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

Q UANTUM COMPUTATION FOR THE DISCOVERY OF NEW MATERIALS AND CHEMISTRY Jarrod R. McClean Alvarez Fellow - Computational Research Division Lawrence Berkeley National Laboratory

Q UANTUM C OMPUTING – W HY N OW ? Practical Applications Quantum Supremacy Quantum Excitement Shor’s Factoring Error Corrected Computation Qubits Beat Threshold Time

W HERE WILL WE WIN ? Pattern matching Simulation of chemical reactions Machine learning Calculating radar cross sections Logistics optimization Breaking RSA encryption Quadratic Speedup Exponential Speedup

W HAT 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.

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

Q UANTUM S YSTEMS

Q UANTUM S IMULATION – T HE Q UANTUM A DVANTAGE Quantum Simulation Abstraction Quantum Computation Factoring Products of Two Large Primes • Linear Partial Differential Equations • Solution of Linear Equations • Prepare Evolution Measurement

Q UANTUM C OMPUTING A BSTRACTION Generic State:

D EBUNKING Q UANTUM M YTHS MYTH 1 TH 1: Faster/better because it can use an exponential number of states 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

C HALLENGES IN Q UANTUM C OMPUTATION Prep Evolution Measurement Information Extraction Number of Qubits +New input/output spec Coherence Time & Fidelity +Scalable manufacture +Full readout loses advantage +Robust control & stable qubits +(N-1) qubit problem +Algorithm timescale problem Co-Design Better Algorithms Better Hardware Previous: Coherence time flexible Future: Improved coherence time flexibility, novel • property extraction, and demonstration Qubit number flexible algorithms and • larger demonstrations

T HINKING 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 Solving the problem, not reproducing the classical algorithm! *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)

E ARLY A PPLICATION A REAS Optimization Relation Representation Quantum Simulation

S IMULATING C HEMISTRY Understanding Control

T HE E LECTRONIC S TRUCTURE P ROBLEM “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

G RAND SOLUTIONS FROM A GRAND DEVICE Fertilizer Humans: Haber Process Nature: Nitrogenase “FeMoco” 25 ° C & 1 atm 400 ° C & 200 atm 1-2% of ALL energy on earth, used on Haber process 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

T HE EXPONENTIAL PROBLEM Electrons: One mole Particles in universe

A R ETURN TO C HEM 101

S IMPLE BUT NOT GOOD ENOUGH

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

T OWARDS AN E XACT S OLUTION Virtual Occupied

Q UANTUM A DVANTAGE IN C HEMISTRY Prep Evolution Measurement Classical: Exponential cost Quantum: Modest polynomial cost Challenge : Algorithm can require > millions of coherent gates Aspuru-Guzik, Dutoi, Love, Head-Gordon, Science 309, 1704–1707 (2005).

A Co-design Perspective Previously: Given a task, design quantum circuit (or computer) to perform it. 42 Problem: General or optimal solution can require millions of gates. Alternative: Given a task and the current architecture, find the best solution possible. 42.02 Peruzzo † , McClean† , Shadbolt, Yung, Zhou, Love, Aspuru-Guzik, O’Brien. Nature Communications , 5 (4213):1– 7, 2014. † Equal Contribution by authors

E ASY T ASK F OR A Q UANTUM C OMPUTER • 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 Variational Formulation: Minimize 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)

Computational Algorithm

E SSENTIALS OF A QUANTUM A DVANTAGE All Possible Quantum States “Classically Easy” “Easy” Quantum States Quantum States

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

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

V ARIATIONAL E RROR S UPPRESSION 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)

S CALABLE S IMULATION OF M OLECULAR E NERGIES IN S UPERCONDUCTING Q UBITS P.J.J. O’Malley, R. Babbush,…, J.R. McClean et al. “Scalable Simulation of Molecular Energies” Physical Review X 6 (3), 031007 (2016)

V ARIATIONAL E RROR S UPPRESSION

V ARIATIONAL E RROR S UPPRESSION

Q UANTUM S UBSPACE E XPANSION (QSE) General Idea: Learn action of H in a subspace Act: Probe: Local Metric S

Q UANTUM S UBSPACE E XPANSION (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)

E XPERIMENTAL H 2 S PECTRUM Linear response (+), measured operators: IZ, ZI, IX, XI, XY, YX • Spurious state disappears, good reconstruction of excited states •

E XCITING TIME FOR Q UANTUM

G RAND SOLUTIONS FROM A GRAND DEVICE Fertilizer Humans: Haber Process Nature: Nitrogenase “FeMoco” 25 ° C & 1 atm 400 ° C & 200 atm 1-2% of ALL energy on earth, used on Haber process 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

S UMMARY 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