quantumcomputing’ infinance...financial modeling esmangnumber’ of’soluons discrete sampling...

Quantum Computing in Finance

Colin P. Williams D-‐Wave Systems Inc.

© 2015 D-‐Wave Systems Inc. All Rights Reserved. Proprietary & ConfidenDal 2

Overview

•  Company background •  Quantum compuDng & why it maJers •  Product (D-‐Wave 2XTM) •  Performance •  Programming •  ApplicaDons


Company Background

Founded in 1999 began surveying field of QC, building IP porSolio, selected “quantum annealing” ~2004

Raised over $176M in venture funding since incepDon; soZware

ecosystem forming; see copy cat quantum effort

appearing

Business model quantum computer

system sales, professional services, and quantum

cloud offering

100+ US patents granted; over 80+ scienDfic papers published; ranked 4th in “patent power” by IEEE; in “Top 50 Smartest Companies” by MIT Technology Review

Premier First Customers


What is Quantum Computing?


What are Quantum Computers?

• Computers that harness quantum physical phenomena not available to convenDonal computers

Quantum Processor


SuperposiDon

Entanglement

Quantum Tunneling

Quantum Effects


How our Quantum Computer Works

•  Cast problem as a energy landscape s.t. opDmal soluDon is locaDon of lowest point

•  Classical algorithms can only walk over this landscape

•  Quantum annealing uses quantum effects to go through the hills

© 2015 D-‐Wave Systems Inc. All Rights Reserved 7


Why Quantum Computing Matters

Most important problems

Time to SoluDon

Problem Complexity / # of Variables

QUANTUM

CLASSICAL


Our Product


D-‐Wave 2XTM System Overview


1,000-‐Qubit “Washington” Processor


Our Superconducting Flux Qubits


Processor Architecture: Network of Binary Units


Wiring layout •  12×12 array of 8-‐qubit unit cells •  Within each unit cell each verDcal qubit is coupled to each horizontal qubit

•  VerDcal (horizontal) qubit coupled to corresponding qubit in verDcal (horizontal) neighboring cells

•  Non-‐planarity of interconnect network makes the problem of finding the lowest energy state of the qubits NP-‐hard

•  NP-‐Hardness guarantees you can map many pracDcal problems to the architecture

Processor interconnect topology ConnecDvity within a unit cell

Physical Layout Physical Unit Cell

Logical Layout Logical Unit Cell


Programming


How do you Program the D-‐Wave 2X?

ComputaDonal Problem to Solve

Map it to an Equivalent Ising Problem

Run Quantum Annealing

Read Out a Spin-‐configuraDon having Low Energy

Load Ising Problem in Quantum Processor Graph

Map Spin-‐ConfiguraDon to Equivalent OpDmal, or Near-‐OpDmal, Bit String

Store Bit-‐String SoluDon & Repeat

Retain all SoluDons (SAMPLING)

Retain Best SoluDon (OPTIMIZATION)

Local Biases Couplings

Goal: Find a configuraDon of qubits that minimize or nearly minimize your objecDve funcDon


Applications


Graph Coloring

Factoring

Diagnosis

Constraint SaDsfacDon

Monte Carlo

Financial Modeling

EsSmaSng Number of SoluSons

Discrete Sampling

Complexity Scaling

Error CorrecSon

Impact of Interconnect Topology

Quantum Research

Discrete OpDmizaDon

Scheduling LogisScs

Planning

Machine Learning

Structured PredicSon

Boltzmann Machines

Applications

OpDmizaDon Sampling

Deep Learning


Performance


D-‐Wave 2XTM Optimization Results

•  RANr: set all hi = 0; set Jij ∈ [−r, r] \ {0}

ttotal = tprogram + R (tanneal + treadout)


D-‐Wave 2XTM Sampling Results Energies of Sam

ples Returne

d

Quantum Classical Fat Tree #1

Classical Fat Tree #2

Classical Selby

Classical SA #1

Classical SA #2

Best sample so far


Increasing Performance at Near Constant Power

Source: hJp://www.extremetech.com/compuDng/116561-‐the-‐death-‐of-‐cpu-‐scaling-‐from-‐one-‐core-‐to-‐many-‐and-‐why-‐were-‐sDll-‐stuck

D-‐Wave Processor Power, ~0.1 μW

Rainier

Vesuvius

Washington

D-‐Wave System Power, ~15.5kW

Classical Power

Classical Performance

D-‐Wave Processor Performance


Technology is Scaling Up Quickly


•  N qubits have 2N configuraDons •  Processed in quantum parallel •  2300 > no. of parDcles in our Universe


Conclusions

•  We offer 1st commercial quantum computer

•  Best suited for discrete opDmizaDon, sampling, A.I., machine learning, constraint saDsfacDon, deep learning

•  Current customers moDvated by potenDal for gaining compeDDve advantage by using quantum compuDng & acquiring IP on low-‐hanging fruit

•  No roadblocks to larger processors


Thank you! Email: [email protected]

quantumcomputing’ infinance...financial modeling esmangnumber’ of’soluons discrete sampling...

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