Scott N. Genin, PhD Head of Materials Discovery [email protected] www.otilumionics.com

Quantum Chemistry on Quantum Annealers March 2019

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 1 What We Do Materials Discovery

Developing advanced materials to solve large scale industrial problems for displays + lighting

Audi A8

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 3 Organic Light Emitting Diode (OLED) Light from organic pigments sandwiched between electrodes

Organic Pigments

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 3 Closed Loop Development with Customer Feedback In-house end-to-end testing from materials discovery up to production testing

Materials Discovery

Tool Builders Detailed Specifications Production Quantum Testing Simulations

MP Ready Materials Panel Makers

Validation Synthesis

OEMs

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 4 Our Materials Discovery Platform Advanced computation + simulation + ML/AI

Properties Structure • Vapor pressure • Optical constants • Electronic structure • Film forming • Crystallinity • Etc.

CPU GPU QPU (Quantum Processing Unit)

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 5 Example: Aerelight for Print™ Flexible OLED module for print + packaging

Materials Discovery

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 6 Example: ConducTorr™ for Transparent Display Automotive Demonstration

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 7 Quantum Chemistry Why do we care?

Understanding and prediction of the Structure -> Property relationship

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 8 Overview of Quantum Chemistry on a Quantum Computer

4 , 78 , , 9 = ∑34 53 64 63 + ∑3478 534 6768 6463 Generate a fermionic Hamiltonian

9 = 2 ;)3 Transform into spin basis (function of Pauli Operators)

, |ψ $ ⟩ = exp *) − *) |ψ-⟩ Construct Ansatz (UCC)

*) = *). + *)0 + ⋯

) 4 , ) 78 , , *. = 2 53 64 63 *0 = 2 534 6768 6463 34 3478

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 9 Variational Quantum Eigensolver

! % % + " = $ &' Where &' = ∏ )* , n = {x,y,z} & j = qubit index

% ,- ≤ $ Ψ' &' Ψ' Where Ψ is wavefunction of the ith Pauli word

With serial processing, time scales linearly with number of Pauli words

BK transformation generates O(N4) Pauli words

*Peruzzo et al. Nat. Comm. 5 (2014)

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 10 Hidden Consequences

Is this “kink” a hardware problem or theory problem?

Kandala et al. (2017) Nature 549, 242-246

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 11 Broken Symmetry Transition – H2 on QPU

Broken symmetry GHF between 1.5 A – 1.6 A, as it transitions from singlet to triplet

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 12 Unitary Coupled Cluster

Quantum computers cannot directly encode

0 = exp(?/ + ?& + ⋯ )

Trotterized

5 5 7 0 ≈ exp 6 exp 8 … : ≥ 1 7 7

Even simplest fermionic operators are lengthy combination of Pauli terms

# # # # !"!$!%!& − !&!%!$!" ) → + , + . + . , − , + − . , . + − , + . − . , . + . + + , . + . + . , . 8 & $ / & % $ & $ / & % $ & $ " / & % $ " & $ " / & % $ " Lengthy combinations of Pauli terms increases quantum circuit depth

LiH/STO-6G, C. Hempel et al. Phys. Rev. X 8, 031022 (2018)

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 13 Qubit Coupled Cluster Method

Ψ ", $ = '& " |$⟩ General form of qubit methods

, 0"+21+ '& " = * exp 21 is Pauli word entanglers 2 + 21 = 89:;

Variational search 4 ", $ ≤ $ ' " 67&' " $ for ground state

https://pubs.acs.org/doi/abs/10.1021/acs.jctc.8b00932

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 14 PES Curve for LiH & H2O

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 15 Quantum Chemistry on Quantum Annealers

Universal Gate Quantum Annealer

Annealer is suitable for solving binary optimization problems (not applicable for quantum chemistry)

IBM Q (20 qubits) D-Wave 2000Q (2048 qubits)

We have developed a quantum solver for quantum chemistry on a quantum annealer 4/9/19 OTI Lumionics Inc. © 2019 - Confidential 16 Qubit Transformation and Domain Folding

& ! ∈ [0, ) * * ' ) ∈ 0, * +, [0, ) . ∈ 0, * +, [0, ) 2 2

/0 → cos !0 50 → cos )0 sin !0 80 → sin )0 sin !0

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 17 Solution on Quantum Annealer

Transform Pauli Generate J and Anneal words to Ising H Couplings Solution model

Classically Optimize

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 18 PES Curves Solved on Quantum Annealer

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 19 Benefit of the use of the annealer

4/9/19 OTI Lumionics Inc. © 2019 - Confidential 20 We are here! Where Are We Today 10,000 qubits Started to test industrial problems

Current state-of-the-art Industrial relevant (vinyl polymer) quantum simulations size materials 500 qubits (IBM, Nature 549, 242–246) 264 qubits ✓ 128 qubits ✓ (Alq3) 70 qubits ✓ (BCP) 14 qubits ✓ (LiQ)

# of qubits for universal gate universal # of qubits for 7 qubits ✓ (phenyl) (H2O) (BeH✓2)

# of electrons We have demonstrated industrial relevant size simulations on quantum hardware 4/9/19 OTI Lumionics Inc. © 2019 - Confidential 21