Let's Build a Quantum Computer!

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1 Let's Build a Quantum Computer! 31C3 29/12/2014 Andreas Dewes Acknowledgements go to "Quantronics Group", CEA Saclay. R. Lauro, Y. Kubo, F. Ong, A. Palacios-Laloy, V. Schmitt PhD Advisors: Denis Vion, Patrice Bertet, Daniel Esteve

2 Motivation

3 Outline Quantum Computing What is it & why do we want it Quantum Algorithms Cracking passwords with quantum computers Building A Simple Quantum Processor Superconductors, Resonators, Microwaves Recent Progress in Quantum Computing Architectures, Error Correction, Hybrid Systems

4 Why Quantum Computing? Quantum physics cannot be simulated efficiently with a classical computer. 1) A computer that makes use of quantum mechanics can do it. It can also be faster for some other mathematical problems. 1)

5 Classical Computing

6 Bits 0 1

7 Bit Registers In A n bits In B... In.. N = 2 n states 0 00, 0 01,, 1 11

8 Logic Gates In A In B f Out

9 Logic Gates NAND-Gate In A In B In A In B Out 0 0 f Out

10 A problem: Password cracking ************ Launch Missile Forgot your pasword?

11 N = 2 n possibilities A Password Checking Function In A In B... f j In.. Out f = 0 i j 1 i = j i, j ,00 001,,

12 A Cracking Algorithm 1. Set register state to i = Calculate f(i) 3. If f(i)= 1, return i as solution 4. If not, increment i by 1 and go to (2)

13 Time Complexity of our Algorithm number of evaluations of f search space size - N

14 Quantum Computing

15 Quantum Bit / Qubit 1> 0> Qubit Two-Level Atom

16 Quantum Superposition 0> 1> ψ = a a e iφ 1

17 How to imagine superposition

18 Quantum Measurements 0> 1> 0 1 ψ = a a e iφ 1

19 Quantum Measurements 0> 0 1 ψ = 0 ; probability = a

20 Quantum Measurements 1> 0 1 ψ = 1 ; probability = 1-a

21 QuBit Registers A B Z... A B Z

22 QuBit Registers A B Z... AB Z

23 Multi-Qubit Superpositions 0.5 1/ / / n times 0.5 n/

24 Multi-Qubit Superpositions 0.5 1/ / / N = 2 n states in superposition 0.5 n/

25 Multi-Qubit Superpositions omitting normalizations

26 Quantum Gates f 0 00 f(0 00) f(0 01) f(1 11)

27 Quantum Entanglement f f( 01 ) =

28 Summary: Qubits Quantum-mechanical two-level system Can be in a superposition state A measurement will yield either 0 or 1 and project the qubit into the respective state Can become entangled with other qubits

29 Back to business... ************ Launch Missile Wrong password!

30 Quantum Searching our Password f j

31 But how we get the solution? f j result = p = 1 N 0 p = 1 1 N

32 Solution: Grover Algorithm repeat N times f j Grover Operator result = p 1 0 p 0 Grover L.K.: A fast quantum mechanical algorithm for database search, Proceedings, 28th Annual ACM Symposium on the Theory of Computing, 1996

33 Efficiency of Grover Search (for 10 qubits) N = iterations required

34 Time Complexity Revisited number of evaluations of f quantum speed-up search space size N

35 Runtime Number Factorization: Shor Alg. r = q s; q,s prime numbers problem size n (number of bits)

36 How to Build a Quantum Processor?

37 University of Innsbruck ( University of Santa Barbara ( photo not CC-licensed photo not CC-licensed Ion Trap Quantum Processors Superconducting Quantum Processors...and many more technologies: Nuclar magnetic resonance, photonic qubits, quantum dots, electrons on superfluid helium, Bose-Einstein condensates...

38 A Simple Two-Qubit Processor Using superconducting qubits (Transmons - Wallraff et al., Nature 431 (2004) ) a) 38 1 mm 100 m 1 m Dewes et al. Phys. Rev. Lett. 108, (2012)

39 mount on microwave PCB and wirebond thermally * anchor and shield from EM fields 39 put in dilution cryostat 20 mk

40 f 01 [f(t)], a(t) Y( /2) Z( /2) X( /2) iswap iswap Running Grover-Search for 2 Qubits 40 Prepare superposition Calculate f j Apply Grover operator Readout 0> Y /2 Z - /2 X / > Y /2 Z - /2 X /2 0 1 readout iswap iswap ns

41 iswap iswap Dewes et. al., PRB Rapid Comm 85 (2012) Single-Run Success Probability 41 Prepare superposition Calculate f j Apply Grover operator Readout 0> Y /2 Z ± /2 X / > Y /2 Z ± /2 X / % f 00 f 01 f 10 f % 62 % 52 % classical benchmark (with "I'm feeling lucky" bonus)

42 Challenges Decoherence Environment measures and manipulates the qubit and destroys its quantum state. Gate Fidelity & Qubit-Qubit Coupling Difficult to reliably switch on & off qubit-qubit coupling with high precision for many qubits And some more: High-Fidelity state measurement, qubit reset,...

43 Recent Trends in Superconducting Quantum Computing

44 Better Qubit Architectures Better Qubits and Resonators Quantum Error Correction Hybrid Quantum Systems (photos not included since not CC-BY licensed)

45 coherence time - ns Moore's Law: Quantum Edition (for superconducting qubits) Superconducting Qubits: Reported Coherence Time (T ) 3D Cavities Quantronium Circuit QED 10 Cooper pair box year

46 Summary Quantum computers are coming!...but still there are many engineering challenges to overcome... Bad News Likely that governments and big corporations will be in control of QC in the short term.

47 Thanks! More "quantum information": Diamonds are a quantum computer s best friend Tomorrow, at 12:45h in Hall 6 by Nicolas Wöhrl Get in touch with me: ich@andreas-dewes.de

Electrical quantum engineering with superconducting circuits

1.0 10 0.8 01 switching probability 0.6 0.4 0.2 00 P. Bertet & R. Heeres SPEC, CEA Saclay (France), Quantronics group 11 0.0 0 100 200 300 400 swap duration (ns) Electrical quantum engineering with superconducting