Lecture 2, March 1, 2018

Transcription

1 Lecture 2, March 1, 2018 Last week: Introduction to topics of lecture Algorithms Physical Systems The development of Quantum Information Science Quantum physics perspective Computer science perspective Further reading: Nielsen & Chuang, Cambridge University Press, 2000 This week: Components of a quantum computer The DiVincenzo criteria Quantum bits Building a quantum computer from electronic circuits Quantum electronic harmonic oscillators Quantum description of electronic circuits The role of loss Quantum bits: non-linear oscillators The Josephson effect The Cooper pair box qubit Andreas Wallraff, Quantum Device Lab 22-Feb-18 38

2 Classical Bits, their Physical Representation and Manipulation Andreas Wallraff, Quantum Device Lab 22-Feb-18 39

3 Quantum Bits Andreas Wallraff, Quantum Device Lab 22-Feb-18 41

4 The Bloch Sphere and Rotations of the Qubit State Vector Pulse sequence for qubit rotation and readout: experimental state vector on the Bloch sphere: experimental density matrix and Pauli set: Andreas Wallraff, Quantum Device Lab 22-Feb-18 42

5 Power Break: Justin Trudeau ( ) Canadian Prime Minister Justin Trudeau schools reporter on quantum computing during press conference Andreas Wallraff, Quantum Device Lab 22-Feb-18 43

6 Components of a Generic Quantum Information Processor qubits: two-level systems 2-qubit gates: controlled interactions single-bit gates readout The challenge: Quantum information processing requires excellent qubits, excellent gates, excellent readout... Conflicting requirements: perfect isolation from environment while maintaining perfect addressability M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000) Andreas Wallraff, Quantum Device Lab 22-Feb-18 44

7 The DiVincenzo Criteria for Implementing a quantum computer in the standard (circuit approach) to quantum information processing (QIP): #1. A scalable physical system with well-characterized qubits. #2. The ability to initialize the state of the qubits. #3. Long (relative) decoherence times, much longer than the gate-operation time. #4. A universal set of quantum gates. #5. A qubit-specific measurement capability. plus two criteria requiring the possibility to transmit information: #6. The ability to interconvert stationary and mobile (or flying) qubits. #7. The ability to faithfully transmit mobile qubits between specified locations. David P. DiVincenzo, The Physical Implementation of Quantum Computation, arxiv:quant-ph/ (2000) Andreas Wallraff, Quantum Device Lab 22-Feb-18 45

8 Building a Quantum Processor with Superconducting Circuits UCSB/NIST CEA Saclay TU Delft Chalmers Delft IPHT Yale NIST Chalmers, NEC Yale ETHZ NEC Chalmers JPL Yale NIST Santa-Barbara Maryland NEC with material from NIST, UCSB, Berkeley, NEC, NTT, CEA Saclay, Yale and ETHZ Andreas Wallraff, Quantum Device Lab 22-Feb-18 46

9 Conventional Electronic Circuits basic circuit elements: first transistor at Bell Labs (1947) basis of modern information and communication technology properties : classical physics no quantum mechanics no superposition principle no quantization of fields Intel Core i7-6700k Processor smallest feature size 14 nm clock speed ~ 4.2 GHz > transistors power consumption > 10 W Andreas Wallraff, Quantum Device Lab 22-Feb-18 48

10 Classical and Quantum Electronic Circuit Elements basic circuit elements: charge on a capacitor: quantum superposition states of: charge Q flux φ current or magnetic flux in an inductor: Q,φ are conjugate variables quantum uncertainty relation Andreas Wallraff, Quantum Device Lab 22-Feb-18 49

11 Constructing Linear Quantum Electronic Circuits basic circuit elements: harmonic LC oscillator: energy: electronic photon typical inductor: L = 1 nh wire in vacuum L ~ 1 nh/mm typical capacitor: C = 1 pf size 10 x 10 µm 2 and dielectric AlOx (ε = 10) of 10 nm thickness: C ~ 1 pf classical physics: quantum mechanics: Review: M. H. Devoret, A. Wallraff and J. M. Martinis, condmat/ (2004) Andreas Wallraff, Quantum Device Lab 22-Feb-18 50

12 Quantization of an Electronic Harmonic LC Oscillator Charge on capacitor Flux in inductor Voltage across inductor Classical Hamiltonian: Conjugate variables: Hamilton operator: Flux and charge operator: Commutation relation: Andreas Wallraff, Quantum Device Lab 22-Feb-18 51

13 Voltages and Currents as Creation and Annihilation Operators Hamilton operator of harmonic oscillator in second quantization: Creation operator Annihilation operator Number operator Charge/voltage operator With characteristic impedance: Flux/current operator Andreas Wallraff, Quantum Device Lab 22-Feb-18 52

14 Why Superconductors? Cooper pairs: bound electron pairs Bosons (S=0, L=0) 2 chunks of superconductors macroscopic wave function density of states: D(E) normal metal superconductor How to make qubit? single non-degenerate macroscopic ground state elimination of low-energy excitations 1 2 Cooper pair density n i and global phase δ i for T < T c : vanishing internal electrical resistance R int Superconducting materials (for electronics): Niobium (Nb): 2 S /h = 725 GHz, T c = 9.2 K Aluminum (Al): 2 S /h = 100 GHz, T c = 1.2 K phase quantization: δ = n 2 π flux quantization: φ = n φ 0 = n h/2e δ φ M. Tinkham, Introduction to Superconductivity, McGraw-Hill Andreas Wallraff, Quantum Device Lab 22-Feb-18 53

15 Internal and External Dissipation in an LC Oscillator internal losses: conductor, dielectric external losses: radiation, coupling total losses quality factor with impedance excited state decay rate for Q = 10 6 and ω 0 ~ 2π 1.5 GHz decay rate Γ 1 = 10 khz corresponding to life time T 1 = 100 µs Andreas Wallraff, Quantum Device Lab 22-Feb-18 54