embedding logical qubits into the d-wave hardware graph keith britt [email protected] february 26...
TRANSCRIPT
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
• Parallelism Scales Exponentially with the Number of Qubits ()
• Several Models of Quantum Computation– Gate/Circuit Model– Adiabatic Model– Topological model (and more…)
• The First Commercially Available Quantum Computer (D-Wave) Uses the Adiabatic Model
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
: State (Spin/Value) of the Qubit ( ): Set of Qubits: Strength of the Qubit Value: Strength of the Qubit-Qubit Interaction: The Total Energy of the System
http://dwave.files.wordpress.com/2010/12/weightedmaxsat_v2.pdf
D-Wave Hardware
http://dwave.wordpress.com/2011/12/01/vesuvius-a-closer-look-512-qubit-processor-gallery/
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
: State (Spin/Value) of the Qubit ( ): Set of Qubits: Strength of the Qubit Value: Strength of the Qubit-Qubit Interaction: The Total Energy of the System
http://dwave.files.wordpress.com/2010/12/weightedmaxsat_v2.pdf
Edge WeightsVertex Weights
Linking Unit Cells
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, 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].
D-Wave Embedding Limits
• Logical Qubit is Not the Same as a Physical Qubit
• Can Always Embed N Logical Qubits onto Physical Qubits
• This is Not a Tight Upper-bound, Even for Complete Graphs
• Choi’s Triad Technique Able to Embed on 128-Qubit Processor ()
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
and values determine a lot about how aligned qubits are with one another. This gets a bit too outside of graph theory, but there’s an easy to read explanation at:
http://www.dwavesys.com/sites/default/files/Map%20Coloring%20WP2.pdf
Edge WeightsVertex Weights
An Example
• Embed into a Unit Cell
http://arxiv.org/pdf/1001.3116v2.pdf
http://arxiv.org/pdf/1001.3116v2.pdf
Embedding
• Start by Embedding in a Unit Cell
Embedding
• Next Embed the Other in a Unit Cell
Embedding
• Next Embed in a Unit Cell
Embedding
• Tada! is embedded in the D-Wave Hardware
Homework Questions
• Embed into the D-Wave Hardware Graph in 6 or Fewer Unit Cells.
Homework Questions
• Embed the Peterson Graph into the D-Wave Hardware Graph (Diamond Isomorphism) in 6 or Fewer Unit Cells.