Principes de l'ordinateur quantique

11/01/2018
Auteurs : Daniel Estève
OAI : oai:www.see.asso.fr:20797:22289
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Principes de l'ordinateur quantique

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PRINCIPES DE L’ORDINATEUR QUANTIQUE ELECT QUAN RONICS UM GROUP Daniel ESTEVE Quantum computing: the rationale (1) Quantum systems are hard to crack,….. quantum resources needed! R. Feynman R. Jozsa D. Deutsch (1) 1982: quantum system needed for simulating a quantum system ! (2) 1985 : entanglement makes quantum algorithms more powerful complexity classes different for classical and quantum hardware ! Universal Turing machine (3) 1995: quantum algorithms solving ‘NP’ problems Main route: the gate-based quantum processor Unitary evolution of a n quantum bit register H 0 0 0 X Y H Z 1 2 3 4.... 2 1 2 3 2 0,1 , , ... N N k i i i i i i a i i i i   1 0 qubit N = 2n computational basis states 010001...1 p  n ideal projective readout Entanglement delivers computing power Emulation world record: 46 on the best hcp machine; Atos 40 on server A POTENTIAL BREAKTHROUGH IN HPC (?) Big players nevertheless attracted, strong partnerships developed Use-cases considered Many-body physics: quantum chemistry, materials … Linear algebra: quantum inversion of sparse matrices Quantum machine learning Strong Eu flagship initiative QC well suited for treating electrons on orbitals and evaluating energy vs parameters needs: >100 qubits small scale demos: variational quantum eigensolver : IBM Kandala et al., Nature 549, 242 (2017) quantum RAM needed ! HHL algorithm Harrow, Hassidim, Lloyd, PRL 103, 150502 (2009) quantum RAM needed ! See Preskill 2018 arXiv: 1801.00862 Gao, Zhang, Duan arXiv:1711.02038 The gate-based quantum processor A quantum register fitted with a universal set of gates & individual qubit readout 0 1 ? 1 0 U2 U1 0 1 ? 1 0 … … U1 … … - single qubit gates 1 U - qubit: 2-level-system resetable to 1 0    a b 0 - a 2-qubit entangling gate 2 U universal set - qubit readout with high fidelity Decoherence Pure dephasing ( ) 0 1   i j t j a be 1 0 01( )  i t i(t) 1 1 2 2 2         T   2 ( )    t i t e e low-frequency noise low-frequency noise 0 1 0 1 2 1 2 1 0,0,...,0 ,0,...,0 , ,..., .. 1 1,1,... 1 . ,             n n Register 1 0 01  Relaxation (spontaneous emission) 1 1 1    T 1 j qubit j environnement Note: qubits cannot be copied! error correction cannot be based on basic redundancy More later Physical implementations ? NMR non scalable nuclear spins are COHERENT But: no perfect initialisation, no single qubit readout, ~1 molecule / algorithm All quantum coherent systems considered Identical single photon sources needed Physical implementations Photons are COHERENT photons weakly interact! other strategy needed measurement based QC resource in an initial cluster state, linear operations, photon detection scalability issue: Postselection overhead Photons ? Trapped ions Physical implementations scalable design The most advanced platform: 20 qubits, hifi gates & readout qubit: electronic levels individual ions addressed & read interaction: Raman transitions collective 1D phonon excitations Scalability : system complexity 50 qubit demonstrator under construction (3 Y) Innsbruck (R. Blatt’s team) Gate-based Quantum computing: electrical circuit implementations superconducting qubits: 2, 4,…19 qubits elementary algorithms & protocols demonstrated Quantum dots in semiconductor structures A. Morello UNSW, Sydney Quantronics 2014 Coherence issue, but microfabrication techniques help scalability From Rigetti Computing arXiv: 1712.05771 A simple quantum circuit based on the Josephson junction ˆ  N̂ bias circuit ext circuit  and N conjugated variables 1 single degree of freedom: Josephson junction 200 nm w01 w12 w23 w34 Transmon regime: a non linear resonator at the single photon level 1 0 2 3  2 ˆ HO H H Kn   Kerr constant ˆ Q ˆ  The Cooper pair box an artificial atom Running quantum algorithms on elementary processors Martinis Lab, UC Santa Barbara Yamamoto et.al. , PRB 82 2010 , Nat Phys 2012 Quantronics, CEA Dewes et. al., PRL & PRB 2012 the Grover search algorithm Shor factorization algorithm (of 15) Classical search: O(N) steps Quantum search : O(√N) steps 4 object benchmark case: 1 try enough!   01 00 11 10 i Oracle 11 iSWAP Z±/2 Z±/2 the four oracles 1 mm 200 µm qubits readout resonator coupling capacitor frequency control (Quantronics 2011) An elementary superconducting processor fixed capacitive coupling  Running quantum algorithms on elementary processors Martinis Lab, UC Santa Barbara Yamamoto et.al. , PRB 82 2010 , Nat Phys 2012 Quantronics, CEA Dewes et. al., PRL & PRB 2012 the Grover search algorithm Shor factorization algorithm (of 15) Classical search: O(N) steps Quantum search : O(√N) steps 4 object benchmark case: 1 try enough   01 00 11 10 i 67 % 55 % 62 % 52 % f00 f01 f10 f11 classical query & check ‘quantum speed-up’ Oracle 13 Dewes et al., PRB 85, 2012 THE SCALABILITY issue : fighting decoherence STRATEGIES ? More robust qubits Schrödinger cat states in high Q resonators & dissipation engineering Yale, LPA-INRIA coherent microscopic entities Fault-tolerant quantum computing Data measurement IBM, Google, QuTech preliminary results Impurity spins in solids 209Bi and/or Keep track of errors Huge resource overhead 1 logical qubit >> 1000 physical qubits surface code fabric see Fowler et al, PRA 86 (2012) Inspired from Kitaev codes UCSB-Google Kelly et al., PRA94 A new route : spins coupled to superconducting circuits Bi+ e- • Electronic spin = 1/2 • Nuclear spin I=9/2 • Large hyperfine coupling