Bob Lucas Federico Spedalieri Information Sciences Institute Viterbi School of Engineering USC
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Transcript of Bob Lucas Federico Spedalieri Information Sciences Institute Viterbi School of Engineering USC
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Bob Lucas Federico Spedalieri
Information Sciences InstituteViterbi School of Engineering
USC
Adiabatic Quantum Computing with the D-Wave One
The End of Dennard Scaling
Need More Capability?
Application Specific SystemsD.E. Shaw Research Anton
Massive Scaling – ORNL Cray XK7
Exploit a New PhenomenonAdiabatic Quantum Processor
D-Wave One
Overview
• Adiabatic quantum computation
• Brief description of D-Wave One
• The three main thrusts of research:
1. Quantumness
2. Benchmarking
3. Applications
Quantum computer Hamiltonian: H(t) = (1- (t))H0 + (t)H1
• Prepare the computer in the ground state of H0
• Slowly vary (t) from 0 to 1
• Read out the final state: the ground state of H1
• Runtime associated with (gmin)-2
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gmin
E0
E1
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Adiabatic Quantum Computation
• Adiabatic QC is universal (can compute any function, just like circuit model)
• But universality may be too much to ask for.• Consider only “classical” final Hamiltonians, i.e.:
Diagonal(in computational basis)
Off-diagonal (in computational basis)
The final state is a classical state that minimizes the energy of H1
Adiabatic Quantum Optimization
Solving Ising models with AQC
• Ising problem: Find
• Adiabatic quantum optimization:
Overview
• Adiabatic quantum computation
• Brief description of D-Wave One
• The three main thrusts of research:
1. Quantumness
2. Benchmarking
3. Applications
USC/ISI’s D-Wave One128 (well, 108) qubit Rainier chip
20mK operating temperature1 nanoTesla in 3D across processor
Qubits and Unit Cell
One qubit SC loop;qubit = flux generated by Josephson current Unit cell
compound-compound Josephson junction (CCJJ) rf SQUIDs flux qubit
Eight Qubit Unit Cell
Tiling of Eight-Qubit Unit Cells
Adiabatic Quantum Optimization
Problem: find the ground state of
Use adiabatic interpolation from transverse field (Farhi et al., 2000)
Graph Embedding implemented on DW-1 via Chimera graph retains NP-hardness V. Choi (2010)
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Program API
Overview
• Adiabatic quantum computation
• Brief description of D-Wave One
• The three main thrusts of research:
1. Quantumness
2. Benchmarking
3. Applications
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Experimental Quantum Signature
(S. Boixo, T. Albash, F. S., N. Chancellor, D. Lidar)
Classical Simulated Annealing
Minimizing a complex cost function we can get trapped in local minima.
Add temperature to go “uphill”.Temperature decreases with time.
Quantum resources: tunneling
Degenerate Ising Hamiltonian
+1
-1
-1
17-fold degenerate ground space:
+/- 1
+/- 1
+/- 1
1
+/- 1
1
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-1
-1
-1
-1-1
-1-1
-1
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Classical Thermalization
Several SA schedules
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Quantum annealing
Quantum Annealing
We want to find the ground state of an Ising Hamiltonian:
Instead of “temperature” fluctuations, we use quantum fluctuationsa transverse field
Slowly remove the transverse field to stay on the ground state:
DW1 Gap
Gap 1.5 GHz(Temp: 0.35 GHz)
Transitions to 4th order in
Small gap ->small coupling!!!
QA closed system
QA open system
QA vs. SA
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Experiments
Embedding
Chip Connectivity Our Quantum Signature problemas it looks in the chip
DW1 Experiments
144 embeddings
Quantum Signature: this state is suppressed
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Entanglement
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Entanglement: a definition
• Separable states
• Entangled states
• It is a classical mixture of product states• It can be constructed locally
ENTANGLEMENT IN DW2• Even numerically, determining if a state is entangled is NP-hard
• How can we experimentally show entanglement?
1. Measure the complete density matrix of the system Quantum State Tomography
2. Measure an observable that distinguishes entangled states Entanglement Witnesses
• Requires a large number of measurements (exponential in the number of qubits)
• The reconstructed density matrix may not be physical (not PSD)
• For DW2, these measurements are not even possible
• For every entangled state there is an entanglement witness
• Measuring the expectation of Z can prove entanglement
• But to find Z we need to know the state (or be very lucky)
• The measurements required will likely not be available in DW2
Separable States
Magnetic susceptibilities in DW2
• Use a weakly coupled probe to measure
• Compute the magnetic susceptibilities as
• Use perturbation theory (and some assumptions) to write
Separability criteria
• Apply PPTSE separability criteria to this general state
• All separable states have a PPTSE for any k
• Search for PPTSE can be cast as a semidefinite program
• Produces a hierarchy of separability tests
• If state is entangled, dual SDP computes an entanglement witness
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Separability criteria with partial information
• Some properties of this approach:
1. If the test fails the state may still be entangled
2. We can use a dual approach that checks if a state satisfying the linear constraints is separable (also a SDP)
3. If both tests fail, we need to go to higher k
4. All entangled states will be detected for some k
5. Going beyond k=2 may be tricky (the size of the SDP gets too big)
6. In theory, this is the best you can do with partial information: if you could run the tests for all k, this approach will eventually prove that all states satisfying the linear constraints are entangled or that there is one such state that is separable
Overview
• Adiabatic quantum computation
• Brief description of D-Wave One
• The three main thrusts of research:
1. Quantumness
2. Benchmarking
3. Applications
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Benchmarking
Benchmarking hard problems10 – 108 qubits
Benchmarking hard problems108 qubits, 5us – 20ms
Classical repetition cost r
Some benchmarking
Exponential run time for the best exact classical solver
Faster exponential run time for the D-Wave (Vesuvius)
Some benchmarking(3BOP h and J)
Overview
• Adiabatic quantum computation
• Brief description of D-Wave One
• The three main thrusts of research:
1. Quantumness
2. Benchmarking
3. Applications
Some NP-complete problems and their applications
Problem Application
Traveling salesman Logistics, vehicle routing
Minimum Steiner tree Circuit layout, network design
Graph coloring Scheduling, register allocation
MAX-CLIQUE Social networks, bioinformatics
QUBO Machine learning (H. Neven, Google)
Integer Linear Programming Natural language processing
Sub-graph isomorphism Cheminformatics, drug discovery
Job shop scheduling Manufacturing
Motion planning Robotics
MAX-2SAT Artificial intelligence
The problem addressed by quantum annealing is NP-Complete
• Given a:– Finite transition system M– A temporal property p
• The model checking problem: – Does M satisfy p?
• It typically requires analyzing every possible path the system can take
• Workarounds:– Binary Decision Diagrams (BDDs)– Abstractions
The Model Checking Problem
Complexity is exponential on the number of states
State space explosion problem
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Abstraction
• Group states together– Eg., localization: neglect some state variables
(make them invisible)
• Eliminate details irrelevant to the property
• Obtain smaller models sufficient to verify the property using traditional model checking tools
• Disadvantage:— Loss of Precision— False positives/negatives
Spurious counterexamples
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Counterexample-Guided Abstraction-Refinement (CEGAR)
Check Counterexample
Obtain Refinement Cue
Model CheckBuild New Abstract Model
M’M
No Bug
Pass
Fail
BugReal CESpurious CE
SATILPMachine learning AQC 48
Summary• DW1 is a programmable superconducting quantum adiabatic processor
• It solves a particular type of combinatorial optimization problem
• We have investigated the quantum nature of the device
• We chose a problem for which classical thermalization and quantum annealing predict different statistics
• Experiments agree with quantum annealing prediction suggesting quantum annealing is surprisingly robust against noise
• Working on an experimental test for entanglement
• Benchmarks show promising scaling when compared with classical solvers
• Currently working to bridge the gap between the device and real applications (non-trivial issues to be addressed)