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? 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 Quantum Computing as a path to solve intractable problems Many problems in business and science are too complex for classical computing systems

“hard” / intractable problems: (exponentially increasing resources with problem size) • Algebraic algorithms (e.g. factoring, systems of equations) for machine learning, cryptography,… • Combinatorial optimization (traveling salesman, Hard Problems for optimizing business processes, risk analysis,…) Classical Computing (NP) • Simulating quantum mechanics (chemistry, material science,…)

Easy Problems Possible with 13 x 7 = ? Quantum Computing 937 x 947 = ? 91 = ? x ? 887339 = ? X ?

Computer science: + quantum physics: two logical states discrete quantum states (qubits) + gates superposition + unitary evolution 1 1 0 0

X H 1-qubit gates

The Quantum Advantage – Simulation of physical systems

How much memory is needed to store a quantum state? How much time does it take to calculate dynamics of a quantum system?

# qubits quantum state coefficients # bytes timescale

1 푎 0 + 푏|1〉 21 = 2 16 Bytes classical 2 푎 00 + 푏 01 + 푐 10 + 푑|11〉 22 = 4 32 Bytes Nanoseconds

8 28 = 256 2kB Microseconds on watch

16 … 216 = 65′536 512 kB Milliseconds on smartphone

32 … ~4 billion 32 GB Seconds on laptop quantum ~ information 128 EB 64 … Years on supercomputer in internet (134 million GB) ~ # of atoms in

256 … … never universe

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.

Superconducting qubit . quantum information carrier

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

Chip with superconducting 0.9K qubits and resonators 0.1K

Microwave electronics 0.015K PCB with the qubit +chip at 15 mK Protected from the environment by multiple shields Refrigerator to cool qubits to 15 mK with a mixture of 3He and 4He © 2018 International Business Machines Corporation – Stefan Filipp – [email protected] IBM qubit processor architectures IBM Q experience (publicly accessible) 16 Qubits (2017) 5 Qubits (2016)

IBM Q commercial 20 Qubits 50 Qubit architecture (2017) Package

Latticed arrangement for scaling

Public quantum computer (up to 16 qubits) and developer ecosystem

IBM QX Features Since launch • Tutorial • > 80,000 users • Simulation • > 3,000,000 experiments • Graphical • > 60 research papers programming • used by 1,500+ colleges • QASM language and universities, 300 high • API & SDK schools, 300 private • Active user institutions community

Experience quantum computing here: research.ibm.com/ibm-qx

(qubit #) x (circuit depth) => =>

depth 1 circuit: Measured HW parameters : • Number of physical qubits N • Connectivity between qubits • Number of gates before errors mask result • Available hardware gate set • Number of operations that can be run in parallel

Measures the useful amount of quantum computing that can be done with a near-term device before errors mask the result.

Challenges ahead:

• In order to increase the quantum volume we need to improve both effective error rate and qubit number

• It is the scaling of the effective error rate that limits the usefulness of a quantum computer with superconducting qubits

• Need to improve connectivity, gate speed and coherence

• Requires better designs, materials and two qubit interactions

© 2018 International Business Machines Corporation – Stefan Filipp – [email protected] The Universal Quantum Computing System Idea: use error correction schemes to make a ‘logical’ qubit out of several ‘good’ physical qubits Logical layer

0 → |00 … 0〉 1 → |11 … 1〉

100-1000 x

Physical layer

Status: physical qubits almost good enough, first demonstrations of logical qubits expected soon [Gambetta, Chow, Steffen, npj Quantum Information 3, 2 (2017)]

Approximate Quantum Computing

Explore the application space of quantum computers before a universal quantum computer can be built

Logical layer

Physical layer

[Gambetta, Chow, Steffen, npj Quantum Information 3, 2 (2017)] Steps towards Universal Quantum Computing

Demonstration of Quantum Advantage & Learning Demonstrate an advantage to using quantum computing for real problems of interest. Create software layer, quantum algorithms and education tools. 50-100 qubits

Commercialization of Approximate Quantum Computer Have commercial impact with useful applications on a quantum computer which does not need full fault tolerance, potentially assisting conventional computers (hybrid quantum computer)

time / complexity / time 100-1000+ qubits

Universal Fault-Tolerant Quantum Computer Run useful quantum algorithms with exponential speed up over their classical counterparts. Requires error correction. 1M-10M qubits

© 2018 International Business Machines Corporation – Stefan Filipp – [email protected] Variational Quantum Eigensolver (VQE): A hybrid quantum-classical (HPC) algorithm Solve problems where the goal is to minimize the energy of a system, e.g. 퐸푚푖푛 = 휓 휃푚푖푛 퐻푒|휓 휃푚푖푛 ⟩

Prepare a quantum state 휓 휃 and compute its energy 퐸(휃) Evaluate 푬 휽 ; use classical optimizer to choose new value of 휃 until 푬풎풊풏 is found Advantages: Use short circuits which fit into our coherence time Improve on best classical estimates by using non-classical trial states

Quantum chemistry Solving interacting fermionic problems is at the core of most challenges in computational physics and high-performance computing: 푁 푁 푀 1 2 푍퐴 1 퐻푒 = − 훻푖 − + 2 푟푖퐴 푟푖푗 푖=1 푖=1 퐴=1 푖=1,푗,푖>1 What can quantum computers do? First Demonstrations: Map fermions (electrons) to qubits and compute molecular structure reaction rates

LiH – Molecule (error mitigated) Sign problem: Monte-Carlo simulations of fermions are NP-hard [Troyer &Wiese, PRL 170201 (2015)] A. Kandala, et al. Nature 549 (2017); arxiv 1805.04492 (2018) © 2018 International Business Machines Corporation – Stefan Filipp – [email protected] Groundstate-energy of simple molecules

A. Kandala, et al. arXiv:1805.04492 (2018)

Traveling Salesman Problem:

- Visit all cities just once - Choose the shortest path - Come back to starting point

17 x … x 5 x 4 x 3 x 2 x 1 = 17! = 355’687’428’096’000 possible paths

16 ausgewählte Städte in der Schweiz can be encoded into a quantum physics problem: find the ground-state of a spin (Ising) system, which encodes the optimal path

푁 푁 푘 푘 푙 퐻퐼푠푖푛푔 = ℎ푘 휎푧 + 훼푘푙 휎푧 ⊗ 휎푧 18 selected cities in Switzerland 푘=1 푘<푙

matching of molecular structures traveling salesman problem risk management finite element method

scheduling 3-SAT portfolio optimization facility location planning

manufacturing

image classification forecasting max cut max inventory management production planning clique

supply chain management mechanical design graph coloring

independent set principal component analysis linear programming data mining

integrated circuit design energy control planning capacity

traffic traffic routing customer segmentation customer

Open Source: www.qiskit.org

Quantum Developers Build Python Interface

Compile Translate & Optimize

Real Devices Simulators Experience

- Step by step Jupiter notebooks on how to run quantum chemistry and combinatorial problems using quantum computers

- Variational quantum eigensolver approach with short-depth trial wavefunctions

- Chemistry tutorial includes H2 and LiH molecules to be run on 2 and 4 qubits. Explicit run of one interatomic distance and full potential energy surface

- Toy optimization problems include Max- Cut and travelling salesman instances

End Users and Domain Experts:

– Seamlessly integrate Quantum capabilities in the existing workflow

– Enjoy Quantum performance and accuracy gains without having to know Quantum

– Easily get high quality results

© 2018 International Business Machines Corporation – Stefan Filipp – [email protected] 26 Grand Challenge: Quantum Computing Goal: Build computers based on quantum physics to solve problems that are otherwise intractable

Roadmap: Small-scale (Demonstration of Medium-scale (Commercializing Large-scale Quantum advantage) approximate QC) (Fault-tolerant Universal QC) . Research level demonstrations . Develop “Hardware-efficient” apps Known and proven speed-up: . Verify chemistry and error correction − Chemical configurations . Factoring principles − Optimization . quantum molecular simulations . Infrastructure & community building − Hybrid quantum-classical computers . Speed-up machine learning . Demonstrate ‘Quantum advantage’ . No full error correction available Enable secure cloud computing

IBM Q 20XX

5-8 qubits 16 qubits 50+100 qubits 100-1000+ qubits 106 -107 qubits