Quantum computation with superconducting qubits

Transcription

1 Quantum computation with superconducting qubits Project for course: Quantum Information Ognjen Malkoc June 10, 2013

2 1 Introduction 2 Josephson junction 3 Superconducting qubits 4 Circuit and Cavity QED 5 Achievements

3 Topics covered: Superconductivity - Josephson junction Superconducting qubits Coupling qubits Cavity and Circuit QED Achievements Summary

4 1 Introduction 2 Josephson junction 3 Superconducting qubits 4 Circuit and Cavity QED 5 Achievements

5 Superconductivity - Josephson junction At low temperature effective positive interaction Excitation gap frictionless flow of electron fluid, supercurrent. Canonical quantization of circuits. Conjugate variables : Charge ˆQ, Phase: ˆφ

6 Superconductivity - Josephson junction For circuit based qubits, need dissipationless circuits. Simplest circuit LC Josephson junction : LC with nonlinearity H LC = 1 LC (a a ) (1) Energies E C, E J determine which variable well defined.

7 1 Introduction 2 Josephson junction 3 Superconducting qubits 4 Circuit and Cavity QED 5 Achievements

8 Superconducting qubits - Cooper pair box Operational sweet point n g = 0.5 Effectively pseudo-spin 1/2 system. Control parameter E J can be tuned with DC-SQUID. E C = (2e)2 2C tot H CP B = E C (ˆn n g ) 2 E J cos ( 2π Φ(t) ) (2) Φ 0 n g = 0.5 HCP B = E C (n g 1/2)σ z 1/2E J σ x. (3)

9 Superconducting qubits - Flux box Operational sweet point Φ g = 0.5 Effectively pseudo-spin 1/2 system. H F B = (2e)2 2C J ˆn 2 E J cos(φ+φ g )+ φ2 2L (4) φ g = 0.5 HF B = E S 2 σ Z + 2ξ E L E S (1/2 Φ ext Φ 0 )σ x (5)

10 Superconducting qubits - Current biased Junction Phase qubit Drive close to critical current Inherent readout mechanism H CBJ = E CJ p 2 Iφ 0 δ I 0 φ 0 cos δ (6)

11 Superconducting qubits - Transmon Hamiltonian idendical to CPB Balance between anharmonicity and sensitivity to offset charge fluctuations. E n (n g ) = ε n + ɛ n (n g ) cos(2πn g ) ɛ n (n g ) E C 2 4m+5 m! 2 π ( ) m EJ E C e 8E J /E C (7)

12 Superconducting qubits - Fluxoniom Flux-based Insensitive to charge fluctuations Retains anharmonicity

13 Superconducting qubits - Direct coupling of qubits Direct coupling Multiple designs CNOT straightforward to implement H = k=i,j [ ε k (V Xk )σ k z ] (k) ĒJkσ x + Π ij (Φ e, Φ Xi, Φ Xj )σ x (1) σ x (2) (8)

14 1 Introduction 2 Josephson junction 3 Superconducting qubits 4 Circuit and Cavity QED 5 Achievements

15 Cavity QED Interaction between cavity modes and atom. Dressed states. Vacuum rabi coupling g. H JC = H 0 + H int + H γ + H κ. (9) H int = Ψ 1 ( p ˆɛ) Ψ 0 E ZP F (a + a)σ x g = Ψ 1 ( p ˆɛ) Ψ 0 E ZP F (10)

16 Cavity QED Rydberg atoms used because of high dipole moment. Strong coupling regime. g κ, γ QND measurements recover pre-measurement distribution. QND measurements possible in dispersive regime. H JC = H 0 + H int + H γ + H κ. (11)

17 Circuit QED 1D Transmission line Fixed position of qubit. Coherence life time enhanced by isolating qubit inside cavity. Only indirect coupling to continuum. Purcell effect greater control of emission rate. g g 2 ωr cl (12) H int = (a a + 1 Ω ω r 2 )σ z. (13)

18 1 Introduction 2 Josephson junction 3 Superconducting qubits 4 Circuit and Cavity QED 5 Achievements

19 Achievements Two transmons coupled to 1D transmission line. Anti-crossing gives photon-mediated interaction strength. Two operation points I and II. Flux pulses into point II adiabatically gives U. Can be tuned to a C-phase gate. U = e iφ e iφ e iφ 11 (14

20 Achievements Dispersive readout qubit-state dependant. Gives two-qubit correlations. Concurrence of > 0.8 Coherence life time µs Sufficient for 10 single gate operations

21 Achievements Grover s search algorithm and Deutsch-Jozsa algorithm demonstrated. C-Phase gate is the Oracle. Reported a fidelity rate of 85% to obtain the right answer in Grover s algorithm.

22 Achievements Photon-mediated interaction between qubits. Distance great enough to avoid tunneling or capacitive coupling. Great news for scalability of S.C. circuits. Design with transmon in 3D S.C cavity has a life time of 100µs

23 Summary cqed offers macroscopic system ( cm ) with quantum effects. Qubits can be constructed to suppress known sources of noise by design. Rapid progress. An improvement in coherence life time, several orders of magnitude in last decade. Precision allowing for single photon detection. Potential for scalability with photon mediated coupling.