (CNOT)

Quantum Memory Reliable memory Refresh units Multiple memory banks

Quantum wires Teleportation Quantum swap gates Cat state [1]

Dynamic Scheduler Dynamic scheduler algorithm takes n Input - logical quantum operations, interleaved with classical control flow constructs n Output - physical individual qubit operations Uses knowledge of data size & physical qubit error rates

Classification Quantum Computer Liquid Quantum Computer Solid Quantum Computer Si 29 Doping Phosphorous Doping

Liquid Quantum Computers NMR Technology Disadvantages n Massive redundancy n Not scalable

Solid Quantum Computers Why silicon Chip design aims n n Capturing & manipulating individual sub atomic particles Harnessing, controlling & coordinating millions of particles at once

Si 29 Doping Need for Silicon 29 (Si 29) doping Fabrication Advantages Disadvantages [9]

Phosphorous doping [3]

Fabrication STM technology to pluck individual atoms from hydrogen n PH 3 used instead of P

Challenges Decoherence Chip fabrication Error correction

Advantages over Classical computers Encode more information Powerful Massively parallel Easily crack secret codes Fast in searching databases Hard computational problems become tractable

Applications Defense Cryptography Accurate weather forecasts Efficient search Teleportation … Unimaginable

Timeline 2003 - A research team in Japan demonstrated the first solid state device needed to construct a viable quantum computer 2001 - First working 7 -qubit NMR computer demonstrated at IBM’s Almaden Research Center. First execution of Shor’s algorithm. 2000 - First working 5 -qubit NMR computer demonstrated at IBM's Almaden Research Center. First execution of order finding (part of Shor's algorithm). 1999 - First working 3 -qubit NMR computer demonstrated at IBM's Almaden Research Center. First execution of Grover's algorithm. 1998 - First working 2 -qubit NMR computer demonstrated at University of California Berkeley. 1997 - MIT published the first papers on quantum computers based on spin resonance & thermal ensembles. 1996 - Lov Grover at Bell Labs invented the quantum database search algorithm 1995 - Shor proposed the first scheme for quantum error correction

Conclusion…will this be ever true? Millions into research With a 100 qubit computer you can represent all atoms in the universe. If you succeed, the world will be at your feet [6]

References [1] [2] [3] [4] [5] [6] [7] [8] [9] http: //www. cs. washington. edu/homes/oskin/Oskin-A-Practical. Architecture-for-Reliable-Quantum-Computers. pdf http: //www. qubit. org http: //www. nature. com http: //www. wikipedia. com http: //www. howstuffworks. com http: //www. physicsweb. org/toc/world/11/3 http: //www. cs. ualberta. ca/~bulitko/qc/schedule/slides/QCSS-2002 -06 -18. ppt http: //physics. about. com/cs/quantumphysics/ http: //www. trnmag. com/Stories/2002/082102/Chip_ design_aims_for_quantum_leap_082102. html

Puzzled? ? ? "I think I can safely say that nobody understands quantum mechanics. " - Richard P. Feynman “Anybody who thinks they understand quantum physics is wrong. " - Niels Bohr