Quantum Computing with Superconducting Qubits: Applications in Chemistry and Physics

Quantum Computing with superconducting qubits: Applications in Chemistry and Physics

Ivano Tavernelli

IBM Research - Zurich

PhD colloquium, University of Pavia, Italy February 14, 2019 New opportunities A look into the new cosmology A look into (quantum) technology

Medieval conception of the universe (Woodcut) By Christian Gralingen Outline

Why quantum computing? Quantum Logic The IBM Q Hardware & Software Applications

Quantum chemistry Many-body physics Optimization Outline

Why quantum computing? Quantum Logic The IBM Q Hardware & Software Applications

Quantum chemistry Many-body physics Optimization 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] Outline

Why quantum computing? Quantum Logic The IBM Q Hardware & Software Applications

Quantum chemistry Many-body physics Optimization The qubit

Bloch Sphere representation one bit one qubit

0 , 1 0 , |1〉 = |!〉

Qubit: linear superposition ϕ , , ! = # 0 + # 1 = cos 0 + ./0 sin 1 $ ' - - with - - #$ + #' = 1 Shown here is the state ! = 0.95 0 + (0.18 + 0.259) 1 90.25 % of the measurements give |0〉 and 9.75 % give |1〉

Ivano Tavernelli - [email protected] Single-qubit gates X Z H 1 0 ≡ X gate (!" matrix) Z gate (!. matrix) Hadamard gate 0 1 1 0 0 → 0 |0〉 → |0〉 + 1 0 1 |0〉 → 1 / = + 1 1 0 # = 0 −1 1 → −|1〉 * = 2 1 0 |1〉 → |0〉 , 1 −1 1 |1〉 ≡ |1〉 → 0 − 1 1 2

Bit-flip Phase-flip Superposition

Ivano Tavernelli - [email protected] Two-qubit gates - entanglement SWAP gate Controlled NOT gate (CNOT) 1 0 0 0 1 0 0 0 0 1 0 0 SWAP = 0 0 1 0 CNOT = 0 1 0 0 x 0 0 0 1 0 0 0 1 0 0 1 0 00 → |00〉 00 → |00〉 01 → |10〉 01 → |01〉 10 → |01〉 x 10 → |11〉 11 → |11〉 11 → |10〉

Preparation of a Bell’s state The simplest entangled state H 1 1 00 → 00 + 10 → 00 + 11 = 12344 2 2 Hadamard CNOT

Given two qubits 15 = 67 0 + 65 1 and 18 = 97 0 + 95 1 a Bell state cannot be represented as

product state 15 : 18 = 6797 00 + 6795 01 + 6597 10 + 6595|11〉 ≠ 12344 Outline

Why quantum computing? Quantum Logic The IBM Q Hardware & Software Applications

Quantum chemistry Many-body physics Optimization Physical qubit realizations

Quantum Bits: Neutral Atoms Ion Traps Two-Level Systems |1〉 |0〉

Example: Atom orbitals with different

energetic levels © Haroche © Blatt & Wineland

|1〉 Quantum Dots e- Superconducting Circuits Photon (Laser) |0〉 e- +

Ivano Tavernelli - [email protected] 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 ENIAC IBM Q Experience in 2016

One of the earliest electronic general-purpose First cloud quantum computing device computers in 1946

Quantum Computing and IBM Q: An Introduction #IBMQ “We’ve come a long way from then, providing the most advanced and most used quantum computers on the cloud” (2018)

Quantum Computing and IBM Q: An Introduction #IBMQ System 1 – IBM January 2019

IBM Q

Quantum Computing and IBM Q: An Introduction #IBMQ Outline

Why quantum computing? Quantum Logic The IBM Q Hardware & Software Applications

Quantum chemistry Many-body physics Optimization 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 > 5.2 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 Outline

Why quantum computing? Quantum Logic The IBM Q Hardware & Software Applications

Quantum chemistry Many-body physics Classical optimization 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 Richard P. Feynman 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 …”

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 N N N ,N 1 N el nu Z el el 1 H = 2 A + el 2 ri r r i=1 i=1 iA i=1,j>i ij X X AX=1 X 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 – Why a challenge? Classically, several approximations have been derived to break the exponential scaling Increasing accuracy MP: Moller-Plesset 8 Ab-initio methods N N2 CC: Coupled Cluster N7 CC: Coupled Cluster DFT: Density Functional 6 principle

N - Theory 5 N: Number of electrons N First (basis functions) N4 N3 N3

Hartree Fock MP2 MP3 CCSD CCSD(T) CCSDT DFT (HF) CISD

Ivano Tavernelli - [email protected] Formal scaling Practical (implementation) Quantum chemistry – the VQE approach

Generate the orbitals Hartree Fock equation (classical algorithms) F ( (r) ) (r)=✏ (r) Compute the system Hamiltonian { i } i i i

Encode the wavefunction in the qubit (✓) = ✓ 1111000000+ | i 1| i space. ✓ 1110100000+ 2| ... i (Parametrized by the qubit angles, ϑi) ✓ 1101000010+ 10| ... i ✓ 0000001111 Nc | i Evaluate the energy on a quantum circuit (✓) E(✓) | i

Minimize the energy in a classical E(✓) CPU ✓10 , ✓20 ,...,✓N0 c device ✓ , ✓ ,...,✓ CPU { } { 1 2 Nc } Ivano Tavernelli - [email protected] Quantum chemistry – the VQE approach

Generate the orbitals Hartree Fock equation (classical algorithms) F ( (r) ) (r)=✏ (r) Compute the system Hamiltonian { i } i i i

Minimize the energy in a classical E(✓) CPU ✓10 , ✓20 ,...,✓N0 c device ✓ , ✓ ,...,✓ CPU { } { 1 2 Nc } Ivano Tavernelli - [email protected] Quantum chemistry – The quantum algorithm The quantum-classical approach: Variational Quantum Eigensolver

Ivano Tavernelli - [email protected] QISKit: Basic workflow 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] Trial Wavefunctions Variational Principle

Heuristic Ansatz === D times ===== (✓~) = Uˆ D(✓~)Uˆ ...Uˆ 1(✓~)Uˆ Uˆ 0(✓~) ==== | i ent ent | 0i z }| { ===

10 00 10 00 i✓2 0 cos 2✓ i sin 2✓ 0 0 cos ✓1 e sin ✓1 0 U (✓)= U1,ex(✓1, ✓2)=0 i✓2 1 2,ex 0 1 0 e sin ✓1 cos ✓1 0 0 i sin 2✓ cos 2✓ 0 B00 01C B00 01C B C B C @ A @ A UCCSD Ansatz Tˆ(✓~) Tˆ†(✓~) ~ m (✓) = e Tˆ (✓~)= ✓ aˆ† 0aˆ 1 i m i | i i;m | i X m 1 m,n Tˆ (✓~)= ✓ aˆ† aˆ Tˆ2(✓~)= ✓ aˆ† aˆ† aˆjaˆi 1 i m i 2 i,j n m i;m i,j;m,n X X ˆ ~ 1 m,n T2(✓)= ✓ aˆ† aˆ† aˆjaˆi Ivano Tavernelli2 - [email protected],j n m i,j;m,n X 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

N N N ,N 1 N el nu Z el el 1 H = 2 A + el 2 ri r r i=1 i=1 iA i=1,j>i ij X X AX=1 X 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

Ivano Tavernelli - [email protected] Hubbard model At some intermediate value of U/t, there will be a “metal-to-insulator” transition: the „Mott“ transition.

HHub = t cj†ci + ci†cj + U ni ni " # i,j , i hXi ⇣ ⌘ X t : hopping term U :in-siterepulsiveterm i, j : adjacent sites h i J. Hubbard, Proc. Roy. Soc. London, A266, 238 (1963

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] Lattice field theory in HEP (1+1) Schwinger model

Problem Real-time propagation of gauge theories is notoriously challenging for classical computers. Digital quantum computers can offer a valid interesting alternative.

Solution strategy (using IBM Q 20-50 qubit devices)

1. Implement fermions and gauge boson in a qubit register (e.g. 1+1 Schwinger model). 2. Static properties: optimization using VQE. 3. Time evolution using the Trotter decomposition of the unitary evolution operator.

E.A. Martinez et al., Nature, 534, 516 (2016) Ivano Tavernelli - [email protected] Outline

Why quantum computing? Quantum Logic The IBM Q Hardware & Software Applications

Quantum chemistry Many-body physics Optimization Polymer folding

Problem find the folded structure of a linear chain of beads (amino acids, AA) in a regular lattice. This is a simplified model of the more complex protein folding problem.

The size of the configuration space scales exponentially with the number of polymer beads (AA).

Solution strategy assign binary variables to the different beads orientations in the sequence and minimize the string of binaries using the QAOA quantum algorithm and/over Grover’s search. The quantum variables are lattice directions of the bonds.

Ivano Tavernelli - [email protected] 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 4 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

FIG. 3. Convergence of the method and classification results: (a) Convergence of the cost function Remp(✓~) after 250 iterations of Spall’s SPSA algorithm. Red (black) curves correspond to l =4(l = 0). The dashed lines are obtained from the standard single- and two-qubit gate times, whereas solid lines correspond to the value of the cost obtained from the estimates ofp ˆk after zero-noise extrapolation. We train three sets of data per depth and perform 20 classifications per trained set. The results of these classifications are shown in (c) as black dots (amounting to 60 per depth), with mean values at each depth represented by red dots. The error bar is the standard error of the mean. The inset shows histograms as a function of the probability of measuring label +1 for a test set 20 points per label ran at l = 4 and which classify with a success 100%. The dashed blue lines show the results of our direct kernel estimation method for comparison, with Sets I and II yielding 100% success and Set III yielding 94.75% success. (b) Example data set used for both methods in this work. The data labels (red for +1 label and blue for 1 label) are generated with a separation gap of magnitude 0.3 between them (white areas). The 20 points per label training set is shown as white and black circles. For our quantum kernel estimation method we show the obtained support vectors (green circles) and a classified test set (white and black squares). Three of the test sets points are misclasified,

labeled as A, B, and C. For each of the test data points xj we plot at the bottom of (b) the amount i ki↵i⇤K(~xi, ~xj )overall support vectors xi, where ki +1, 1 are the labels of the support vectors. Points A, B, and C, all belonging to label +1, 2 { } P give i ki↵i⇤K(~xi, ~xj ) = -1.033, -0.367 and -1.082, respectively. P

of experimental shots taken, we fixed R = 200 to avoid decision rule pk(~x) >pk(~x)+kb can be restated gradient problems, even though we took 2000 shots in asm ˜ (x) = sign( (~x) W †(✓~)fW (✓~) (~x) + b). The the actual experiment. variational circuith W followed| by a| binaryi measure- After each training is completed, we use the trained ment can be understood as a separating hyperplane set of parameters ✓~ to classify 20 di↵erent test sets in quantum state space. Choose an orthogonal, 2n 2n -randomly drawn each time- per data set. We run these hermitian, matrix basis P↵ ⇥ ,where n { } ⇢n classification experiments at 10,000 shots, versus the ↵ =1,...,4 with tr P↵†P =2↵, such as the 2,000 used for training. The classification of each data Pauli-group on n-qubits. Expand both the quantum ⇥ ⇤ point is error-mitigated and repeated twice, averaging state (~x) (~x) and the measurement W †(✓~)fW (✓~) | ih | the success ratios obtained in each of the two classifi- in this matrix basis. Both the expectation value of cations. Figure 3 (c) shows the classification results for the binary measurement and the decision rule can be

our quantum variational approach. We clearly see an expressed in terms of w↵(✓~)=tr W †(✓~)fW (✓~)P↵ and increase in classification success with increasing circuit (~x)= (~x) P (~x) . For any variational unitary depth, reaching values very close to 100% for depths ↵ ↵ h i the classificationh | rule| cani be restated in the familiar larger than 1. This classification success remarkably n ~ remains up to depth 4, despite the fact that d =4 SVM formm ˜ (x) = sign 2 ↵ w↵(✓)↵(~x)+b .The classifier can only be improved when the constraint is training and classification circuits contain 8 CNOTs. ⇣ P ⌘ lifted that the w↵ come from a variational circuit. The A path to quantum advantage: Such variational circuit optimal w↵ can alternatively be found by employing classifiers are directly related to conventional SVMs kernel methods and considering the standard Wolfe - [13, 19]. To see why a quantum advantage can only dual of the SVM [13]. Moreover, this decomposition in- be obtained for feature maps with a classically hard dicates that one should think of the feature space as the quantum state space with feature vectors (~x) (~x) to estimate kernel, we point out the following: The | ih | High energy physics

Classification (machine learning and SVM) Collaboration CERN/IBM Reserach

> Select/identify relevant LHC events

> Reconstruction of tracks – jets tracking

Ivano Tavernelli - [email protected] The Future

… is quantum

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