Quantum Computing at IBM

Home , Qiskit, Quantum bus, Transmon

Ivano Tavernelli

IBM Research - Zurich

Quantum Computing for High Energy Physics CERN - Geneva November 5-6, 2018 Outline

Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications

Quantum chemistry Many-body physics Optimization and HEP Outline

Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications

Quantum chemistry Many-body physics Optimization and HEP Future of computing Alternative (co-existing) architectures:

1958 1971 2014 next generation systems (3D/hybrid)

First integrated circuit Moore’s Law is Born IBM P8 Processor ~ 650 mm2 2 Size ~1cm Intel 4004 22 nm feature size, 16 cores 2 Transistors 2,300 transistors > 4.2 Billion Transistors neuromorphic (cognitive)

quantum computing

Ivano Tavernelli - ita@zurich.ibm.com Types of Quantum Computing Fault-tolerant Universal Quantum Annealing Approximate NISQ-Comp. Q-Comp.

Optimization Problems Simulation of Quantum Systems, Execution of Arbitrary Quantum •Machine learning Optimization Algorithms •Fault analysis • Material discovery • Algebraic algorithms •Resource optimization • Quantum chemistry (machine learning, cryptography,…) • etc… • Optimization • Combinatorial optimization (logistics, time scheduling,…) • Digital simulation of quantum systems • Machine Learning

Surface Code: Error correction in a Quantum Computer

Many ‘noisy’ qubits can be built; Hybrid quantum-classical approach; Proven quantum speedup; large problem class in optimization; already 50-100 “good” physical qubits error correction requires significant qubit amount of quantum speedup unclear could provide quantum speedup. overhead.

Ivano Tavernelli - [email protected] Types of Quantum Computing Fault-tolerant Universal Quantum Annealing Approximate Q-Comp. Q-Comp.

Surface Code: Error correction in a Quantum Computer

Ivano Tavernelli - [email protected] Hard or memory intensive problems and quantum speedups Quantum Factoring computing may provide a “Hard” Problems For classical computing (NP) new path to Possible with quantum solve some of computing the hardest or Material, 13x7=? Chemistry most memory 937x947=? 91=? x ? Machine 887339 = ? x ? Learning intensive problems in business and Optimization science. Simulating Quantum Mechanics

Quantum Computing and IBM Q: An Introduction #IBMQ Outline

Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications

Quantum chemistry Many-body physics Optimization and HEP IBM: Superconducting Qubit Processor

Superconducting qubit (transmon): § quantum information carrier § nearly dissipationless → T1, T2 ~ 70 µs lifetime, 50MHz clock speed

Microwave resonator as: § read-out of qubit states § quantum bus § noise filter

Ivano Tavernelli - [email protected] Inside an IBM Q quantum 40K computing system 3K Microwave electronics Refrigerator to cool qubits to 10 - 15 0.9K mK with a mixture of 3He and 4He 0.1K

0.015K

PCB with the qubit chip Chip with at 15 mK protected from superconducting the environment by qubits and resonators multiple shields IBM qubit processor architectures

IBM Q experience (publicly accessible) 16 Qubits (2017) 5 Qubits (2016)

IBM Q commercial 20 Qubits 50 Qubit architecture Package

Latticed arrangement for scaling The power of quantum computing is more than the number of qubits

Quantum Volume depends upon

Number of physical QBs

Connectivity among QBs 25 Available hardware gate set 10,000 Error and decoherence of gates 40,000 Number of parallel operations Outline

Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications

Quantum chemistry Many-body physics Optimization and HEP IBM released the IBM Q Experience in 2016

In May 2016, IBM made a quantum computing platform available via the IBM Cloud, giving students, scientists and enthusiasts hands-on access to run algorithms and experiments

Quantum Computing and IBM Q: An Introduction #IBMQ IBM released the IBM Q Experience in 2016

QX is a fantastic tool for teaching.

Proving Bell’s inequality using IBM QX is a few minutes task.

With QX you have access to a ‘quantum laboratory’ from home.

Test simple quantum algorithms without the need to learn any programming language.

… but you may need more …. Quantum Computing and IBM Q: An Introduction. The IBM Q Experience has seen extraordinary adoption First quantum computer on the cloud > 100,000 users All 7 continents > 6.5 Million experiments run > 120 papers > 1500 colleges and universities, 300 high schools, 300 private institutions

Quantum Computing and IBM Q: An Introduction #IBMQ IBM Q Experience executions on real quantum computers (not simulations) May 11, 2018

state characterization, error mitigation, optimal control classical simulation of quantum circuits

core programming tools and API to hardware

Panagiotis Barkoutsos - [email protected] QISKit: Terra

Panagiotis Barkoutsos - [email protected] QISKit: Aqua

Panagiotis Barkoutsos - [email protected] Available for free: https://quantumexperience.ng.bluemix.net/qx/editor

IBM QX Devices QISKit: Basic workflow Quantum Program Quantum and Classical Registers At the highest level, quantum programming in QISKit is broken up into three parts:

1. Building quantum circuits Quantum Circuits 2. Compiling quantum circuits to run on a specific backend

3. Executing quantum circuits on a backend and analyzing results Backend Directory

Important: Step 2 (compiling) can be done automatically so that a basic user only needs to deal with steps 1 and 3.

Execution Results State Counts 00000 439 00011 561

Panagiotis Barkoutsos - [email protected] QISKit: Basic workflow Quantum Program Quantum and Classical Registers At the highest level, quantum programming in QISKit is broken up into three parts:

Quantum Circuits

Backend Directory

Execution Results State Counts 00000 439 00011 561

Panagiotis Barkoutsos - [email protected] Qiskit Aqua Chemistry Example

Panagiotis Barkoutsos - [email protected] Outline

Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications

Quantum chemistry Many-body physics Classical optimization and HEP Quantum Chemistry & Physics International Journal of Theoretical Physics, VoL 21, Nos. 6/7, 1982

“I'm not happy with all the Simulating Physics with Computers analyses that go with just the Richard P. Feynman classical theory, because nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical …”

Ivano Tavernelli - [email protected] Possible application areas for quantum computing

We believe the following areas might be useful to explore for the early applications of quantum computing: Chemistry Material design, oil and gas, drug discovery Artificial Intelligence

Classification, machine learning, linear algebra Financial Services

Asset pricing, risk analysis, rare event simulation

Quantum Computing and IBM Q: An Introduction #IBMQ Quantum chemistry: Where is it a challenge? molecular structure

Solving interacting fermionic problems is at the core of most challenges in computational physics and high-performance computing: reaction rates 1 N Nel Nnu Z Nel,Nel 1 H r2 A el = X i X X + X 2 riA rij i=1 i=1 A=1 i=1,j>i

Full CI (exact): Classical !(exp(&)) reaction pathways Quantum !(&()

Sign problem: Monte-Carlo simulations of fermions are NP- hard [Troyer &Wiese, PRL 170201 (2015)]

Ivano Tavernelli - [email protected] Quantum chemistry

Basis set orbitals 1 (HF) for the Hˆ = h aˆ† aˆ + h aˆ† aˆ†aˆ aˆ generation of the elec X pq p q 2 X pqrs p q r s Hamiltonian in pq pqrs second quantization

∞ ⊗n Fν (H)=M Sν H n=0 = C ⊕ H ⊕ (Sν (H ⊗ H)) ⊕ (Sν (H ⊗ H ⊗ H)) ⊕ ...

|Ψiν = |Ψ0iν |Ψ1iν |Ψ2iν ... Fock space with blocks with = a0|0ia1|ψ1i aij|ψ2i, ψ2jiν ... X N=0,1,2,3,4 ij particles 1 |ψ2 , ψ2 iν = (|ψ2 i⌦|ψ2 i + ν |ψ2 i⌦|ψ2 i) 2 Sν (H ⌦ H) i j 2 i j j i

Ivano Tavernelli - [email protected] Quantum chemistry Electrons and qubits fulfill different statistics:

a ,a =0, a†,a† =0, a ,a† = δ 1 Fermions: { i i} { i i } { i i } i,j ˆ † † † H = h aˆ aˆ + h aˆ aˆ aˆ aˆ σ , σ , σ†, σ† , σ , σ† δ elec X pq p q 2 X pqrs p q r s Spins: [ i i]=0 [ i i ]=0 [ i j ]= i,j pq pqrs

The Jordan--Wigner is the most commonly used mapping in ∞ the context of electronic-structure Hamiltonians: ⊗n Fν (H)=M Sν H j−1 a σz σx iσy n=0 j = ⊗ i ⊗ j + j i=1 = C ⊕ H ⊕ (Sν (H ⊗ H)) ⊕ (Sν (H ⊗ H ⊗ H)) ⊕ ... j−1 a† = σz σx iσy j ⊗ i ⊗ j − j i=1

|Ψiν = |Ψ0iν |Ψ1iν |Ψ2iν ... The terms in the Hamiltonian transform as: = a0 0 a1 ψ1 a ψ2 , ψ2 ν ... h a† a†a a h a†a†a a | i | iX ij| i ji pqrs p q r s + srqp s r q p ij

σxσxσxσx − σxσxσyσy σxσyσxσy s r q p s r q p + s r q p + 1 < (hpqrs) +σyσxσxσy + σyσxσyσx − σyσyσxσx+ |ψ2i , ψ2jiν = (|ψ2ii⌦|ψ2ji + ν |ψ2ji⌦|ψ2ii) 2 Sν (H ⌦ H) 8 s r q p s r q p s r q p r 1 p 1 0 0 +σxσyσyσx + σyσyσyσy 1 1 2 σz σz s r q p s r q p k k σyσxσxσx σxσyσxσx − σxσxσyσx 0 1 B @ s r q p + s r q p s r q p +A C k=s+1 ! k=q+1 B =(h ) C O O B+ pqrs −σxσyσyσy − σyσxσyσy + σyσyσxσy+ C @ A B 8 0 s r q p s r q p s r q p 1C B +σyσyσxσy + σyσyσyσx C B s r q p s r q p C Ivano Tavernelli - [email protected] @ @ AA Quantum chemistry – The quantum algorithm The quantum-classical approach: Variational Quantum Eigensolver

Ivano Tavernelli - [email protected] Trial Wavefunctions

Variational Principle

Heuristic Ansatz

D−times z }| { ~ D ~ 1 ~ 0 ~ ===== |Ψ(✓)i = Uˆ (✓)Uˆent ...Uˆ (✓)Uˆent Uˆ (✓)|Φ0i ====

−−− 10 00 10 00    θ iθ2 θ  θ −i θ −−−− θ θ 0 cos 1 e sin 1−−−0 U θ 0 cos 2 sin 2 0 U1,ex( 1, 2)= −iθ2 2,ex( )= 0 e sin θ1 − cos θ1 0 0 −i sin 2θ cos 2θ 0     00 01 00 01

UCCSD Ansatz ~ Tˆ ✓~ −Tˆ† ✓~ |Ψ(✓)i = e ( ) ( )|Φ i X 0 − ~ m † ~ 1 m,n † † −Tˆ (✓)= ✓ aˆ aˆ Tˆ2(✓)= ✓ aˆ aˆ aˆjaˆi− 1 X i m i 2 X i,j n m i;m i,j;m,n

Ivano TavernelliX - [email protected] Quantum chemistry – the VQE approach Ground state-energy of simple molecules

!": 2 qubits #$!: 4 qubits %&!": 6 qubits 5 Pauli terms, 2 sets 100 Pauli terms, 25 sets 144 Pauli terms, 36 sets

[A. Kandala et al. Nature 549, 242-246, 2017] Ivano Tavernelli - [email protected] Quantum chemistry – the VQE approach with error corr. Ground state-energy of simple molecules

Ivano Tavernelli - [email protected] Quantum chemistry Excited state energies

Interaction of light arXiv:1809.05057 with matter:

• Photocatalysis • Artificial Photochemistry of H2 photosynthesis • Light harvesting

1 N Nel Nnu Z Nel,Nel 1 H r2 A el = X i X X + X 2 riA rij i=1 i=1 A=1 i=1,j>i

Full CI (exact): Classical !(exp(&)) Quantum !(&()

Ivano Tavernelli - [email protected] Quantum chemistry – Recent and Medium term developments Example: excited state energies of 2 and 3 atomic systems

Will come soon

Ivano Tavernelli - [email protected] Hubbard model VQE entanglers for ground state calculations

† † HHub = −t c c σ + c c σ + U n n X ⇣ jσ i iσ j ⌘ X i" i# hi,ji,σ i t : hopping term U :in-siterepulsiveterm hi, ji : adjacent sites

J. Hubbard, Proc. Roy. Soc. London, A266, 238 (1963 Will come soon Study physical properties with a quantum algorithm:

1. Ground state with VQE 2. Time-dependent properties using time-propagation 3. Excited states and dynamics 4. Phase transitions and statistical physics

Ivano Tavernelli - [email protected] Simulation of molecular magnetic systems

Measuring the spin-spin time-dependent correlation function

$% * % !"# & = ⟨)" &)# ⟩

scales exponentially with the number of sites.

[E. M.Pineda et al., Chemical Science, 2017, 8, 1178] Ivano Tavernelli - [email protected] Simulation of molecular magnetic systems

Measuring the spin-spin time-dependent correlation function

$% * % !"# & = ⟨)" &)# ⟩

scales exponentially with the number of sites.

Quantifying entanglement. (a-c) Inelastic neutron scattering spectra as a function of the normalized transferred for three different 2 spin system with decreasing entanglement. (d-f) Corresponding inelastic [E. M.Pineda et al., Chemical Science, 2017, 8, 1178] neutron scattering signals integrated over Qz. Ivano Tavernelli - [email protected] Outline

Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications

Quantum chemistry Many-body physics Optimization and HEP Recent Results by IBM Research

Support vectors arXiv:1804.11326

Possible applications: - Customer segmentation - Image classification - Fraud detection

Maximize the margin

Hyperplane Recent Results by IBM Research

The data may not be linearly separable arXiv:1804.11326

Possible applications: Lift to higher - Customer segmentation dimension - Image classification - Fraud detection

Support Quantum Support Vector Machines (SVM) may offer vectors performance advantages to classical SVMs by using kernels that cannot be computed efficiently classically

! Demonstrated on real quantum device 0 Recent Results by IBM Research

Example training and test set for the Kernel method:

Trained 3 sets of data (20 pts/label) and performed 20 classifications/label per trained set. trial step (c)

kernel method variational method Success [100%] Success

! = +1 training data ! = −1 test data success classification support vectors misclassi6ied test data variational circuit depth …. and high energy physics

Classification (machine learning and SVM) Select/identify relevant LHC events (talk of Wen Guan) Reconstruction of tracks – jets tracking

Quantum Computing Time-evolution: lattice gauge theory (Schwinger’s model and beyond)

Quantum Minimization VQE optimization in lattice gauge theory

E.A. Martinez et al., nature, 534, 516 (2016)

Ivano Tavernelli - [email protected] The Future

Quantum Computing and IBM Q: An Introduction #IBMQ We have built the quantum computation centers of today …

IBM Q

Quantum Computing and IBM Q: An Introduction #IBMQ Thank you for your attention

Acknowledgements

IBM Q team (YKT, ZRL, Almaden, Tokyo)

Quantum Computing and IBM Q: An Introduction #IBMQ