Q UANTUM C OMPUTING W HY N OW ? Practical Applications Quantum - - PowerPoint PPT Presentation

QUANTUM COMPUTATION FOR THE

DISCOVERY OF NEW MATERIALS AND CHEMISTRY

Jarrod R. McClean Alvarez Fellow - Computational Research Division Lawrence Berkeley National Laboratory

QUANTUM COMPUTING – WHY NOW?

Time Quantum Excitement

Shor’s Factoring Qubits Beat Threshold Quantum Supremacy Practical Applications Error Corrected Computation

WHERE WILL WE WIN?

Exponential Speedup Quadratic Speedup Simulation of chemical reactions Calculating radar cross sections Breaking RSA encryption Pattern matching Machine learning Logistics optimization

WHAT IS “QUANTUM”?

“Classical” “Quantum” Quantum m Syste stem m – A physical system operated in a regime where we need effects like discrete energy levels and interference are required to accurately describe it.

SIMULATION

Orrery Antikythera Mechanism (125 B.C) Quantum System  Quantum System

QUANTUM SYSTEMS

QUANTUM SIMULATION – THE QUANTUM ADVANTAGE

Measurement Evolution Prepare Quantum Simulation

• Factoring Products of Two Large Primes
• Linear Partial Differential Equations
• Solution of Linear Equations

Quantum Computation Abstraction

QUANTUM COMPUTING ABSTRACTION

Generic State:

DEBUNKING QUANTUM MYTHS

MYTH 2: Faster/better because bits can be 0 and 1 at the same time. MYTH 3: Work by computing all the answers in parallel *https://www.smbc-comics.com/comic/the-talk-3 MYTH 1 TH 1: Faster/better because it can use an exponential number of states

Coherence Time & Fidelity

+Robust control & stable qubits +Algorithm timescale problem

Number of Qubits

+Scalable manufacture +(N-1) qubit problem

Information Extraction

+New input/output spec +Full readout loses advantage

Better Hardware Co-Design Better Algorithms Previous: Coherence time flexible Future:

• Improved coherence time flexibility, novel

property extraction, and demonstration

• Qubit number flexible algorithms and

larger demonstrations Measurement Evolution Prep

CHALLENGES IN QUANTUM COMPUTATION

THINKING DIFFERENTLY FOR SPEEDUPS

Classi assical: Solution translates to writing down the entries of x Quantum*: Solution translates to preparing state x from which one can sample

*A. Harrow, A. Hassidim, S. Lloyd, Phys. Rev. Lett. 103 103, 150502 (2009) **B. D. Clader, B. C. Jacobs, and C. R. Sprouse Phys. Rev. Lett. 110, 250504 (2013)

Solving the problem, not reproducing the classical algorithm!

EARLY APPLICATION AREAS

Optimization Relation Representation Quantum Simulation

SIMULATING CHEMISTRY

Understanding Control

THE ELECTRONIC STRUCTURE PROBLEM

“The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.”

• Paul Dirac

GRAND SOLUTIONS FROM A GRAND DEVICE

Nature: Nitrogenase “FeMoco” Humans: Haber Process Fertilizer 1-2% of ALL energy on earth, used on Haber process 400°C & 200 atm 25° C & 1 atm Beyond all current classical methods Both electronic structure and substrate attachment almost totally unknown Classically – No clear path to accurate solution Quantum Mechanically – 150-200 logical qubits for solution

THE EXPONENTIAL PROBLEM

Electrons: One mole Particles in universe

A RETURN TO CHEM 101

SIMPLE BUT NOT GOOD ENOUGH

CLASSICAL PRE-CALCULATIONS

Problem Input: “Second-Quantized Electronic Hamiltonian” Atom Centered Basis Hartree-Fock (Mean-Field) Molecular Orbitals

TOWARDS AN EXACT SOLUTION

Virtual Occupied

QUANTUM ADVANTAGE IN CHEMISTRY

Aspuru-Guzik, Dutoi, Love, Head-Gordon, Science 309, 1704–1707 (2005).

Measurement Evolution Prep Classical: Exponential cost Quantum: Modest polynomial cost Challenge: Algorithm can require > millions of coherent gates

A Co-design Perspective

Previously: Given a task, design quantum circuit (or computer) to perform it. Problem: General or optimal solution can require millions of gates. Alternative: Given a task and the current architecture, find the best solution possible. 42 42.02

Peruzzo†, McClean†, Shadbolt, Yung, Zhou, Love, Aspuru-Guzik, O’Brien. Nature Communications, 5 (4213):1– 7, 2014. † Equal Contribution by authors

EASY TASK FOR A QUANTUM COMPUTER

• Efficient to perform on any prepared quantum state
• In general, it may be very hard to calculate this expectation

value for a classical representation, containing an exponential number of configurations

Back to Basics

Decompose as: By Linearity: Easy for a Quantum Computer: Easy for a Classical Computer: Suggests Hybrid Scheme:

• Parameterize Quantum State with Classical Experimental Parameters
• Compute Averages using Quantum Computer
• Update State Using Classical Minimization Algorithm (e.g. Nelder-Mead)

Variational Formulation: Minimize

Computational Algorithm

All Possible Quantum States

ESSENTIALS OF A QUANTUM ADVANTAGE

“Easy” Quantum States “Classically Easy” Quantum States

STATE ANSATZ

Use the complexity of your device to your advantage Coherence time requirements are set by the device, not algorithm Quantum Hardware Ansatz: “Any Quantum Device with knobs” Unitary Coupled Cluster Ansatz (A-)diabatic State Preparation

QUANTUM ERRORS

Quantum Device Coherent Errors E.g. Over-rotation Environm nment nt Incoherent Errors E.g. Dephasing

VARIATIONAL ERROR SUPPRESSION

McClean, J.R., Romero, J., Babbush, R, Aspuru-Guzik, A. “The theory of variational hybrid quantum-classical algorithms” New Journal of Physics 18, 023023 (2016)

SCALABLE SIMULATION OF MOLECULAR ENERGIES IN SUPERCONDUCTING QUBITS

P.J.J. O’Malley, R. Babbush,…, J.R. McClean et al. “Scalable Simulation of Molecular Energies” Physical Review X 6 (3), 031007 (2016)

VARIATIONAL ERROR SUPPRESSION

VARIATIONAL ERROR SUPPRESSION

QUANTUM SUBSPACE EXPANSION (QSE)

General Idea: Learn action of H in a subspace Act: Probe: Local Metric S

QUANTUM SUBSPACE EXPANSION (QSE)

Expand to Linear Response (LR) Subspace Quantum State on Quantum Device Extra Quantum Measurements Classical Generalized Eigenvalue Problem Excited State Energy and Properties

Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States McClean, J.R., Schwartz, M.E, Carter, J., de Jong, W.A. Physical Review A 95 (4), 042308 (2017)

• Linear response (+), measured operators: IZ, ZI, IX, XI, XY, YX
• Spurious state disappears, good reconstruction of excited states

EXPERIMENTAL H2 SPECTRUM

EXCITING TIME FOR QUANTUM

GRAND SOLUTIONS FROM A GRAND DEVICE

Nature: Nitrogenase “FeMoco” Humans: Haber Process Fertilizer 1-2% of ALL energy on earth, used on Haber process 400°C & 200 atm 25° C & 1 atm Beyond all current classical methods Both electronic structure and substrate attachment almost totally unknown Classically – No clear path to accurate solution Quantum Mechanically – 150-200 logical qubits for solution

SUMMARY

150-200 Logical Qubits

Acknowledgements

LBNL: Wibe A. De Jong Jonathan Carter Cal Tech: Garnet Chan Google Quantum AI Labs Ryan Babbush Peter O’Malley Hartmut Neven John Martinis UC Berkeley: Irfan Siddiqi James Colless Vinay Ramasesh Dar Dahlen