Quantum logic synthesis (srikanth)
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This document discusses quantum logic synthesis. It begins by comparing traditional and quantum circuits, describing features like superposition and entanglement in quantum computers. It then covers reversible computation and common quantum gates like CNOT, Toffoli, and Fredkin. Various synthesis frameworks are introduced, including RMRLS, DDS, and their hybrid RMDDS. The document provides examples of quantum gate applications and references several foundational works.
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Quantum logic synthesis (srikanth)
- 1. QUANTUM LOGIC SYNTHESIS Srikanth Bitra (10881A0451) Under guiedence of C.Padmini ECE dept.
- 2. Contents Introduction Differences between traditional and quantum circuits Reversible computation Reversible gates NOT C-NOT Toffoli RSWAP Fredkin Synthesis frame works RMRLS DDS RMDDS
- 3. Features of quantum computer: Super position Interference Entanglement Measurement
- 7. Quantum vs Classical Quantum Computation Bijective or Reversible Input and output vectors have same bit-width No information loss Classical Computation Irreversible Different input and output bit-width Loss of information
- 8. Need for reversibility Fundamental physics dictates that energy must be dissipated when information is erased, in the amount KT ln2 per bit erased, where K is Boltzmann constant(k=1.38x1023JK-1) and T is absolute temperature in K
- 9. NOT
- 12. Fredkin(CSWAP) Logic:p=a, q=if(a=1) then c else b, r=if(a=1) then b else c
- 13. Synthesis methods of quantum circuits QBC synthesis Reed muller reversible logic synthesis Decision diagram synthesis RMRLS + DDS RMDDS
- 14. Reed Muller Reversible Logic Synthesis(RMRLS) Any Boolean function can be described by an exclusive-OR sum-of-products (ESOP) expression ex: for a boolean expression y= a+b’c SOP=a+b’c ESOP=a a’b’c Two types of expressions: PPRM :All variables are un-complemented PPRM=abc ac bc a c FPRM:Either x or x’ appear throughout FPRM=a’b’c a’ 1
- 15. Reed Muller Reversible Logic Synthesis (cont..) Synthesis flow Find factors for any outptut a0 without literal a (target) Build a node in a search tree, where: #PPRM terms is reduced by Toffoli gate Create a child node Insert the node into Priority Queue (PQ) EX: a0 = a bc 1 ac Valid factors :bc,1 Target : a Sort Priority queue Priority α # PPRM terms eliminated Pop the queue ,repeat above steps
- 19. Decision Diagram Synthesis Boolean functions are represented by a DD (Decision Diagrams) DD:acyclic graph G=(V, E) where decompositions are applied to each node v ϵ V Shannon decomposition(S) : f=xi’.fxi=0 xi.fxi=1 Positive Davio decomposition(pD): f=xi’.fxi=0 xi.fxi=2 Negative Davio decomposition(nD): f=xi’.fxi=1 xi.fxi=2 fxi=0 and fxi=1 f =f are co-factors w.r.t. xi’ and xi f
- 20. Decision Diagram Synthesis (DDS) Synthesis flow Build DD(Decision Diagrams) Depth first search Map each gate to Toffoli gate Note: DDS method automatically transforms an irreversible specification into reversible
- 23. RMRLS vs DDS RMRLS DDS Pros Fewer qubits(lines) Low quantum cost Low synthesis time Able to synthesize large circuits Can synthesize irreversible specifications Cons High synthesis time Only able to synthesize small circuits Large no. of garbage outputs
- 24. Reed-Muller Decision Diagram Synthesis (RMDSS) Hybrid of RMRLS and DDS A flexible and efficient reversible circuit synthesizer Qubits can be traded off for QC User defined time limit
- 25. User constriants
- 26. Applications of quantum gates Efficient white light LED’s Processor’s designed for complex scientific calculations Artificial intelligence cryptography
- 27. Acknowledge Susmita Sur-Kolay (Indian Statistical Institute)
- 28. References D. P. Di Vincenzo, “Quantum Computation,” Science, 270, 1995, pp. 255-256. K. Iwama, Y. Kambayashi, S. Yamashita, “Transformation Rules for Designing CNOTBased Quantum Circuits,” Design Automation Conference,2002, pp.419-424. P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 1st Edition, 1930.