Embedding Logical Qubits into the D-Wave Hardware Graph Keith Britt February 26 th, 2014

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

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.)

Quantum Computing

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

Ising Model

D-Wave Hardware

So is Hardware Just a Line Graph? Not Valid

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

Ising Model Edge Weights Vertex Weights

Linking Unit Cells

Not Valid

Linking Unit Cells Valid

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

Literature Review Choi, Vicky. Minor-Embedding in Adiabatic Quantum Computation: I. The Parameter Setting Problem. Quantum Information Processing, 7, pp 193 – 209, arXiv: v1 [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: v2 [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: v2 [quant-ph].

D-Wave Embedding Limits

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

Something We’re Not Going Over Edge Weights Vertex Weights

An Example

Homework Questions

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