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Quantum Computing
- 1. Quantum Computing Programming andAlgorithms Cars.com Tech Tailgate 2016 Stephen Habegger
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- 3. 3 Quantum Computing •Mathematics •Quantum Physics •QuantumComputer Architecture •Quantum Algorithms •Building a Quantum Circuit • www.research.ibm.com/quantum/ •Quantum Computing Software •Quantum Computing Hardware •Questions
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- 5. 5 Complex Numbers ● Imaginary ●Complex ● Complex Conjugate ● Modulus
- 6. 6 Complex Numbers ● PolarRepresentation ● Euler’s Formula https://en.wikipedia.org/wiki/Complex_number
- 7. 7 Linear Algebra: MatrixMultiplication
- 8. 8 Linear Algebra: TensorProduct
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- 12. 12 Qubits: The BlochSphere
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- 14. 14 State Vectors The stateof a bit/qubit can be represented by a vector. In the case of a qubit this serves as a complementary representation to the Bloch sphere, where the probability of measuring a given state is given by the modulus of the associated value.
- 15. 15 State Transitions •Operations onbits/qubits can be described as matrices •Multiplying a matrix which represents an operation by an input state vector returns the resulting output state vector
- 16. 16 Multiple Qubits Multiple independentqubits (or operations on qubits) can be represented by the tensor product of the two state vectors (or operation matrices)
- 17. 17 Classical Logic Gates IDENTITYNOT AND OR XOR
- 18. 18 Quantum Logic Gates X(NOT) Z S T Y Hadamard (H) Sqrt NOT
- 19. 19 Reversible Logic Gates:Toffoli
- 20. 20 Reversible Logic Gates:Toffoli
- 21. 21 Quantum AND Gatevia Toffoli
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- 23. 23 General Quantum Algorithm 1.Qubitsstart in some classical state - e.g. 0000 or 1001 2.System is placed into a superposition of states 3.Act upon qubits using unitary operations 4.Measure some of the qubits (collapsing to a classical state)
- 24. 24 Deutsch’s Algorithm •Determines whethera function is “balanced” or “constant” •Operates on functions in the space •Classical algorithms require 2 calls to the function, while the quantum algorithm requires 1. This is achieved by a “change of basis” in the problem space.
- 25. 25 Deutsch’s Algorithm Balanced FunctionConstant Function 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
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- 27. 27 Grover’s Algorithm Find anelement in a set in expected time 1.Start with a selector function 2.Repeat times a.Perform phase inversion using selector function (selected element takes opposite phase from other elements) b.Perform inversion about the mean (amplitude of selected element is increased) 3.Measure
- 28. 28 Grover’s Algorithm Phase InversionInversion About Mean
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- 30. 30 Cryptography •Public key cryptography(RSA) • Relies on difficulty of factoring large numbers (with large prime factors) • Shor’s algorithm can factor integers in polynomial expected time •Quantum private key generation & eavesdropping • Classical bits randomly generated and transmitted as qubits in randomly selected bases • Qubits measured in randomly selected bases • Subset of qubits transmitted/measured in same bases are compared; rest are used as private key
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- 32. 32 Quantum Assembly •Based onQRAM architecture • Provably equivalent to Quantum Circuit and Quantum Turing Machine architectures •Act upon a register of qubits •Commands • INITIALIZE • SELECT • APPLY • CONCAT • TENSOR • INVERSE • MEASURE •QASM (IBM, MIT, etc.)
- 33. 33 Higher-Level Quantum Languages •Types(other than quantum bit sequences) •Functions (must be reversible) •QCL • C-like syntax • QReg type • User-defined operators and functions •Q •QFC • Flowchart-type syntax • Classical control statements
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- 35. 35 Quantum Hardware •Challenges • Allowentanglement • Avoid decoherence •Ion Trap • Confine ionized atoms in electromagnetic field • Excited vs ground state (optical pumping via lasers) •Optical Quantum Computers • Light polarization
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- 38. 38 Resources Yanofsky, Noson S.;Mannucci, Mirco A. (2008-08-11). Quantum Computing for Computer Scientists. Cambridge University Press - A. Perry, Riley Tipton (2012-07-11). Quantum Computing from the Ground Up. Wspc. IBM Quantum Experience. www.research.ibm.com/quantum/ Microsoft Language-Integrated Quantum Operations: LIQUi|>. https://www.microsoft.com/en-us/research/project/language-integrated- quantum-operations-liqui/ Quantum Simulator. https://github.com/shabegger/quantum-emulate
- 39. 39 Appendix B: PhaseInversion Calculations
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