Quantum Computing at IBM

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1 Quantum Computing at IBM Ivano Tavernelli IBM Research - Zurich Quantum Computing for High Energy Physics CERN -Geneva November 5-6, 2018

2 Outline Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications Quantum chemistry Many-body physics Optimization and HEP

3 Outline Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications Quantum chemistry Many-body physics Optimization and HEP

4 Future of computing Alternative (co-existing) architectures: next generation systems (3D/hybrid) First integrated circuit Size ~1cm 2 2 Transistors Moore s Law is Born Intel ,300 transistors IBM P8 Processor ~ 650 mm 2 22 nm feature size, 16 cores >4.2 Billion Transistors neuromorphic (cognitive) quantum computing Ivano Tavernelli - ita@zurich.ibm.com

5 Types of Quantum Computing Quantum Annealing Optimization Problems Machine learning Fault analysis Resource optimization etc Approximate NISQ-Comp. Simulation of Quantum Systems, Optimization Material discovery Quantum chemistry Optimization (logistics, time scheduling, ) Machine Learning Fault-tolerant Universal Q-Comp. Execution of Arbitrary Quantum Algorithms Algebraic algorithms (machine learning, cryptography, ) Combinatorial optimization Digital simulation of quantum systems Surface Code: Error correction in a Quantum Computer Many noisy qubits can be built; large problem class in optimization; amount of quantum speedup unclear Ivano Tavernelli - ita@zurich.ibm.com Hybrid quantum-classical approach; already good physical qubits could provide quantum speedup. Proven quantum speedup; error correction requires significant qubit overhead.

6 Types of Quantum Computing Quantum Annealing Optimization Problems Machine learning Fault analysis Resource optimization etc Approximate Q-Comp. Simulation of Quantum Systems, Optimization Material discovery Quantum chemistry Optimization (logistics, time scheduling, ) Machine Learning Fault-tolerant Universal Q-Comp. Execution of Arbitrary Quantum Algorithms Algebraic algorithms (machine learning, cryptography, ) Combinatorial optimization Digital simulation of quantum systems Surface Code: Error correction in a Quantum Computer Many noisy qubits can be built; large problem class in optimization; amount of quantum speedup unclear Ivano Tavernelli - ita@zurich.ibm.com Hybrid quantum-classical approach; already good physical qubits could provide quantum speedup. Proven quantum speedup; error correction requires significant qubit overhead.

7 Hard or memory intensive problems and quantum speedups Hard Problems For classical computing (NP) Possible with quantum computing 13x7=? 937x947=? 91=? x? =? x? Factoring Material, Chemistry Optimization Machine Learning Simulating Quantum Mechanics Quantum computing may provide a new path to solve some of the hardest or most memory intensive problems in business and science. Quantum Computing and IBM Q: An Introduction #IBMQ

8 Outline Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications Quantum chemistry Many-body physics Optimization and HEP

9 IBM: Superconducting Qubit Processor Superconducting qubit (transmon): quantum information carrier nearly dissipationless T 1, T 2 ~70 µs lifetime, 50MHz clock speed Microwave resonator as: read-out of qubit states quantum bus noise filter Ivano Tavernelli - ita@zurich.ibm.com

10 Inside an IBM Q quantum computing system Microwave electronics 40K 3K 0.9K 0.1K Refrigerator to cool qubits to mk with a mixture of 3 He and 4 He 0.015K PCB with the qubit chip at 15 mk protected from the environment by multiple shields Chip with superconducting qubits and resonators

11 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

12 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

13 Outline Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications Quantum chemistry Many-body physics Optimization and HEP

14 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

15 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.

16 Quantum Computing and IBM Q: An Introduction.

17 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

18 IBM Q Experience executions on real quantum computers (not simulations) May 11, 2018 IBM Q16 IBM Q5 IBM Research / DOC ID / March XX, 2018 / 2018 IBM Corporation 18

19 Panagiotis Barkoutsos - bpa@zurich.ibm.com Qiskit high level quantum applications: chemistry, optimization, AI, finance state characterization, error mitigation, optimal control classical simulation of quantum circuits core programming tools and API to hardware

20 QISKit: Terra Panagiotis Barkoutsos - bpa@zurich.ibm.com

21 QISKit: Aqua Panagiotis Barkoutsos - bpa@zurich.ibm.com

22 IBM QX Devices Available for free:

23 QISKit: Basic workflow At the highest level, quantum programming in QISKit is broken up into three parts: 1. Building quantum circuits 2. Compiling quantum circuits to run on a specific backend 3. Executing quantum circuits on a backend and analyzing results Quantum Program QuantumandClassicalRegisters Quantum Circuits 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 Panagiotis Barkoutsos - bpa@zurich.ibm.com

24 QISKit: Basic workflow At the highest level, quantum programming in QISKit is broken up into three parts: Quantum Program QuantumandClassicalRegisters Quantum Circuits Backend Directory Execution Results State Counts Panagiotis Barkoutsos - bpa@zurich.ibm.com

25 Qiskit Aqua Chemistry Example Panagiotis Barkoutsos - bpa@zurich.ibm.com

26 Outline Why quantum computing? The IBM Q Hardware The IBM Q Software platform Qiskit Applications Quantum chemistry Many-body physics Classical optimization and HEP

27 Quantum Chemistry & Physics International Journal of Theoretical Physics, VoL 21, Nos. 6/7, 1982 I'm not happy with all the analyses that go with just the 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 Simulating Physics with Computers Richard P. Feynman Ivano Tavernelli - ita@zurich.ibm.com

discovery Artificial Intelligence Classification, machine learning, linear algebra Financial Services

28 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?

computational physics and high-performance computing: H el = 1 2 NX i=1 r 2 i XN

(& ( ) Z A r ia + NX el,n el i=1,j>i 1 r ij molecular structure reaction rates

29 Quantum chemistry: Where is it a challenge? Solving interacting fermionic problems is at the core of most challenges in computational physics and high-performance computing: H el = 1 2 NX i=1 r 2 i XN el i=1 XN nu A=1 Full CI (exact): Classical!(exp(&)) Quantum!(& ( ) Z A r ia + NX el,n el i=1,j>i 1 r ij molecular structure reaction rates reaction pathways Sign problem: Monte-Carlo simulations of fermions are NPhard [Troyer &Wiese, PRL (2015)] Ivano Tavernelli - ita@zurich.ibm.com

Quantum chemistry Ĥ elec = X pq h pq â pâ q + 1 2 X pqrs h pqrs â pâ qâ r â s Basis set orbitals (HF) for the generation of the Hamiltonian in second quantization M F ν (H)= S ν H n n=0 = C H (S ν (H

30 Quantum chemistry Ĥ elec = X pq h pq â pâ q X pqrs h pqrs â pâ qâ r â s Basis set orbitals (HF) for the generation of the Hamiltonian in second quantization M F ν (H)= S ν H n n=0 = C H (S ν (H H)) (S ν (H H H))... Ψi ν = Ψ 0 i ν Ψ 1 i ν Ψ 2 i ν... X = a 0 0i a 1 ψ 1 i a ij ψ 2i,ψ 2j i ν... ij Fockspace with blocks with N=0,1,2,3,4 particles ψ 2i,ψ 2j i ν = 1 2 ( ψ 2ii ψ 2j i+ν ψ 2j i ψ 2i i) 2 S ν (H H) Ivano Tavernelli - ita@zurich.ibm.com

31 Quantum chemistry Electrons and qubits fulfill different statistics: Ĥ elec = X pq h pq â pâ q X h pqrs â pâ qâ r â s Fermions: Spins: {a i,a i } =0, {a i,a i } =0,{a i,a i } = δ i,j [σ i,σ i ]=0, [σ i,σ i ]=0,[σ i,σ j ]=δ i,j pqrs M F ν (H)= S ν H n n=0 = C H (S ν (H H)) (S ν (H H H))... Ψi ν = Ψ 0 i ν Ψ 1 i ν Ψ 2 i ν... X = a 0 0i a 1 ψ 1 i a ij ψ 2i,ψ 2j i ν... ψ 2i,ψ 2j i ν = 1 2 ( ψ 2ii ψ 2j i+ν ψ 2j i ψ 2i i) 2 S ν (H H) Ivano Tavernelli - ita@zurich.ibm.com ij The Jordan--Wigner is the most commonly used mapping in the context of electronic-structure Hamiltonians: Or 1 k=s+1 σ z a j = j 1 i=1 a j = j 1 i=1 Op 1 k=q+1 σ z k 0 1 A σ z i σ x j +iσ y j σ z i σ x j iσ y j The terms in the Hamiltonian transform as: h pqrs a pa qa r a s +h srqp a sa ra q a p <(h pqrs ) 8 + =(h pqrs) σsσ x rσ x qσ x p x σsσ x rσ x qσ y p y +σsσ x rσ y qσ x p+ y +σsσ y rσ x qσ x p y +σsσ y rσ x qσ y p x σsσ y rσ y qσ x p+ x A 0 +σsσ x rσ y qσ y p x +σsσ y rσ y qσ y p y 1 σsσ y rσ x qσ x p x +σsσ x rσ y qσ x p x σsσ x rσ x qσ y p+ x σsσ x rσ y qσ y p y σsσ y rσ x qσ y p y +σsσ y rσ y qσ x p+ y AA +σsσ y rσ y qσ x p y +σsσ y rσ y qσ y p x

32 Quantum chemistry The quantum algorithm The quantum-classical approach: Variational Quantum Eigensolver Ivano Tavernelli - ita@zurich.ibm.com

33 Trial Wavefunctions Variational Principle Heuristic Ansatz Ψ( ~ )i = D times z } { Û D ( ~ )Ûent...Û1 ( ~ )ÛentÛ0 ( ~ ) Φ 0 i = U 1,ex (θ 1,θ 2 )= 0 cosθ 1 e iθ 2 sinθ e iθ 2 sinθ 1 cosθ 1 0 U 2,ex(θ)= 0 cos2θ isin2θ 0 0 isin2θ cos2θ UCCSD Ansatz Ψ( )i ~ ) ˆT = eˆt( ~ X ( ) ~ Φ 0 i ˆT 1 ( )= ~ X i m â mâ i ˆT 2 ( )= ~ 1 2 i;m X Ivano Tavernelli - ita@zurich.ibm.com X i,j;m,n m,n i,j â nâ mâ j â i

34 Quantum chemistry the VQE approach Ground state-energy of simple molecules! " : 2 qubits 5 Pauli terms, 2 sets #$!: 4 qubits 100 Pauli terms, 25 sets %&! " : 6 qubits 144 Pauli terms, 36 sets [A. Kandalaet al. Nature 549, , 2017] Ivano Tavernelli - ita@zurich.ibm.com

35 Quantum chemistry the VQE approach with error corr. Ground state-energy of simple molecules Ivano Tavernelli - ita@zurich.ibm.com

Quantum chemistry Excited state energies

2 i XN el i=1 XN nu A=1 Z A r ia + NX el,n

36 Quantum chemistry Excited state energies Interaction of light with matter: arxiv: Photocatalysis Artificial photosynthesis Light harvesting Photochemistry of H 2 H el = 1 2 NX i=1 r 2 i XN el i=1 XN nu A=1 Z A r ia + NX el,n el i=1,j>i 1 r ij Full CI (exact): Classical!(exp(&)) Quantum!(& ( ) Ivano Tavernelli - ita@zurich.ibm.com

37 Quantum chemistry Recent and Medium term developments Example: excited state energies of 2 and 3 atomic systems Will come soon Ivano Tavernelli - ita@zurich.ibm.com

38 Hubbard model VQE entanglers for ground state calculations H Hub = t X hi,ji,σ t : hopping term U :in-siterepulsiveterm hi,ji : adjacent sites c jσ c iσ +c iσ c jσ +U X i J. Hubbard, Proc. Roy. Soc. London, A266, 238 (1963 Study physical properties with a quantum algorithm: n i" n i# Will come soon 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 - ita@zurich.ibm.com

39 Simulation of molecular magnetic systems Measuring the spin-spin time-dependent correlation function! "# $% & = ) " * & ) # % scales exponentially with the number of sites. Ivano Tavernelli - ita@zurich.ibm.com [E. M.Pineda et al., Chemical Science, 2017, 8, 1178]

, Chemical Science, 2017, 8, 1178] Quantifying entanglement.

40 Simulation of molecular magnetic systems Measuring the spin-spin time-dependent correlation function! "# $% & = ) " * & ) # % scales exponentially with the number of sites. Ivano Tavernelli - ita@zurich.ibm.com [E. M.Pineda et al., Chemical Science, 2017, 8, 1178] 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 neutron scattering signals integrated over Q z.

41 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.

42 Recent Results by IBM Research Support vectors arxiv: Possible applications: - Customer segmentation - Image classification - Fraud detection Maximize the margin Hyperplane

43 Recent Results by IBM Research The data may not be linearly separable arxiv: Lift to higher dimension Possible applications: - Customer segmentation - Image classification - Fraud detection Support vectors Quantum Support Vector Machines (SVM) may offer performance advantages to classical SVMs by using kernels that cannot be computed efficiently classically! 0 Demonstrated on real quantum device

Trained 3 sets of data (20 pts/label) and

44 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)!=+1!= 1 training data test data support vectors classification success Success [100%] variational method kernel method misclassi6ied test data variational circuit depth

.and high energy physics Classification (machine learning and

Reconstruction of tracks jets tracking Quantum Computing

beyond) Quantum Minimization VQE optimization in lattice gauge

45 .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 - ita@zurich.ibm.com

46 The Future Quantum Computing and IBM Q: An Introduction #IBMQ

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

48 Thank you for your attention Acknowledgements IBM Q team (YKT, ZRL, Almaden, Tokyo) Quantum Computing and IBM Q: An Introduction #IBMQ

Quantum computing with superconducting qubits Towards useful applications

Quantum computing with superconducting qubits Towards useful applications Stefan Filipp IBM Research Zurich Switzerland Forum Teratec 2018 June 20, 2018 Palaiseau, France Why Quantum Computing? Why now?