qc-programming-101.pdf

Introduction to
Quantum Programming
Copyright © D-Wave Systems Inc.
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D-Wave At a Glance
MARKET LEADER
STRONG CUSTOMER BASE
WORLD-CLASS INVESTORS
THOUGHT LEADERSHIP
5,000+ qubit system 250+ early applications
First real-time quantum
cloud platform
Top five quantum
patent portfolio
globally
20% PhDs
200+ U.S. patents
granted and 100+
pending worldwide
Over 100 scientific
papers published
Volkswagen
Johnson & Johnson
FOUNDED: 1999
HQ: Vancouver, B.C.
EMPLOYEES: 180+ (70% R&D)
OFFERINGS: Quantum computing system,
hybrid solvers, platform-as-a-service, professional
services, training and enablement
EXAMPLE USE CASES: Portfolio optimization,
supply chain optimization, traffic routing, bin
packing, protein design, patient trials, machine
learning model training

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Cloud access to the D-Wave quantum
computer & quantum hybrid solvers
99% up-time
with real time access
QUANTUM COMPUTERS CLOUD-SERVICE DEVELOPER TOOLS PROFESSIONAL SERVICES
5 generations of
annealing quantum computers
Currently
5000+ Qubits
Open-source developer tools
built in Python
Available through Leap IDE
or local download
Customer onboard to
quantum computing applications
4 Phase
engagement model
Comprehensive, Full-Stack, Commercial Quantum Platform

Constrained quadratic model solvers
• More native representation of problem
• Unlocks larger application problems
• Up to 100,000 constraints
• Inequality & equality constraints
Binary quadratic model solvers
• Up to 1,000,000 variables
• Enables enterprise-scale problem solving
• Accepts problems with binary variables
Powerful Hybrid Solvers
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SOLVERS THAT
RUN PROBLEMS ON A
COMBINATION OF QUANTUM
AND CLASSICAL RESOURCES
BUSINESS APPLICATION
HYBRID
Classical Computing

SEAMLESS AND INTEGRATED EXPERIENCE
• More productivity, efficiency, and customization
• UI/UX improvements
• Run Jupyter notebooks right from IDE
• Run Docker right from within the workspace
• Integrated docs and user guide right from the editor
ON LATEST GREATEST, MODERN INFRASTRUCTURE
• Hosted on latest Kubernetes
• Faster access to new features and bug fixes
ALL NEW EDITOR FOR LIGHTNING-FAST CODING
• Full power of Visual Studio Code at your fingertips
• Third-party extension support for extensions and customizations
Leap IDE: Lightening Fast Cloud Developer Environment

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Building a
Constrained
Quadratic Model
(CQM)

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Example:
Delivery Truck Packing

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In North America there are over 100 standard
box sizes that consumer goods are shipped in.
Optimally loading delivery trucks with packages,
especially when additional considerations such
as priority shipping status, order date and
weight/size limits of the trucks are considered is
a difficult combinatorial optimization problem.
Delivery Truck Packing Problem

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Let’s consider a simplified version of this
problem where we have
• 1 truck
• 1 package size
• Up to 100 packages
We need to consider
• Priority shipping status
• Days since the order was placed
• The delivery truck’s weight capacity
• The delivery truck’s size capacity
Delivery Truck Packing Problem

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1. Write out the objective and constraints in your problem domain.
2. Define the binary, integer, and/or continuous variables for your problem.
3. Convert the objective and constraints to math statements with binary, integer,
and/or continuous variables.
4. Build the CQM model in Ocean from the individual objectives and constraints.
CQM Development Process

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Objectives:
1. Maximize the number of packages selected with priority shipping
2. Minimize the number of days the packages are in transit
Constraints:
1. Do not exceed the maximum number of packages that can fit on the
truck (100)
2. Do not exceed the maximum weight capacity of the truck (3000 lbs)
1. Objective and Constraints

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We need to choose which packages to load onto the delivery
truck, so we’ll use binary variables.
𝑥! = #
1
0
if package i is selected
if package i is not selected
2. Define the variables

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Objective #1 – Maximize priority shipping:
Maximize the number of packages selected with a high priority shipping status
min − %
!"𝟎
$
𝑝!𝑥!
3. Define the objective/s
𝑝!= priority of package 𝑖
𝑥!= decision variable for package 𝑖

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Objective #2 – Minimize wait time:
Minimize the number of days customers need to wait for their packages
min − %
!"%
$
𝑑!𝑥!
3. Define the objective/s
𝑑! = number of days since package 𝑖 was ordered
𝑥! = decision variable for package 𝑖

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Constraint #1 – Maximum parcels:
Select the maximum number of packages that can fit inside the delivery truck
!
𝒊"𝟎
𝑵
𝑥% = 𝑃
3. Define the constraints
𝑥! = decision variable for package 𝑖
𝑃 = maximum number of packages that can fit on the delivery truck

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Unconstrained: Equality Constraints
%
!"%
$&'
𝑥! = 𝑃
%
!"%
$&'
𝑥! − 𝑃
(
1 − 𝑃 𝑥! + 𝑥" + ⋯ + 𝑥# + 2(𝑥!𝑥" + 𝑥! 𝑥$ + 𝑥#%"
𝑥#) + 𝑃$
CQM: Equality Constraints
%
!"%
$&'
𝑥! = 𝑃
Direct implementation:

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Constraint #2 – Maximum capacity:
The weight of all the packages selected cannot exceed the maximum weight of
the delivery truck
!
%"&
'
𝑤%𝑥% ≤ 𝑊
𝑤& = weight of package 𝑖
𝑥' = decision variable for package 𝑖
𝑊 = maximum weight the delivery truck can hold

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Constraint #2 – Maximum capacity:
The weight of all the packages selected cannot exceed the maximum weight of
the delivery truck
!
%"&
'
𝑤%𝑥% ≤ 𝑊

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In Ocean,
1. Instantiate a ConstrainedQuadraticModel
2. Add the objectives to the model
3. Add the constraints to the model
4. Build the CQM

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Instantiate a ConstrainedQuadraticModel
4. Build the CQM

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Create the variables
4. Build the CQM

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Add the objective/s to the CQM
4. Build the CQM

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Add the constraints to the CQM
4. Build the CQM

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Tunable parameter: Time Limit
5. Solve and interpret results

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Sampleset for a CQM
Variable values
Energy of the
objective
function
Constraint
satisfaction
array
Solution
feasibility

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Get the first feasible sample
*Samplesets are sorted by energy by default, whereby the lowest energy samples are first

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Demo

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Recommended Training: Quantum Programming 101 – Core
With this comprehensive, hands-on, and expert-led training you can quickly
put theory into practice with real-world quantum applications.
This 5-day course will enable you to ’think quantum,’ so that you can:
• Identify Quantum Use Cases: Identify quantum use cases cross different verticals
and application areas
• Formulate Quantum Problems: Break down optimization problems into distinct
objectives and constraints
• Write QUBOs: Formulate optimization problems as quadratic models
• Start Coding: Write an Ocean program to run on D-Wave’s quantum computer and
hybrid solver
• Get Solutions: Analyze and interpret results given by D-Wave’s solvers
• Learn the Stack: Understand how D-Wave software tools interact with the hardware

qc-programming-101.pdf

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