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

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Randell Summers
5 years ago
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4 Simulating 250 interacting qubits requires ~ classical bits! State of N interacting qubits: ~ 2 N bits of info!

5 Time to Factor N-bit Number RSA-2048 Challenge Problem Number of bits N

6 LIQ

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

9 H 2 HF H 2 O NH 3 CH 4 HCl F 2 H 2 S Geometries and molecular models from

10 H = h pq a p a q h pqrs a p a q a r a s pq pqrs

11 LIQUi SoLi and QCoDeS

12 Nitrogen fixation s-1000s 100s-1000s

13 Ion traps Superconductors Linear optics NV centers Quantum dots Topological

17 Build experiment as described Measure zero-bias peak See that it goes away if we remove any of the necessary components Mourik, Kouwenhoven

19 Growth by Diana Car, Sébastien Plissard and Erik Bakkers V I

21 From: Nick Bonesteel talk at KITP UCSB

22 After Hyart et al

23 Data Energy -15 Data Energy -19

25 Mott Insulators Transition Metal Compounds Cuprates (e.g., High Tc SC) Lanthanides and Actinides Kondo Physics (Low temperature Resistance) from Magnetic Impurities Quantum Dots

26 H hub = UΣ i n i n i tσ <i,j>,σ c iσ c jσ H imp = Un n Σ k,σ t k c σ a bath k,σ + h. c. + H bath Solids have regular structure that can be modeled as lattices The Hubbard model only implements H pp and H pqqp terms This doesn t cover many of the materials we re interested in One can choose a single site in the lattice to model The effect of the rest of the lattice can be modeled in terms of its effect on this site U t k U H bath t

27 Impurity Bath

28 G solver ω ω G k, ω Feedback G n ω Δ n (ω) Model Classical Quantum G solver (ω)= c i ω c j ω

29 G imp ω 1 = ω + μ + i0 ± S h imp Σ ω Δ ω Mott Insulator, the diagram HF Solution Spin Freezing

30 E gs = H FF + θ ij H j + M(H k ) k i j Good Bad Feedback Classical Model Quantum

31 Gates Samps/Pt Samps Evals Energy Overlap Error Hours E Measures E E Speed E E E egs E E E E E Average E

32 SoL SoLi 300 Kelvin - Room CPU CMOS Memory 77K-Nitrogen CPU Superconducting Memory 4K-Helium Control Quantum Qubits.02K-He 3 /He 4

33 R Op.Unitary CR QFT H CR Control1 R Unitary Operations are defined by their matrices Meta-operations (control, adjoint) understand how to re-write the AST (including the classical generators) Joint Measurement is a fundamental operation (depends on Machine Model for implementation) Target code will be unrolled at the discretion of the target Machine Model Adjoint QFT will reverse the code order, run the loops backwards and adjoint all the unitary operations

34 The compiler front end maps the quantum algorithm to quantum intermediate language (QIL) The back end rewrites the QIL for execution on actual hardware H Different quantum computers will require different rewrites of the original QIL We have designed and built a layered architecture to support flexible rewriting CR

35 QCoDeS Where we are now: - Igor (based on Alex Johnson code circa 2002) - QTLab (Delft Python package circa 2008) - LabVIEW + Mathematica - MATLAB (various ad-hoc efforts) - Some other lightweight Python code

36 QCoDeS data = Loop(c0[-20:20:0.1], 0.1).run() data2 = Loop(c1[-15:15:1], 0.1).each( Task(c0.set, -10), qubit1.t1, fridge.mc_temp, Loop(c0[-15:15:1], 0.01).each(meter.amplitude), Task(c0.set, -10), Wait(0.1), Loop(c2[-10:10:0.2], 0.01), Task(c2.set, 5) ).run()

Quantum Computing: Transforming the Digital Age

Quantum Computing: Transforming the Digital Age Krysta Svore Quantum Architectures and Computation (QuArC) Microsoft Research Quantum Optimization Workshop 2014 Antikythera mechanism (100 BC) Babbage