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Embedding Logical Qubits into the D-Wave Hardware Graph Keith Britt keithbritt@utk.edu February 26 th, 2014

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Agenda A Little Bit About Quantum Computing A Little Bit About D-Wave The D-Wave Hardware Transforming the Hardware into a Graph Embedding Literature “Review” Embedding Limits Example Embedding(s) Homework Problems

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Quantum Computing In the Quantum World, classical physics give way to 2 phenomena: – Superposition – Entanglement We can use these phenomena to massively parallelize computation and also do some crazy stuff that is otherwise impossible (truly random numbers, data teleportation, etc.)

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Quantum Computing

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D-Wave Canadian Company Founded by Physicists and Material Scientists Created a Quantum Chip Using Adiabatic Model Running at Extremely Cold Temperatures and Minimal Interference Very Controversial… Is the Computer Really Quantum? Is It Worth It? – Simulations Beat It – Classical Adiabatic Computer Matched It

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Ising Model http://dwave.files.wordpress.com/2010/12/weightedmaxsat_v2.pdf

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D-Wave Hardware http://dwave.wordpress.com/2011/12/01/vesuvius-a-closer-look-512-qubit-processor-gallery/

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So is Hardware Just a Line Graph? Not Valid

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Unit Cell Graph Representation Each Qubit Becomes a Vertex Each Coupler Becomes an Edge Between Vertices Valid

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Ising Model http://dwave.files.wordpress.com/2010/12/weightedmaxsat_v2.pdf Edge Weights Vertex Weights

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Linking Unit Cells

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Not Valid

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Linking Unit Cells Valid

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512 Vertices (Qubits) 16 Intra Unit Cell Edges per Unit Cell 8 – 16 Inter Unit Cell Edges per Unit Cell

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Literature Review Choi, Vicky. Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem. Quantum Information Processing, 7, pp 193 – 209, 2008. arXiv:0804.4884v1 [quant-ph]. Choi, Vicky. Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design. Quantum Information Processing: Volume 10, Issue 3 (2011), Page 343. arXiv:1001.3116v2 [quant-ph]. Klymko, C., Sullivan, B., Humble, T. Adiabatic quantum programming: minor embedding with hard faults. Quantum Information Processing: Volume 13, Issue 3 (2014), pp 709 – 729. arXiv:1210.8395v2 [quant-ph].

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D-Wave Embedding Limits

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Logical to Physical A Logical Qubit can be Spread Over Multiple Physical Qubits as Long as There is a Common Path Between All The Physical Qubits NOT VALID VALID

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Something We’re Not Going Over Edge Weights Vertex Weights

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An Example

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http://arxiv.org/pdf/1001.3116v2.pdf

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Homework Questions

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Embed the Peterson Graph into the D-Wave Hardware Graph (Diamond Isomorphism) in 6 or Fewer Unit Cells.

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