When and How will we Build a Quantum Computer?

Transcription

1 When and How will we Build a Quantum Computer? M. Mariantoni Institute for Quantum Computing, University of Waterloo 4 th ETSI/IQC Workshop on Quantum-Safe Cryptography

2 Why? Quantum simulations Digital quantum simulators o Quantum chemistry/strongly correlated electrons with O(N 4 ) instead of O(N), N: Orbitals Phys. Rev. A 92, (2015) Analog quantum emulators Quantum walks Exit from graph in time O(log N) instead of O(N 1/6 ), N: Steps o Boolean formulae o Markov chains Linear equations From time poly(n) to poly(log N) for NxN matrix (with FEM) Search and optimization O(2 m/2 poly(m)) rather than the O(2 m poly(m)) for certificate length m (Grover) Adiabatic optimization? Slow enough to remain in ground state Cryptography From exp(o(log N) 1/3 (log log N) 2/3 )) 12 to O(log N) 3, with N integer to factorize npj Quantum Information 2, (2016)

3 How? The Stages of Quantum Computing Science 339, (2013)

4 Operations on Single Physical Qubits Nature 398, (1999)

5 The Stages of Quantum Computing Science 339, (2013)

6 Algorithms on Multiple Physical Qubits Science 334, (2011) Superconducting qubit: Nonlinear LLLL oscillator LL: Josephson junctions (nonlinearity) Operated at 10 mk Controlled by microwaves, ff q 5 GHz Nearest neighbor interactions

7 The Stages of Quantum Computing Science 339, (2013)

8 QND Measurements for Error Correction and Control Qubit control XX and ZZ: 99.92% CNOT: 99.4% in 40 ns (R. Barends et al., Nature 508, (2014)) Qubit measurement MM zz 99.8% in 140 ns (E. Jeffrey et al., Phys. Rev. Lett. 112, (2014)) J. Kelly et al., Nature 519, (2015) A.D. Córcoles, Nat. Commun. 6, 6979 (2015) D. Ristè et al., Nat. Commun. 6, 6983 (2015)

9 The Stages of Quantum Computing Science 339, (2013)

10 Logical Qubit: Surface Code 2D grid with nearest neighbor interactions Physical qubit: Two-level system with states g and e Energy separation = hff q g e : XX rotations Tuning ff q : ZZ rotations e : MM zz measurement Entangling gates between neighboring qubits (e.g., CNOT) XX errors: e g (bit flip) ZZ errors: g + e g e (phase flip) A.G. Fowler, M.M., J.M. Martinis, and A.N. Cleland, Phys. Rev. A 86, (2012)

11 Surface Code: Basic Definitions Face and vertex (ZZ- and XX-stabilizers) A.Yu. Kitaev, Annals of Physics 303, 2 (2003)

12 Surface Code: Stabilizers ZZ-stabilizer ψ 1 1 g z ψ 3 2 M 3 Zˆ Zˆ Zˆ Zˆ = ψ Z1234 ψ Z1234 = ψ 2 4 ψ 4

13 Surface Code: Stabilizers Quiescent state Code distance dd = 5

14 Surface Code: Quantum Error Detection Time (cycles) Xˆ Ẑ Bit-flip error Xˆ Zˆ Zˆ Zˆ Zˆ ( Xˆ ψ ) Z ( Xˆ ψ ) Phase-flip error Ẑ Xˆ Xˆ Xˆ Xˆ 1234 ( Zˆ ψ ) X ( Zˆ ψ ) E. Dennis, A. Y. Kitaev, A. Landahl, and J. Preskill, J. Math. Phys. 43, 4452 (2002) time Detection effective XX, ZZ, CNOT, and MM zz must be better than pp th 10 1 (FF 99%) 3D ZZ 2 lattice gauge theory with quenched disorder

15 Surface Code: Error Chains and Logical Qubits PP L ~0.03 pp pp th dd/2 Logical error rate PP L FF % pp th Physical error rate pp FF 99.9%

16 QND Measurements for Error Correction and Control Qubit control XX and ZZ: 99.92% CNOT: 99.4% in 40 ns (R. Barends et al., Nature 508, (2014)) Qubit measurement MM zz 99.8% in 140 ns (E. Jeffrey et al., Phys. Rev. Lett. 112, (2014)) Yet, not truly scalable (extensible) Quantum-classical interface = Wiring Classical electronics J. Kelly et al., Nature 519, (2015) A.D. Córcoles, Nat. Commun. 6, 6979 (2015) D. Ristè et al., Nat. Commun. 6, 6983 (2015)

17 The Wiring Problem NN Wire bonds are not scalable ~4NN Two-dimensional quantum architecture ~NN 2 NN Possible solution: The quantum socket three-dimensional wires J.H. Béjanin M.M., Phys. Rev. App. (2016) D-Wave Systems Inc.

18 The Quantum Socket

19 Extensible Architecture 100 Qubits (= 1 Logical) qubits: 72 mm 72 mm Largest square in 4" wafer C.R.H.McRae M.M., in preparation npj Quantum Information 2, (2016)

20 When??? years?? $ 10/15 years (?) 1 B$ (?) 5/10 years ~ 100 M$ (?) 2/3 years ~ 10 M$ Science 339, (2013)

21 IQC team: J.H. Béjanin T.G. McConkey J.R. Rinehart C.T. Earnest C.R.H. McRae D. Shiri (now at Chalmers) J.D. Bateman (now at UofT) Y. Rohanizadegan Waterloo MBE team: J. Tournet (now at Monpellier) D. Gosselink M. Jaikissoon Z.R. Wasilewski Ingun team: B. Penava P. Breul S. Royak M. Zapatka Quantum Google: A.G. Fowler