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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Challenges to Practical End-to-end Implementation

• f Quantum Optimization Approaches for

Combinatorial problems

Davide Venturelli, Ph.D. USRA Research Institute for Advanced Computer Science Quantum Artificial Intelligence Laboratory NASA Ames Research Center

davide.venturelli@nasa.gov

Collaborators: Eleanor Rieffel (NASA), Stuart Hadfield (Columbia), Zhihui Wang (USRA),

Immanuel Trummer (Cornell), Bryan O’Gorman (UC Berkeley), Rupak Biswas (NASA), Dominic Marchand (1QBIT), Bibek Pokharel (UCLA)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

The Quantum AI Laboratory @ NASA Ames – and RIACS

Machine Learning: Data Analysis and Data Fusion Air Traffic Management Mission Planning and Scheduling, and Coordination Anomaly Detection and Decision Making QuAIL is the space agency's hub for an experiment to assess the potential of quantum computers to perform calculations that are difficult or impossible using conventional supercomputers.

https://ti.arc.nasa.gov/tech/dash/physics/quail/

RIACS conducts basic and applied research in computer science for the nation’s aeronautics and space-related missions and programs, with the goal to enable a high degree of automation for every aspect of scientific research and engineering.

We are hiring (postdocs, senior researchers)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Computing for Combinatorial Optimization

• Real-world combinatorial optimization is empirically HARD for current methods.

→ It is worth to investigate if disruptive approaches could help.

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Computing for Combinatorial Optimization

• Real-world combinatorial optimization is empirically HARD for current methods.

→ It is worth to investigate if disruptive approaches could help.

• S.o.A. methods to be practical require to be fine-tailored, and industry often

employs suboptimal heuristics without performance guarantee. → It is worth to investigate “general purpose methods” that could deliver some speedup if hybridized or if it is not practical to exploit the domain knowledge.

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Computing for Combinatorial Optimization

• Real-world combinatorial optimization is empirically HARD for current methods.

→ It is worth to investigate if disruptive approaches could help.

• S.o.A. methods to be practical require to be fine-tailored, and industry often

employs suboptimal heuristics without performance guarantee. → It is worth to investigate “general purpose methods” that could deliver some speedup if hybridized or if it is not practical to exploit the domain knowledge.

• Figure of merit could be: speed, solution quality, diversity of solutions

→ The unique sampling properties of quantum methods could be a competitive advantage.

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Computing for Combinatorial Optimization

Hard Constraints + Quality Metric

• Real-world combinatorial optimization is empirically HARD for current methods.

→ It is worth to investigate if disruptive approaches could help.

• S.o.A. methods to be practical require to be fine-tailored, and industry often

employs suboptimal heuristics without performance guarantee. → It is worth to investigate “general purpose methods” that could deliver some speedup if hybridized or if it is not practical to exploit the domain knowledge.

• Figure of merit could be: speed, solution quality, diversity of solutions

→ The unique sampling properties of quantum methods could be a competitive advantage.

• Devised quantum methods that are “quick” (shallow circuits or analog) and

“dirty” (not explicitly relying on coherence as fundamental working mechanism, but speedup potential not clear). → They can be tested, solving the chicken-and-egg paradox of quantum computing.

They define the rules

• f the game, the

“feasible subspace” 3

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Computing for Combinatorial Optimization Combinatorial Optimization for Quantum Computing

• Embedding efficiently a

problem into a quantum analog annealer

• Finding the optimal

parameters for annealing time and encoding penalties

• Determining the compilation

that maximizes fidelity of computation

• Finding the optimal

parameters for QAOA ansatz

• Calibration of a manufactured

chip…

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Computing for Combinatorial Optimization Combinatorial Optimization for Quantum Computing

• Embedding efficiently a

problem into a quantum analog annealer

• Finding the optimal

parameters for annealing time and encoding penalties

• Determining the compilation

that maximizes fidelity of computation

• Finding the optimal

parameters for QAOA ansatz

• Calibration of a manufactured

chip… Build a Quantum Computer Prototype Effectively Program a Quantum Algorithm Run Quantum Optimization

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Annealing (from Simulated Annealing )

Universities Space Research Association

e−∆E/kT e−∆E/kT e−∆E/kT Physics-inspired Monte-Carlo updates solution

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Universities Space Research Association

e−∆E/kT e−∆E/kT e−∆E/kT Physics-inspired Monte-Carlo updates

E({z}) E({z}) E({z}) Temperature Time

Bit flips activated by temperature solution

Quantum Annealing (from Simulated Annealing )

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Universities Space Research Association

3 Key differences:

1) Superposition of bit-strings (tunneling) 2) Energy landscape changes over time 3) Equilibration and Adiabatic Theorem

Quantum Annealing (from Simulated Annealing )

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Universities Space Research Association

3 Key differences:

1) Superposition of bit-strings (tunneling) 2) Energy landscape changes over time 3) Equilibration and Adiabatic Theorem

Quantum Annealing (from Simulated Annealing )

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Universities Space Research Association

3 Key differences:

1) Superposition of bit-strings (tunneling) 2) Energy landscape changes over time 3) Equilibration and Adiabatic Theorem

E({z},τ=1) {z} E({*}, τ<1) E({*}, τ=0) {z} {z} Time, τ

tunneling

Bit flips activated by tunneling

Quantum Annealing (from Simulated Annealing )

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Universities Space Research Association

3 Key differences:

1) Superposition of bit-strings (tunneling) 2) Energy landscape changes over time 3) Equilibration and Adiabatic Theorem

E({z},τ=1) {z} E({*}, τ<1) E({*}, τ=0) {z} {z} Time, τ

tunneling

Bit flips activated by tunneling

probability

000 001 010 011 111 110 101 100

PSR(τ) =1-ε for sufficiently large τ

Quantum Annealing (from Simulated Annealing )

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Universities Space Research Association

E({z},τ=1) {z} E({*}, τ<1) E({*}, τ=0) {z} {z} Time, τ

tunneling

B(t) (∑ij Jij σz

i σz j + ∑i hi σz i)

+ A(t) ∑i σx

i

σx

i =

σz

i =

Quantum Annealing (à la D-Wave)

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Minimum of ∑ijQij xi xj

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

The Quantum Annealing Testbeds – Analog Devices and Collaboration Opportunities http://www.usra.edu/quantum/rfp

(submit next 15 days or next cutoff February 2018) D-Wave 2000Q™

2048 (8x16x16) qubit “Whistler” 2038 qubits working – 97% yield 6016 J programmable couplers 15 mK Max operating temperature (nominal to be measured) To be measured. Annealing time improved 5x (1µs) Initial programming time improved 20% (9 ms). New anneal features: offset, pause, quench, reverse anneal. 8

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

The Quantum Annealing Testbeds – Analog Devices and Collaboration Opportunities http://www.usra.edu/quantum/rfp

(submit next 15 days or next cutoff February 2018) D-Wave 2000Q™

2048 (8x16x16) qubit “Whistler” 2038 qubits working – 97% yield 6016 J programmable couplers 15 mK Max operating temperature (nominal to be measured) To be measured. Annealing time improved 5x (1µs) Initial programming time improved 20% (9 ms). New anneal features: offset, pause, quench, reverse anneal.

Relaxation and thermalization in action

• V. Smelyanskiy,
• D. Venturelli,
• A. Perdomo-Ortiz et al.
• Phys. Rev. Lett. (2017)

Pause!

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Workflow for problems on quantum annealers

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Instance selection and decomposition

Strategy of attack

1) paradigmatic problems that teach us universal features and techniques (JSP, GC, ART etc..) 2) high-value surrogates of real-world problems (Satcomm, ATM, SIGINT/IMINT etc..) 11

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Instance selection and decomposition

Rieffel, Venturelli, Hen et al. (2014) Wang, O’Gorman, Tran et al. (2017) Importance of small scale hard problems Definition of “critical” Single-Machine-Scheduling instances

Strategy of attack

1) paradigmatic problems that teach us universal features and techniques (JSP, GC, ART etc..) 2) high-value surrogates of real-world problems (Satcomm, ATM, SIGINT/IMINT etc..) 11

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Instance selection and decomposition

Stollenwerk et al. (in preparation)

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• Identified all non-trivial

trajectory intersections by means of a coarse-grained decomposition algorithm n2 complexity

• Eliminated the trivial ones

and kept the structured networks (up to 64 flights)

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Mapping and Compiling (Embedding)

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∑ijQij xi xj

q1 q5 q3 q4 q7 q6

MaxCut 3GraphColoring

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

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Minimum of ∑ijQij xi xj

XA XB

Real physical circuits somewhere

• n the chip

Real magnetic energy coupling the circuits

From QUBO to Embedded QUBO

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

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Minimum of ∑ijQij xi xj

xi={0,1} Qij∈R Qij = 0 if (i,j)∉Ε

Under the conditions

*precision issues

XA XB

Real physical circuits somewhere

• n the chip

Real magnetic energy coupling the circuits

From QUBO to Embedded QUBO

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

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Minimum of ∑ijQij xi xj

xi={0,1} Qij∈R Qij = 0 if (i,j)∉Ε

Under the conditions

*precision issues

XA XB +λ( xA – xA1 )2 +λ( xA1 – xA2 )2

Qij

Real physical circuits somewhere

• n the chip

Real magnetic energy coupling the circuits

From QUBO to Embedded QUBO

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Minimum of ∑ijQij xi xj

Universities Space Research Association

≈ +N2/4

From QUBO to Embedded QUBO

Find_embedding(QUBO)

Cai et al. (2014)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

From QUBO Problem to Embedded QUBO

QUBO HARDWARE ISING Database Virtual Hardware QUBO analysis

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

From QUBO Problem to Embedded QUBO

QUBO HARDWARE ISING Database Virtual Hardware QUBO analysis QUBO HARDWARE ISING Database QUBO analysis Problem ClusterForm Representation Virtual Hardware

Venturelli, Trummer (in preparation) See AQC talk 2017 (video)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Running and Analyzing

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Running and Analyzing

• Most of the work done so far on “native or quasi-native spin-glasses” because of

embedding overhead (see Job, Lidar 2017 for review – spoiler: no speedup but competitive in certain cases)

• But also:
• *Job Shop Scheduling (Venturelli et al. 2015 - ICAPS)
• *Infinite Dimension Spin-Glass (Venturelli et al. 2016 – Phys.Rev.X)
• *Fault Diagnostics (Perdomo-Ortiz et al. 2017 – IOP QST)
• Database Query (Trummer et al. 2016 - VLDB)
• Biclustering (Bottarelli et al. 2017 - ICTPN)
• Portfolio Optimization (Rosenberg 2015 – IEEE JSTSP)
• Air Traffic Management (Stollenwerk 2017)
• …

* Provide comparison

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Metrics and Hopes for Quantum Heuristics

Ronnow et al. (2014) Mandra et al. (2016)

Compare with classical: Ratios of the quantiles, Quantiles of the ratio Compare “time to solution with 99% probability”

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Metrics and Hopes for Quantum Heuristics

f(N)2N → αeβNχ

with f(N)/α ≈ 104 β,χ ≈ ½

This would be a huge deal also theoretically, disproving the “quantum exponential time hypothesis” Ronnow et al. (2014) Mandra et al. (2016)

Compare with classical: Ratios of the quantiles, Quantiles of the ratio Compare “time to solution with 99% probability”

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Metrics and Hopes for Quantum Heuristics

f(N)2N → αeβNχ

with f(N)/α ≈ 104 β,χ ≈ ½

This would be a huge deal also theoretically, disproving the “quantum exponential time hypothesis” Ronnow et al. (2014) Mandra et al. (2016)

Compare with classical: Ratios of the quantiles, Quantiles of the ratio Compare “time to solution with 99% probability” BUT: Parameter Setting? Parallelization? Pre/post processing? Compilation?

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Some early attempts

SK model (also with noise)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Some early attempts

SK model 3-coloring (also with noise) (now seems better by means of annealing time)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Some early attempts

DW2X SK model 3-coloring Fault diagnostics of multiplier circuits (also with noise) (now seems better by means of annealing time) JSP (against complete solvers)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Some early attempts

DW2X SK model 3-coloring Fault diagnostics of multiplier circuits (also with noise) (now seems better by means of annealing time) JSP (against complete solvers) Take home message:

• No evidence of speedup, evidence of competitiveness with single core if tuned

and if the problems are right.

• Huge room for improvement from algorithmical perspective (embeddings,

architecture)

• Huge room for improvement from physics perspective (New features, D-Wave

Pegasus, Google Annealer 2.0, QEO)

• Practically, it seems that D-Wave is able to improve the machine significantly

from generation to generation

• Special purpose techniques: need to find suitable applications that take

advantage of the architecture

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Approximate Optimization

QAOA ≈ Digitized, controlled, optimized (by quantum or classical)

Mixing Phase Separation Mixing Phase Separation

time

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Approximate Optimization

QAOA ≈ Digitized, controlled, optimized (by quantum or classical)

Mixing Phase Separation Mixing Phase Separation

time

• Idea is less than 2 years old, less than 10 papers have been published.
• Formally demonstrated that it can achieve quantum supremacy in sampling.
• Provably outperforms quantum annealing on certain problems.
• Formally demonstrated by optimal control theory that it can be optimal in certain cases.
• Recently demonstrated quadratic speedup on search.
• Inherits most of the merits and drawbacks of quantum annealing.

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

The Quantum Computing Testbeds for NASA (2017)

• Gate Model Universal Prototypes

16 Qubits available on the cloud 8 Qubits available (collaborations) 21 and 40 qubits planned 9 Qubits available (collaborations) 22 Qubits testing (collaborations) 49 Qubits announced [2018] 17 Qubits in testing (proprietary) 10 Qubits in testing (collaborations) 22

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Approximate Optimization

• 1. Design a binary optimization encoding soft constraints

(“phase separation”)

Fahri et al. (2014) Hadfield et al. (2017)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Approximate Optimization

• 1. Design a binary optimization encoding soft constraints

(“phase separation”)

• 2. Design a unitary operator that evolves the states within the hard

constraints (“mixing”)

Fahri et al. (2014) Hadfield et al. (2017)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Approximate Optimization

• 3. Prepare a QAOA state for some parameters
• 1. Design a binary optimization encoding soft constraints

(“phase separation”)

• 2. Design a unitary operator that evolves the states within the hard

constraints (“mixing”)

Fahri et al. (2014) Hadfield et al. (2017)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Approximate Optimization

• 3. Prepare a QAOA state for some parameters
• 4. Measure the state in the computational value and compute the exp. value of C(z)
• 1. Design a binary optimization encoding soft constraints

(“phase separation”)

• 2. Design a unitary operator that evolves the states within the hard

constraints (“mixing”)

Fahri et al. (2014) Hadfield et al. (2017)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Approximate Optimization

• 3. Prepare a QAOA state for some parameters
• 4. Measure the state in the computational value and compute the exp. value of C(z)
• 1. Design a binary optimization encoding soft constraints

(“phase separation”)

• 2. Design a unitary operator that evolves the states within the hard

constraints (“mixing”)

Fahri et al. (2014) Hadfield et al. (2017)

• 5. Change the parameters if they are not proven optimal and repeat 3-4

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Quantum Alternate Operator Ansatz

24

Some initial state respecting:

• It is a superposition of several

solutions in the feasible subspace

• It can be prepared efficiently

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Some unitary respecting:

• Is diagonal in the

computational basis

• The spectrum of HP

encodes the objective function

Quantum Alternate Operator Ansatz

24

Some initial state respecting:

• It is a superposition of several

solutions in the feasible subspace

• It can be prepared efficiently

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Some unitary respecting:

• Preserve the feasible

subspace

• Provide all-to-all nonzero

transitions between all feasible states

• Non-necessarily time

evolution of a local Hamiltonian

Some unitary respecting:

• Is diagonal in the

computational basis

• The spectrum of HP

encodes the objective function

Some initial state respecting:

• It is a superposition of several

solutions in the feasible subspace

• It can be prepared efficiently

“Bang-Bang” control is optimal by means of Pontryagin’s principle (Z.Yang et al. PRX 2017)

Quantum Alternate Operator Ansatz

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Mixing Operators: XY ring

Respects the Hamming Weight constraint

Exp(iHring) is difficult to implement → alternative “approx.” unitary

Hen et al. (2016)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Mixing Operators: XY ring

Respects the Hamming Weight constraint

Exp(iHring) is difficult to implement → alternative “approx.” unitary

Hen et al. (2016)

1 3 5 7 2 4 6 8

∏a∈parityExp(iXaXa+1+YaYa+1)

25

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Mixing Operators: XY ring

Respects the Hamming Weight constraint

Exp(iHring) is difficult to implement → alternative “approx.” unitary

Hen et al. (2016)

1 3 5 7 2 4 6 8

UM=[U1U3U5U7] [U2U4U6U8] [U1U3U5U7] [U2U4U6U8]…

This couples only distance 2; has to be repeated k/2 times

∏a∈parityExp(iXaXa+1+YaYa+1) All these 2-qubit k2/2 gates need to be scheduled

25

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Example: Scheduling (Graph Coloring) Xu,c=1

Node u is colored by c Phase Separator (QUBO objective function) Mixer permutes among 4 colors

Minimizing the number of conflicts by assigning up to k colors

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Example: Scheduling (Max Induced k-colorable subgraph) Xu,c=1

Node u is colored by c

• r uncolored

(c=0) Mixer swaps between uncolored and colored (applied twice for all-to-all transitions)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Example: Scheduling (Max Induced k-colorable subgraph) Xu,c=1

Node u is colored by c

• r uncolored

(c=0) Mixer swaps between uncolored and colored (applied twice for all-to-all transitions)

Finding the largest induced subgraph colorable by k colors

XY

All these gates need to be scheduled

XY x x x x =

Still needs to be compiled to 2 qubit gates 25

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Zoology of Mixers and Phase Separators

In traveling salesman encoding Xvj=1 if city v is visited as jth (partitioned using edge coloring and parity ≈(n-1)n2/4 mixers) (needs to be repeated n(n-1)/2 times for all-to-all)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Zoology of Mixers and Phase Separators

In traveling salesman encoding Xvj=1 if city v is visited as jth (partitioned using edge coloring and parity ≈(n-1)n2/4 mixers) (needs to be repeated n(n-1)/2 times for all-to-all) In single machine scheduling Xjt=1 if job j starts at time t (But if we add release dates then we need controls on the no-overlap constraint)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Zoology of Mixers and Phase Separators

Bitflip mixers

• Maximum Cut
• Max-SAT, Min-SAT, NAE-SAT
• Set Splitting
• MaxE3LIN2

… Controlled Bitflip mixers

• MaxIndependentSet
• MaxClique
• MinVertexCover
• MaxSetPacking
• MinSetCover

… XY mixers

• Max-ColorableSubgraph
• Graph Partitioning
• Maximum Bisection
• Max Vertex k-Cover

… Controlled XY mixers

• Max-k-ColorableInducedSubgraph
• MinGraphColoring
• MinCliqueCover

... Permutation mixers

• TSP
• SMS with various metrics and constraints

… Arxiv:1709.03489

Stuart Hadfield , Zhihui Wang, Bryan O’Gorman, Eleanor G. Rieffel, Davide Venturelli, Rupak Biswas

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Example of compilation: MaxCut

q1 q5 q3 q4 q7 q6

Interaction graph

• btained from

quadratic objective function (MAXCUT)

• Every edge is a gate that needs to be

executed (in arbitrary order)

• The same graph has to be executed

multiple times (p rounds).

• Every qubit has to complete all the gates of

round p before being involved in p+1

Counts the edges in the cut Defines the cut

∑iXi

Mixes the two partitions

UPS=∏<jk>Exp(iβZjZk) UM=∏jExp(iγXj)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Real World Superconducting Architectures

Real world quantum chips are complex and not symmetric!

(From IBM Github README repository)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Real World Superconducting Architectures

Real world quantum chips are complex and not symmetric!

(From IBM Github README repository)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Real World Superconducting Architectures

Real world quantum chips are complex and not symmetric!

(From IBM Github README repository)

Gates are calibrated to have different durations across the chip. Gates are not available everywhere. Crosstalks, Error rates..

IDENTIFYING THE SEQUENCE OF GATES COULD BE SEEN AS A TEMPORAL PLANNING PROBLEM 29

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Real World Superconducting Architectures

Real world quantum chips are complex and not symmetric!

(From IBM Github README repository)

SWAP 11 13 12 16 14 14 10 10 10 13 12 13 11 13 10 10 12 11 16 10 P-S 10 11 10 13 12 12 9 9 9 11 10 11 9 11 9 9 10 10 13 9

=

Plus crosstalk constraints … Surrogate example: Inspired by Rigetti (Sete et al. 2016)

iSWAP and CZ, no crosstalk UPS=∏<jk>Exp(iβZjZk) UM=∏jExp(iγXj)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Example of compilation: MaxCut

n8 n1 n2 n3 n4 n6 n7 n5

q1 q5 q3 q4 q7 q6

Initial assignment qi → ni 1 3 4 5 6 7

Interaction graph

• btained from

quadratic objective function (MAXCUT)

• Every edge is a gate that needs to be

executed (in arbitrary order)

• The same graph has to be executed

multiple times (p rounds).

• Every qubit has to complete all the

gates of round p before being involved in p+1

30

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Example of compilation: MaxCut

n8 n1 n2 n3 n4 n6 n7 n5

q1 q5 q3 q4 q7 q6

Initial assignment qi → ni 1 3 4 5 6 7

Interaction graph

• btained from

quadratic objective function (MAXCUT)

• Every edge is a gate that needs to be

executed (in arbitrary order)

• The same graph has to be executed

multiple times (p rounds).

• Every qubit has to complete all the

gates of round p before being involved in p+1

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Universities Space Research Association

1 3 4 5

q1 q5 q3 q4 q7 q6

Q14

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

1 3 4 5

q1 q5 q3 q4 q7 q6

Q14 Q13

1 3 4 5

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

1 3 4 5

q1 q5 q3 q4 q7 q6

Q14 Q13

1 3 4 5 1 3 4 5

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

1 3 4 5

q1 q5 q3 q4 q7 q6

Q14 Q13 Q15

1 3 4 5 1 3 4 5 3 1 4 5

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

1 3 4 5

q1 q5 q3 q4 q7 q6

Q14 Q13 Q15

1 3 4 5 1 3 4 5 3 1 4 5

All actions of round 1 are completed – qubit can be mixed. Qubit 1 can start participating to round 2.

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

1 3 4 5

q1 q5 q3 q4 q7 q6

Q14 Q13 Q15 Q14 Q13 Q15

1 3 4 5 1 3 4 5 3 1 4 5 3 1 4 5 4 1 3 5 3 1 4 5 3 1 4 5

PS2

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

n8 n1 n2 n3 n4 n6 n7 n5

q1 q5 q4 q6

Example of compilation by TFD P-S(3,7) is fast on n1, n4 P-S(3,7) is slow on n4, n6

q3 q7

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

q1 q5 q4 q6

Example of compilation by TFD

q3 q7

Could be even more complex (calibrations… crosstalks… fidelity…) GOOD PROBLEM FOR PLANNING!

n8 n1 n2 n3 n4 n6 n7 n5

P-S(3,7) is fast on n1, n4 P-S(3,7) is slow on n4, n6

Example of compilation: MaxCut

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Temporal Planning Techniques for Compilation

D.Venturelli, M. Do, E. Rieffel, J. Frank arXiv: 1705.08927 (IJCAI 2017) To appear in QST special issue 32

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Temporal Planning Techniques for Compilation

N=21 N=8

p=2 p=2 p=2

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Temporal Planning Techniques for Compilation

LPG SGPlan TFD CPT* POPF

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Temporal Planning Techniques for Compilation

LPG SGPlan TFD CPT* POPF

• Scaling up & solution quality improvement:
• Separate multiple PS-mixing steps
• Using classical sequential planners + post-processing
• Compare with other methods (i.e. CP – Booth et al. to be submitted to ICAPS18)
• Extend the problem scope:
• Also solve the qubit initial assignment problem
• Add composite gates swap+P-S; swap+Mix in the search
• Handle quantum teleport and crosstalk
• Objectives beyond makespan – fidelity/performance (for some particular circuit)
• Handle more difficult compilations with different graphs to be scheduled (general

QAOA for combinatorial problems – also multiqubit)

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

The rise of Compilers for Quantum Computing Devices

Quipper— Functional language Open source. Scaffold— C-like language Open source. Liquid— Functional language with a highly optimized compiler written in F#. Closed source. Project Q— Language and Python-based system. Open source. QUIL— A new language with an emphasis on the classical-quantum interface. Open source. Google’s—(to be launched soon)

Review Fred Chong Nature Comm. (2017) From Haner et al (2016) From McCaskey et al (2017) 35

Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Conclusions

Take home message:

• QAOA can beat quantum annealing but it is more resource-hungry.
• QAOA might well take an important role in the “post quantum supremacy

chasm” and it is interesting to start doing resource consumption calculations for sanity checks.

• Compiling quantum programs is now a business ! Ideas and framework from

CS can help. Only now we know how quantum computing will unfold in the next decade and a lot of early theoretical analysis need to be relooked at.

• Performance guarantees or estimation in optimization are still completely

missing.

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Challenges to Practical End-to-end Implementation of Quantum Optimization Approaches for Combinatorial problems QTML Workshop – Verona, Nov 6 (2017) - Davide Venturelli – davide.venturelli@nasa.gov

Thanks

Davide Venturelli, Ph.D. USRA Research Institute for Advanced Computer Science Quantum Artificial Intelligence Laboratory NASA Ames Research Center

davide.venturelli@nasa.gov

Collaborators: Eleanor Rieffel (NASA), Stuart Hadfield (Columbia), Zhihui Wang (USRA),

Immanuel Trummer (Cornell), Bryan O’Gorman (UC Berkeley), Rupak Biswas (NASA), Dominic Marchand (1QBIT), Bibek Pokharel (UCLA)

https://ti.arc.nasa.gov/tech/dash/physics/quail/ http://www.usra.edu/quantum/rfp

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