Lecture 6, March 30, 2017

Size: px

Start display at page:

Download "Lecture 6, March 30, 2017"

Leon Tate
5 years ago
Views:

1 Lecture 6, March 30, 2017 Last week: This week: Brief revisit of the Transmon qubit Gate charge insensitivity Anharmonicity and driving of qubit Tuning by magnetic flux Qubit-Qubit coupling in circuit QED 2-qubit gates by virtual photon interaction Qubit-Qubit coupling in circuit QED The controlled NOT gate Creating entangled states The Toffoli gate Single Photons generation and Qubit Photon Entanglement J. Koch et al., Phys. Rev. A 76, (2007) A. Blais, et al., Phys. Rev. A 69, (2004) Andreas Wallraff, Quantum Device Lab 30-Mar

Reading: Books Nielsen, M. A. & Chuang, I. L.

University Press, New York, USA, (2006) Gerry, C. & Knight, P. L.

2 Reading: Books Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information, Cambridge University Press (2000) Haroche, S. & Raimond, J.-M.; Exploring the Quantum: Atoms, Cavities, and Photons, Oxford University Press, New York, USA, (2006) Gerry, C. & Knight, P. L. Introductory Quantum Optics, Cambridge University Press (2005) Andreas Wallraff, Quantum Device Lab 30-Mar

3 Reading: Papers, Reviews, Other Material Read (some of) the research papers mentioned on the slides. First read abstract and discussion/summary Try to understand essence of the paper reading it once, not caring for the details Don t be put off by not understanding everything immediately Read a different paper to get another authors view of the same subject Research you will do in the lab (Semester Thesis, Master Thesis) aims at going beyond (all of) the papers that you read in preparation. E.g.: A. Blais, et al., PRA 69, (2004) Quantum Machines: Measurement and Control of Engineered Quantum Systems: Lecture Notes of the Les Houches Summer School: Volume 96, July 2011 chapters: (link on QIP II web site) 3 Circuit QED: superconducting qubits coupled to microwave photons S. M. Girvin Department of Physics, Yale University 4 Quantum logic gates in superconducting qubits J. M. Martinis Department of Physics, University of California, Santa Barbara, CA 93111, USA 6 Readout of superconducting qubits D. Esteve Quantronics Group Service de Physique de l Etat Condensé/IRAMIS/DSM (CNRS URA 2464) CEA Saclay ETH Zurich, TU Delft, (Imperial College), RWTH Aachen IDEA league summer school series. Lectures slides, videos, homework sets: Andreas Wallraff, Quantum Device Lab 30-Mar

The Economist Quantum leaps An entangled web: The promise of quantum encryption Cue bits: Why all eyes are on quantum computers Here, there and everywhere: Quantum technology is beginning to come

4 The Economist Quantum leaps An entangled web: The promise of quantum encryption Cue bits: Why all eyes are on quantum computers Here, there and everywhere: Quantum technology is beginning to come into its own Commercial breaks: The uses of quantum technology Program management: Quantum computers will require a whole new set of software Andreas Wallraff, Quantum Device Lab 30-Mar

5 Industry & Startups IBM Q Google/UCSB Rigetti Computing Microsoft D-Wave Systems Intel Andreas Wallraff, Quantum Device Lab 30-Mar

evolution of states during interaction: Initial state intermediate state final state

6 Virtual Photon Exchange Controlled by Detuning qubit 1 qubit 2 Frequency J Frequency tuning by magnetic flux: tunable interaction time τ compensation of dynamic phase evolution of states during interaction: Initial state intermediate state final state Salathé et al., PRX 5, (2015) Andreas Wallraff, Quantum Device Lab 30-Mar

drive lines four flux bias lines tune qubit transition 1 mm Salathé et

7 4 Qubit Device with Nearest Neighbor Resonator-Mediated Coupling four qubits four resonators mediate coupling two readout lines four microwave drive lines four flux bias lines tune qubit transition 1 mm Salathé et al., PRX 5, (2015) Andreas Wallraff, Quantum Device Lab 30-Mar

8 Virtual Photon Coupling (01-10): Calculation Initial condition: Qubit 1: 0 Qubit 2: 1 Single qubit Bloch spheres Pure state on surface Fully mixed state in center Pauli operator expectation values Single qubit IX, IY, IZ and XI, YI, ZI Two qubit correlators XX, XY, XZ, YX, Entanglement measure: negativity N G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, (2002). Salathé et al., PRX 5, (2015) Andreas Wallraff, Quantum Device Lab 30-Mar

Virtual Photon Coupling (01-10): Experimental Data Maximal entanglement at (2n+1) π/2 for n = 0, 1,2,3, Maximally mixed single qubit states Maximal two qubit correlators Maximal negativity High

9 Virtual Photon Coupling (01-10): Experimental Data Maximal entanglement at (2n+1) π/2 for n = 0, 1,2,3, Maximally mixed single qubit states Maximal two qubit correlators Maximal negativity High fidelity with expected state maximally entangled state Indicated by state fidelity: 99.7 % Experimental data extracted from 2-qubit quantum state tomography Salathé et al., PRX 5, (2015) Andreas Wallraff, Quantum Device Lab 30-Mar

10 Virtual Photon Coupling (01-10): Calculation Initial conditions: Qubit 1 : 0 Qubit 2: (0+1) Salathé et al., PRX 5, (2015) Andreas Wallraff, Quantum Device Lab 30-Mar

Virtual Photon Coupling (01-10): Experimental Data Maximal entanglement at (2n+1) π/2 for n = 0, 1, 2, 3, Partially mixed single qubit states Non-zero two qubit

11 Virtual Photon Coupling (01-10): Experimental Data Maximal entanglement at (2n+1) π/2 for n = 0, 1, 2, 3, Partially mixed single qubit states Non-zero two qubit correlators Non-zero negativity High fidelity with expected state state fidelity: F = 99.4 % Salathé et al., PRX 5, (2015) Andreas Wallraff, Quantum Device Lab 30-Mar

12 Universal Two-Qubit Non-Adiabatic Controlled Phase Gate (11-20) Make use of qubit states beyond 0, 1 qubit A qubit B Interaction mediated by virtual photon exchange through resonator Full 2π rotation induces phase factor -1 Tune levels into resonance using magnetic field proposal: F. W. Strauch et al., Phys. Rev. Lett. 91, (2003). first implementation: L. DiCarlo et al., Nature 460, 240 (2010). Andreas Wallraff, Quantum Device Lab 30-Mar

Universal Two-Qubit Controlled Phase Gate Make use of qubit states beyond 0, 1 qubit A qubit B Qubits in states 01, 10 and 00 do not interact and thus acquire no phase shift C-Phase gate: Universal

13 Universal Two-Qubit Controlled Phase Gate Make use of qubit states beyond 0, 1 qubit A qubit B Qubits in states 01, 10 and 00 do not interact and thus acquire no phase shift C-Phase gate: Universal two-qubit gate. Used together with single-qubit gates to create any quantum operation. proposal: F. W. Strauch et al., Phys. Rev. Lett. 91, (2003). first implementation: L. DiCarlo et al., Nature 460, 240 (2010). Andreas Wallraff, Quantum Device Lab 30-Mar

14 Two-Excitation Manifold of System Spectroscopy of higher excited states Two-excitation manifold Avoided crossing (160 MHz) Flux bias on right transmon (a.u.) Strauch et al., PRL (2003): proposed using interactions with higher levels for computation in phase qubits slide adapted from L. DiCarlo (TUD) Andreas Wallraff, Quantum Device Lab 30-Mar

15 Adiabatic Controlled Phase Gate f + f t f ϕa = 2 π δ fa() t dt t excitation manifold 1-excitation manifold 01 ζ iϕ 11 e e iϕ 10 iϕ 01 e 0 f ϕ11 = ϕ10 + ϕ01 2 π ζ() t dt 10 1 t t 0 Flux bias right transmon (a.u.) slide credit: L. DiCarlo (TUD) Andreas Wallraff, Quantum Device Lab 30-Mar

16 Implementing the C-Phase Gate with One Flux Pulse Uˆ e i e 0 iϕ iϕ10 e 0 ϕ Uˆ Adjust timing of flux pulse so that only quantum amplitude of 11 acquires a minus sign: How to verify the operation of this gate? slide credit: L. DiCarlo (TUD) Andreas Wallraff, Quantum Device Lab 30-Mar

17 Process Tomography: C-Phase Gate arbitrary quantum process decomposed into χ operator basis positive semi definite Hermitian matrix characteristic for the process Controlled phase gate Measured χ-matrix: Re[χ] ( Im[χ] <0.04) Andreas Wallraff, Quantum Device Lab 30-Mar

18 Process Tomography of a C-NOT Gate Controlled-NOT gate Measured χ-matrix: Re[χ] ( Im[χ] <0.08) = Andreas Wallraff, Quantum Device Lab 30-Mar

, ETHZ F = 88%: DiCarlo et al. Nature 467, (2010) F = 62%: Neeley et al.

19 GHZ State with 3 Qubits Protocol Measured (color) and ideal (wireframe) density matrix: Real Imaginary GHZ class states, e.g. 000>+ 111> created using: single qubit gates C-PHASE gates This data: J. Heinsoo et al., ETHZ F = 88%: DiCarlo et al. Nature 467, (2010) F = 62%: Neeley et al. Nature 467, (2010) F = 96%: Barends et al. Nature 508, (2014) Fid(σσ,ρρ) = Tr ρρσσ ρρ 2 = 88.9% (MLE) Andreas Wallraff, Quantum Device Lab 30-Mar

= 74.8% (MLE) This data: J. Heinsoo et al., ETHZ F = 86.

20 GHZ-like State with 4 Qubits Protocol Measured (color) and ideal (wireframe) density matrix: Real Imaginary Fid(σσ,ρρ) = Tr ρρσσ ρρ 2 = 74.8% (MLE) This data: J. Heinsoo et al., ETHZ F = 86.3%: Barends et al. Nature, 2014, 508 Andreas Wallraff, Quantum Device Lab 30-Mar

21 A Three Qubit Gate: The Toffoli Gate proposed by Tommaso Toffoli in 1980 any reversible computation can be performed with only the Toffoli gate function: inverts qubit C only if qubits A and B are in selected basis states applications: for universal reversible classical computation for simplification of complex quantum circuits used in quantum error-correction schemes (essential for any practical quantum processor) Andreas Wallraff, Quantum Device Lab 30-Mar

22 Implementation of a Toffoli Gate with only single and two-qubit gates requires: 6 CNOT gates 10 single qubit gates Inefficient decomposition Not ideal at limited coherence Alternative Approach suggested by T. C. Ralph et. al., PRA 75, (2007): use higher levels (qutrits) for efficient decomposition Andreas Wallraff, Quantum Device Lab 30-Mar

23 Circuit Diagram Alternative approach: use qubit-qutrit gates for the more efficient decomposition! CC-PHASE inverts the sign for only one basis state Equivalent to Toffoli up to single qubit rotations Initial state: Final state A B π 3π C same amount of resources, more efficient A. Fedorov et al., Nature (London) 481, 170 (2012) Andreas Wallraff, Quantum Device Lab 30-Mar

making use of avoided crossing between 11 and 20 states A. Fedorov et al.

24 Implementation sequence of: five resonant single qubit microwave pulses three single qubit flux pulses realizing qubit-qubit and qubit-qutrit gates making use of avoided crossing between 11 and 20 states A. Fedorov et al., Nature (London) 481, 170 (2012) Andreas Wallraff, Quantum Device Lab 30-Mar

Process Tomography of Toffoli Gate Fully characterizes the process by evaluating χ-matrix (ML) Fidelity 69 +- 3 % Monte Carlo process certification does not rely on maximum-likelihood procedures [da

25 Process Tomography of Toffoli Gate Fully characterizes the process by evaluating χ-matrix (ML) Fidelity % Monte Carlo process certification does not rely on maximum-likelihood procedures [da Silva et al., PRL 107, (2011), Steffen et al., Phys. Rev. Lett. 108, (2012)] % A. Fedorov et al., Nature (London) 481, 170 (2012) Andreas Wallraff, Quantum Device Lab 30-Mar

Truth Table of Toffoli Gate characterizes the action of the Toffoli gate on the basis input states Fidelity This implementation: Realization and full characterization of 3 qubit Toffoli gate, also

26 Truth Table of Toffoli Gate characterizes the action of the Toffoli gate on the basis input states Fidelity This implementation: Realization and full characterization of 3 qubit Toffoli gate, also with efficient process certification A. Fedorov et al., Nature (London) 481, 170 (2012) L. Steffen et al., Phys. Rev. Lett. 108, (2012) Related work: Toffoli gate used for correcting an artificial error in an error correction protocol M. D. Reed et al., Nature (London) 482, 382 (2012) Realization of Toffoli-class gate with only two qubits (used resonator as 3 rd qubit) and limited characterization (phase fidelity) M. Mariantoni et al., Science 334, 61 (2011) A. Fedorov et al., Nature (London) 481, 170 (2012) Andreas Wallraff, Quantum Device Lab 30-Mar

27 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 30-Mar

Quantum Computing with Superconducting Circuits Protocols: Teleportation L.

, PRL 108, 040502 (2012) Architectures: Circuit QED A. Blais et al.

Sillanpaa et al., Nature 449, 438 (2007) H. Majer et al.

DiCarlo et al., Nature 460, 240 (2009) L. DiCarlo et al.

, Nature 481, 170 (2012) Error Correction M. Reed et al.

28 Quantum Computing with Superconducting Circuits Protocols: Teleportation L. Steffen et al., Nature 500, 319 (2013) M.. Baur et al., PRL 108, (2012) Architectures: Circuit QED A. Blais et al., PRA 69, (2004) A. Wallraff et al., Nature 431, 162 (2004) M. Sillanpaa et al., Nature 449, 438 (2007) H. Majer et al., Nature 449, 443 (2007) M. Mariantoni et al., Science 334, 61 (2011) R. Barends et al., Nature 508, 500 (2014) Deutsch & Grover Algorithms, Toffoli Gate L. DiCarlo et al., Nature 460, 240 (2009) L. DiCarlo et al., Nature 467, 574 (2010) A. Fedorov et al., Nature 481, 170 (2012) Error Correction M. Reed et al., Nature 481, 382 (2012) Corcoles et al., Nat. Com. 6, 6979 (2015) Ristè et al., Nat. Com. 6, 6983 (2015) Kelly et al., Nature 519, (2015) Adiabatic Quantum Computation R. Barends et al., Nature, 534, (2016) Andreas Wallraff, Quantum Device Lab 30-Mar

Quantum Simulation Applications with Superconducting Circuits Quantum Chemistry:

Atomic Physics: two-mode fermionic Hubbard models Barends et al., Nat. Com.

, PRX 6, 031007 (2016) Solid State and Atomic Physics: Digital simulation of

cavity and/or qubit arrays Houck et al., Nat. Phys. 8, 292 (2012) Raftery et al.

29 Quantum Simulation Applications with Superconducting Circuits Quantum Chemistry: simulation of correlated systems using variational approach Solid State and Atomic Physics: two-mode fermionic Hubbard models Barends et al., Nat. Com. 6, 7654 (2015) Eichleret al., PRX 5, (2015) O Malley et al., PRX 6, (2016) Solid State and Atomic Physics: Digital simulation of exchange, Heisenberg, Ising spin models Photonics: Analog simulations with cavity and/or qubit arrays Houck et al., Nat. Phys. 8, 292 (2012) Raftery et al., PRX 4, (2014) Salathe et al., PRX 5, (2015) Andreas Wallraff, Quantum Device Lab 30-Mar

Quantum Optics with Superconducting Circuits Strong Coherent

, Nature 431, 162 (2004) Schuster et al.

, Nature 454, 315 (2008) Deppe et al., Nat. Phys.

5, 105 (2009) Microwave Fock and Cat States Hofheinz et al.

, Nature 459, 546 (2009) Kirchmair et al.

Castellanos-Beltran et al., Nat. Phys. 4, 928 (2008) Abdo et al.

30 Quantum Optics with Superconducting Circuits Strong Coherent Coupling Chiorescu et al., Nature 431, 159 (2004) Wallraff et al., Nature 431, 162 (2004) Schuster et al., Nature 445, 515 (2007) Root n Nonlinearities Fink et al., Nature 454, 315 (2008) Deppe et al., Nat. Phys. 4, 686 (2008) Bishop et al., Nat. Phys. 5, 105 (2009) Microwave Fock and Cat States Hofheinz et al., Nature 454, 310 (2008) Hofheinz et al., Nature 459, 546 (2009) Kirchmair et al., Nature 495, 205 (2013) Vlastakis et al., Science 342, 607 (2013) Wang et al., Science 352, 1087 (2016) Parametric Amplification & Squeezing Castellanos-Beltran et al., Nat. Phys. 4, 928 (2008) Abdo et al., PRX 3, (2013) Waveguide QED Qubit Interactions in Free Space Astafiev et al., Science 327, 840 (2010) I.-C. Hoi et al. PRL 107, (2011) van Loo et al., Science 342, 1494 (2013) Andreas Wallraff, Quantum Device Lab 30-Mar

Hybrid Systems with Superconducting Circuits Quantum Dots: CNT, Gate Defined 2DEG, nanowires

, Nature 490, 380 (2012) Radiation Emission: Liu et al.

, PRL 115, 046802 (2015) Strong Coupling Cavity QED: Mi et al.

05214 (2016) Spin Ensembles: e.g. NV centers Schuster et al.

, PRL 105, 140502 (2010) Polar Molecules, Rydberg, BEC Rabl et al, PRL 97, 033003 (2006)

31 Hybrid Systems with Superconducting Circuits Quantum Dots: CNT, Gate Defined 2DEG, nanowires Delbecq et al., PRL 107, (2011) Frey et al., PRL 108, (2012) Petersson et al., Nature 490, 380 (2012) Radiation Emission: Liu et al., Science 347, 285 (2015) Stockklauser et al., PRL 115, (2015) Strong Coupling Cavity QED: Mi et al., Science 355, 156 (2017) Stockklauser et al., PRX 7, (2017) Bruhat et al., arxiv: (2016) Spin Ensembles: e.g. NV centers Schuster et al., PRL 105, (2010) Kubo et al., PRL 105, (2010) Polar Molecules, Rydberg, BEC Rabl et al, PRL 97, (2006) Andre et al, Nat. Phys. 2, 636 (2006) Petrosyan et al, PRL 100, (2008) Verdu et al, PRL 103, (2009) Nano-Mechanics Teufel et al., Nature 475, 359 (2011) Zhou et al., Nat. Phys. 9, 179(2013) Rydberg Atoms Hoganet al., PRL 108, (2012) x z vz Andreas Wallraff, Quantum Device Lab 30-Mar

32 10 5 Improvement in Coherence Time in 13 Years M. Devoret, R. Schoelkopf Science 339, 1169 (2013) Andreas Wallraff, Quantum Device Lab 30-Mar

Towards Quantum Error Correction X A T X D T D M 0 encode D B X α 000 + β 111 X Discretize, signal errors using quantum parity checks ˆP A M IBM: Corcoles et al., Nat. Com.

33 Towards Quantum Error Correction X A T X D T D M 0 encode D B X α β 111 X Discretize, signal errors using quantum parity checks ˆP A M IBM: Corcoles et al., Nat. Com. 6, 6979 (2015), ArXiv: QuTech: Ristè, Poletto, Huang et al., Nat. Com. 6, 6983 (2015), ArXiv: X X ˆP UCSB/Google: Kelly et al., Nature 519, (2015), ArXiv: Slide courtesy of L. DiCarlo

34 Design Andreas Wallraff, Quantum Device Lab 30-Mar

35 Fabrication Andreas Wallraff, Quantum Device Lab 30-Mar

36 Control Andreas Wallraff, Quantum Device Lab 30-Mar

37 Automation Andreas Wallraff, Quantum Device Lab 30-Mar

38 Cryogenics Andreas Wallraff, Quantum Device Lab 30-Mar

39 Quantum Science and Engineering Andreas Wallraff, Quantum Device Lab 30-Mar

Driving Qubit Transitions in J-C Hamiltonian

Qubit Control Driving Qubit Transitions in J-C Hamiltonian Hamiltonian for microwave drive Unitary transform with and Results in dispersive approximation up to 2 nd order in g Drive induces Rabi oscillations