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Melina Dorsey
5 years ago
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8 30 qubits 40 qubits 50 qubits Exponential Scaling

9 Simulating 260 qubits requires more memory than there are atoms in the universe

10 RSA-2048 Challenge Problem Classical Quantum billion years seconds

11 CAFFEINE MOLECULE FEMOCO MOLECULE

12 Calculation Time Classical Computing Age of the Universe Number of Atoms

13 Error Rate Low High Number of Qubits

14 Majorana Fermions Predicted by Ettore Majorana in 1937

16 Inspiration

19 Insulator: Normal S-Wave Superconductor: Topological Superconductor: Electron Fractionalization Superposition

20 Inca Quipu

23 Richard Feynman: Shut up & calculate! Quantum 2.0: Shut up & engineer!

25 Quantum Programming Language Compiler Abstract Syntax Tree Code Gen Quantum Hardware C# Toffoli Simulator CHP Simulator Local Simulator Azure Simulator Resource Estimator

26 Domain-specific language for quantum algorithms and development Functional in flavor Visual Studio integration Quantum-specific features Extensive libraries, samples, and documentation

27 State-of-the-Art Local Simulator State-of-the-Art Azure Simulator Resource Estimator Quantum Hardware

DistillT: 1Q=65 2Q=100 LogQ=81 Frames=277 Connect Dim Data Rows Phys Qubits Data Teleport Block Tele Par Tele Depth Rect 10x10 All 42 15/9 20/9 4*(9+9)=72 Rect

31 DistillT: 1Q=65 2Q=100 LogQ=81 Frames=277 Connect Dim Data Rows Phys Qubits Data Teleport Block Tele Par Tele Depth Rect 10x10 All 42 15/9 20/9 4*(9+9)=72 Rect 5x9 All 39 18/13 25/13 4*(13+13)=104 Rect 3x18 Half 39 40/31 40/31 4*(31+31)=248 Diag 3x9 Half 26 15/9 15/9 4*(9+9)=72 Diag 2x18 Half 34 39/24 36/24 4*(24+24)=192

32 Ferredoxin Fe 2 S 2 Classical algorithm! INTRACTABLE Quantum algorithm 2012 ~24 BILLION YEARS Quantum algorithm 2015 ~1 HOUR

42 Quantum Chemistry H = h pq a p a q h pqrs a p a q a r a s pqrs pq Can quantum chemistry be performed on a small quantum computer: Dave Wecker, Bela Improving Bauer, Bryan Quantum K. Clark, Algorithms Matthew for B. Quantum Hastings, Chemistry: Matthias M. B. Troyer Hastings, Ferredoxin D. Wecker, B. Bauer, (Fe M. Troyer The Trotter Step Size Required 2 S 2 ) used in many metabolic reactions for Accurate Quantum Simulation of Quantum Chemistry As quantum computing We present technology several David improvements Poulin, M. B. improves and to Hastings, On quantum the the standard Chemical Dave Wecker, computers Trotter-Suzuki Basis of Nathan Trotter-Suzuki Wiebe, Andrew Errors in C. Quantum Doherty, Matthias Chemistry Troyer Simulation including energy transport in photosynthesis with a small but based non-trivial algorithms number used of in N the > 100 simulation qubits Ryan appear of Babbush, quantum feasible Jarrod chemistry in McClean, on a Dave Wecker, Alán Aspuru-Guzik, Nathan Wiebe the near future quantum the question computer. The simulation of possible First, applications we modify of molecules how of small Jordan-Wigner is a widely anticipated application of quantum computers. However, recent quantum computers gains transformations studies importance. One are frequently implemented \cite{wbch13a,hwbt14a} mentioned to Although reduce application their have simulation cost cast is from a linear of shadow quantum or on this chemistry hope by is one revealing of the that most the anticipated complexity in Feynman's original logarithmic proposal Intractable in of the gate simulating number count of of quantum on such orbitals a simulations applications classical systems, to a constant. increases and of computer in quantum Our with computing, the number the of spin scaling orbitals of known N as N8, upper which bounds becomes on the particular the electronic modification structure does prohibitive not of molecules require even additional for molecules and complexity materials. ancilla of In of qubits. modest this these Then, algorithms size N 100. we is This daunting. study Prior was partly work has based bounded on a scaling errors analysis due to paper, we analyze demonstrate the computational how of the many Trotter requirements operations step required Trotterization can for one be for parallelized, an ensemble of the terms leading of of the random to norm a artificial of the error molecules. operator Here, and we analyzed revisit scaling this analysis with standard algorithms further to linear Assumed perform decrease and find quantum in instead quantum the chemistry parallel that respect the on depth scaling: a quantum to of the is closer number circuit, ~24 to at of N6 the spin-orbitals. billion cost worst case years However, for real (Nmodel 11 we find scaling) molecules that these we error have bounds studied, can be computer. We focus of a small on the constant indicating quantum factor that resources increase the random required in loose number by ensemble to find up of to qubits the sixteen fails required. to orders accurately of magnitude capture the for statistical some molecules. properties Furthermore, of real-world numerical ground state of Thirdly, a molecule we First modify molecules. twice paper: as the large term Actual as order scaling what ~850 current results the may Trotter-Suzuki for be significantly better than this due to averaging effects. We then present classical thousand small systems years fail to reveal to any solve clear (N correlation 9 scaling) between ground state error computers can decomposition, an solve exactly. We significantly alternative find that while reducing simulation such and the scheme a problem number error at and of given spin-orbitals. show Trotter- that it We can instead sometimes argue outperform that chemical existing properties, schemes, such but as that the requires about Suzuki a ten-fold timestep. this increase A possibility final the improvement depends number of maximum qubits modifies crucially over nuclear the on the current Hamiltonian charge details in of to a the molecule simulated and molecule. the filling We fraction obtain of further orbitals, can be decisive Second technology, the reduce required errors increase introduced improvements paper: the number by the using ~30 non-zero a version of for gates determining years Trotter-Suzuki of the to coalescing that can be the solve cost timestep. of a scheme (N 7 quantum scaling) of \cite{wbch13a}; simulation. Our analysis this scheme motivates is based several on coherently executed All of is these many techniques using different orders of are magnitude validated Trotter larger. strategies using steps This numerical for to different suggests use classical simulation terms. processing The and method to we further use reduce to bound the the required complexity Trotter of step size and that for quantum detailed computation gate Third counts simulating to become paper: are given a given useful for ~5 molecule for realistic to quantum estimate days molecules. is efficient, to the necessary solve in contrast (N number 5.5 to the scaling) of approach steps, without of \cite{wbch13a,hwbt14a} requiring additional quantum which relied on exponentially costly classical exact simulation. chemistry problems, drastic algorithmic improvements resources. will be Finally, needed. we demonstrate improved methods for state preparation techniques which are asymptotically superior to proposals the simulation literature. Fourth paper: ~1 hour to solve (N 3, Z 2.5 scaling)

Revolutionary topological approach Our quantum approach brings theory to reality, harnessing topological qubits that perform computations longer and more consistently, with fewer errors.

43 Revolutionary topological approach Our quantum approach brings theory to reality, harnessing topological qubits that perform computations longer and more consistently, with fewer errors. Bold investments and a global team For more than a decade, we ve made consistent investments and built the quantum dream team with collaboration across universities, industries, and more. Scalable, end-to-end technology Our full-stack quantumcomputing solution is designed so you and your developers can approach quantum computing right away, with the ability to scale.

Simulating 250 interacting qubits requires ~ classical bits! State of N interacting qubits: ~ 2 N bits of info!

Hours (on Cray XE6) Simulating 250 interacting qubits requires ~ classical bits! State of N interacting qubits: ~ 2 N bits of info! Time to Factor N-bit Number RSA-2048 Challenge Problem Number of bits