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Quantum Circuit Placement: Optimizing Qubit-to-qubit Interactions through Mapping Quantum Circuits into a Physical Exper

Quantum Circuit Placement: Optimizing Qubit-to-qubit Interactions through Mapping Quantum Circuits into a Physical Experiment. D. Maslov (spkr) – IQC/UWaterloo, Canada. S. M. Falconer – UofVictoria, Canada. M. Mosca – IQC/UWaterloo, Canada. Outline. Why quantum computing? Background

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Quantum Circuit Placement: Optimizing Qubit-to-qubit Interactions through Mapping Quantum Circuits into a Physical Exper

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  1. Quantum Circuit Placement:Optimizing Qubit-to-qubit Interactions through Mapping Quantum Circuits into a Physical Experiment D. Maslov (spkr) – IQC/UWaterloo, Canada S. M. Falconer – UofVictoria, Canada M. Mosca – IQC/UWaterloo, Canada

  2. Outline • Why quantum computing? • Background • Circuit placement technique • Results page 1/10

  3. Algorithms Implementation Why quantum computing? Algorithms:Abelian stabiliser, Bernstein-Vazirani parity problem, Deutsch-Jozsa, differential equations, discrete logarithm, Eigenvalues, factoring, group theory, Grover (database search), hidden subgroup problem, Jones polynomials, Median, NAND tree evaluation, numerical integration, pattern recognition, physical simulation, Poincare recurrences, polynomial shift equivalence, random walks, random number generation, Simon, etc. page 2/10

  4. Algorithms Implementation Why quantum computing? Complexity separation Algorithms:Abelian stabiliser, Bernstein-Vazirani parity problem, Deutsch-Jozsa, differential equations, discrete logarithm, Eigenvalues, factoring, group theory, Grover (database search), hidden subgroup problem, Jones polynomials, Median, NAND tree evaluation, numerical integration, pattern recognition, physical simulation, Poincare recurrences, polynomial shift equivalence, random walks, random number generation, Simon,etc. page 2/10

  5. Algorithms Implementation Why quantum computing? Complexityseparation Famous Algorithms:Abelian stabiliser, Bernstein-Vazirani parity problem, Deutsch-Jozsa, differential equations, discrete logarithm, Eigenvalues, factoring, group theory, Grover (database search), hidden subgroup problem, Jones polynomials, Median, NAND tree evaluation, numerical integration, pattern recognition, physical simulation, Poincare recurrences, polynomial shift equivalence, random walks, random number generation, Simon, etc. page 2/10

  6. Algorithms Implementation Why quantum computing? Complexity separation Most Practical Famous Algorithms:Abelian stabiliser, Bernstein-Vazirani parity problem, Deutsch-Jozsa, differential equations, discrete logarithm, Eigenvalues, factoring, group theory, Grover (database search), hidden subgroup problem, Jones polynomials, Median, NAND tree evaluation, numerical integration, pattern recognition, physical simulation, Poincare recurrences, polynomial shift equivalence, random walks, random number generation, Simon, etc. page 2/10

  7. Algorithms Implementation Why quantum computing? Complexity separation Most Practical Commercially Available Famous Algorithms:Abelian stabiliser, Bernstein-Vazirani parity problem, Deutsch-Jozsa, differential equations, discrete logarithm, Eigenvalues, factoring, group theory, Grover (database search), hidden subgroup problem, Jones polynomials, Median, NAND tree evaluation, numerical integration, pattern recognition, physical simulation, Poincare recurrences, polynomial shift equivalence, random walks, random number generation, Simon, etc. page 2/10

  8. Algorithms Implementation Why quantum computing? Implementation:liquid Nuclear Magnetic Resonance, solid NMR, ion traps, neutral atoms, cavity QED, optic technologies, solid state, superconducting (Josephson junctions), etc. page 3/10

  9. Algorithms Implementation Why quantum computing? Mostdeveloped Implementation:liquid Nuclear Magnetic Resonance, solid NMR, ion traps, neutral atoms, cavity QED, optic technologies, solid state, superconducting (Josephson junctions), etc. page 3/10

  10. Algorithms Implementation Why quantum computing? Likely most promising Mostdeveloped Implementation:liquid Nuclear Magnetic Resonance, solid NMR, ion traps, neutral atoms, cavity QED, optic technologies, solid state, superconducting (Josephson junctions), etc. page 3/10

  11. Quantum CAD tools Why quantum computing? Algorithms Implementation Quantum CAD tools:circuit optimization, error correction, synthesis, testing, verification. In this work:placement. page 4/10

  12. 3D space time Background Algorithms are circuits. page 5/10

  13. Hydrogen Nitrogen Carbon Histidine Background Implementation: Liquid NMR Communication via chemical bonds. page 6/10

  14. Circuit placement Problem: given a circuit and a quantum mechanical system, assign qubits as to optimize the runtime. Theorem: the above problem is NP-Complete. Additional complication: it might be possible to place subcircuits nicely, but the total runtime is high. Solution: Place subcircuits Permute qubit assignments page 7/10

  15. Circuit placement Place subcircuits Place subcircuits Permute qubit assignments Permute qubit assignments page 8/10

  16. Circuit placement Place subcircuits Circuit is a graph: nodes are logic qubits, edges are two-qubit gates. Physical implementation is a graph: nodes are physical qubits (e.g., nuclei), edges are “fast” connections (e.g., chemical bonds). Solution: place subcircuits using graph monomorphism techniques. Permute qubit assignments page 8/10

  17. Circuit placement Permute qubit assignments Permute qubit assignments Permute qubit assignments page 8/10

  18. Circuit placement Permute qubit assignments Problem: given two qubit-to-nuclei assignments, permute one into the other. Trans-crotonic acid page 9/10

  19. WHITE BLACK Circuit placement Permute qubit assignments Cut the graph into two maximally balanced connected components. Color vertices black and white according to which subgraph we want to permute their values to. page 9/10

  20. WHITE BLACK Circuit placement Permute qubit assignments Cut the graph into two maximally balanced connected components. Color vertices black and white according to which subgraph we want to permute their values to. page 9/10

  21. Circuit placement Permute qubit assignments page 9/10

  22. Circuit placement Permute qubit assignments White is air, black is water. Step 1: SWAP(4,5) SWAP(6,7) page 9/10

  23. Circuit placement Permute qubit assignments White bubbles rise. Step 1: SWAP(4,5) SWAP(6,7) Step 2: SWAP(3,4) page 9/10

  24. Circuit placement Permute qubit assignments White bubbles rise. Step 1: SWAP(4,5) SWAP(6,7) Step 2: SWAP(3,4) Step 3: SWAP(2,3) SWAP(4,6) page 9/10

  25. Circuit placement Permute qubit assignments White bubbles rise. Step 1: SWAP(4,5) SWAP(6,7) Step 2: SWAP(3,4) Step 3: SWAP(2,3) SWAP(4,6) Step 4: SWAP(3,4) page 9/10

  26. Circuit placement Permute qubit assignments The problem falls into two. We proved that with some natural restrictions the solution has linear depth. page 9/10

  27. Results Placement is identical to that by experimentalists. 6-qubit quantum Fourier transform/trans-crotonic acid. page 10/10

  28. END Thank you for your attention!

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