Remote entanglement of transmon qubits

Transcription

1 Remote entanglement of transmon qubits 3 Michael Hatridge Department of Applied Physics, Yale University Katrina Sliwa Anirudh Narla Shyam Shankar Zaki Leghtas Mazyar Mirrahimi Evan Zalys-Geller Chen Wang Luigi Frunzio Steven Girvin Robert Schoelkopf Michel Devoret

2 What is remote entanglement and why is it important? 34 How do we engineer interactions over arbitrary length scales? Q 1 Q N+1 Q 2 Q N+2 Alice Q 3 Direct interaction Remote entanglement via msmt of ancilla Q N+3 Bob Monroe, Hanson, Zeilinger

3 ALICE G arnie g bert g Remote entanglement with flying qubits How can we do this with a superconducting system? R x π/2, Instead of qubits 1/ 2 Gg + Ee use coherent states 1/ 2 Gg + Ee How well can we transmit our flying qubit? How do we entangle flying qubits? How do we build efficient detector? measure X (sign) measure Z (parity) 1/ 2 GG + EE or 1/ 2 GG EE or 1/ 2 GE + EG or 1/ 2 GE EG 33 BOB G R x π/2, quantum-limited amplification

4 Part 1: measurement with coherent states 32

5 Dispersive measurement: classical version 31 g microwave cavity transmission line phase meter coherent pulse dispersive cavity/pulse interaction

6 Dispersive measurement: classical version 3 microwave cavity transmission line e g phase meter coherent pulse dispersive cavity/pulse interaction

7 Now a wrinkle: finite phase uncertainty 29 microwave cavity transmission line e g phase meter coherent pulse dispersive cavity/pulse interaction

8 Measurement with bad meter (still classical) 28 microwave cavity noise added by amp. AND signal lost in transmission e g phase meter coherent pulse dispersive cavity/pulse interaction Each msmt tells us only a little State after msmt not pure! This example optimistic, best commercial amp adds 2-3x noise We fix this with quantum-limited amplification

9 Ideal phase-preserving amplifier 27 Signal in 18 hybrid (beam splitter) Phase-sensitive amps α G 1 φ = 18 hybrid (beam splitter) Signal out Idler in G 1 Idler out φ = π 2 Adds its inputs, outputs 2 copies of combined inputs Adds minimum fluctuations to signal output * These ports are often internal degrees of freedom, in our amp they are accessible. We ll use this for remote entanglement * σ out 2 = 2σ in 2 (Caves Thm) Caves, Phys Rev D (1982)

10 Quantum-limited amplification: projective msmt 2 microwave cavity only quantum fluctuations e g phase meter w/ P. P. pre-amp coherent pulse coherent superposition state of qubit pure after each msmt For unknown initial state c g g + c e e, repeat many times to estimate c g 2, ce 2

11 Quantum-limited amplification: partial msmt 2 microwave cavity only quantum fluctuations e g phase meter w/ P. P. pre-amp coherent superposition WEAK coherent pulse state of qubit pure after each msmt counter-intuitive, but is achievable in the laboratory

12 Part 2: Partial measurement with transmon qubit and JPC 24

13 The Josephson tunnel junction 23 1nm φ C J I SUPERCONDUCTING TUNNEL JUNCTION L J I = I sin φ φ 2e Al/AlO x /Al tunnel junction 2 nm nonlinear inductor shunted by capacitor

14 Superconducting transmon qubit 22 Josephson junction with shunting capacitor anharmonic oscillator Potential energy f e g f lowest two levels form qubit f ge ~.2 GHz, f ef ~ 4.8 GHz Koch et al., Phys. Rev. A (27)

15 readout pulse at f d Measurement configuration HEMT I m = Ref Q m = T m I t dt T m 21 Q t dt + qubit pulses Qubit + resonator JPC Sig Idl Pump vacuum Ω Readout amplitude I m 2 + Q m 2 e dispersive shift χ g f f d Readout phase tan 1 Q m Im π 2 π 2 e width κ θ = 2 tan 1 χ κ g f

16 Isolating the transmon from the environment 2 input coupler waveguide-sma adapter output coupler transmon Purcell filter 1 mm 2 mm Cavity f c,g = GHz 1/ = 3 ns Qubit f Q =.22 GHz T 1 = 3 s T 2R = 8 s

17 G (db) The 8-junction Josephson Parametric Converter 19 Idler Signal Direct G (db) 2 1 m not a defect! quantum jumps of connected qubit ~88% of output noise is quantum noise! quantum fluctuations on an oscilloscope F 7. x1 9 Frequency (GHz) Bergeal et al Nature (21) See also Roch et al PRL (212)

18 Q m /σ Preparation by measurement + post-selection 18 Q m /σ State preparation R x π or Id Confirm state Rotate to z= R x π/2 n 11 n 11 T m 32 ns 4 ns M A T rep = 2 µs 1 g e 1 g e 8. σ 1 4 f, f, I m /σ I m /σ 1 See also Riste et al PRL (212) Johnson et al PRL (212)

19 Q m /σ Preparation by measurement + post-selection 17 Q m /σ State preparation R x π or Id Confirm state Rotate to z= R x π/2 n 11 n 11 T m 32 ns 1 4 ns M A M B M A = g T rep = 2 µs Id g R x π e Now that we have 1 outcomes M A g = g g e either do nothing to retain g OR rotate qubit by R f, x π to create e e f, I m /σ I m /σ 1

20 Q m /σ How ideal is this operation? Q m /σ 1 Id g R x π e 1 g e 1 g e 1 4 f, f, I m /σ I m /σ 1 Fidelity=.994! Strong measurements allow rapid, high-fidelity state preparation and tomography

21 A picture is worth a thousand math symbols * : Mapping (I m, Q m ) to the bloch vector 1 Q m z I m x y I m gives latitude information Q m gives longitude information The equator is a dangerous place: lost information pulls trajectory towards the z-axis * Gambetta, et al PRA (28); Korotkov/Girvin, Les Houches (211); M. Hatridge et al Science (213)

22 qubit cavity Back-action characterization protocol State preparation R x π/2 Tomography R x π/2, R y π/2, or Id n 11 variable n n 11 T m 32 ns 7ns Variable strength measurement (I m, Q m ) 14 z x y x f, y f, z f X = 1 or Y = 1 or Z = 1

23 Q m /σ Measurement with I m σ =.4 Q m /σ bability of ground 13 histogram of measurement after p/2 pulse tomography along X, Y and Z after measurement Im σ X c Y c - I m /σ - I m /σ - 1 Counts Max - Z c -1

24 Q m /σ Measurement with I m σ = 1. Q m /σ bability of ground 12 histogram of measurement after p/2 pulse Im tomography along X, Y and Z after measurement σ X c Y c - I m /σ - I m /σ - 1 Counts Max - Z c -1

25 Q m /σ Measurement with I m σ = 2.8 Q m /σ bability of ground 11 histogram of measurement after p/2 pulse tomography along X, Y and Z after measurement Im σ X c Y c - I m /σ - I m /σ - Counts f, show at ~1-4 contamination 1 Max - Z c -1

26 x- and y-component along I m = 1 1 I m σ =.82 X c, Y c -1 - Q m /σ X c = sin Y c = cos Q m σ Q m σ Im σ + θ exp I m σ Im σ + θ exp I m σ 2 1 η η 2 1 η η Amplitude determined by one fit parameter: η =.7 ±.2 η. 3 body entanglement (qubit, signal, idler)

27 Part 3: remote entanglement experiment 9

28 Two qubit readout schematic 8 Ω f p = 1.8 GHz f r d = 7.44 GHz f r d = 9.11 GHz

29 Simultaneous readout of two qubits 7 Signal Alone Q m I m encodes Z info e s I m ee Joint Readout Q m ge Idler Alone Q m g s e i Together Q m encodes Z info ee e s eg ge e i g i eg g s I m gg gg I m g i

30 How to perform entangling readout Signal Alone e s Q m I m encodes Z info Entangling Readout g i e i Idler Alone Q m e i g s g i I m I m encodes Z info I m Together ee ee Q m (sign) ge, eg ge, eg gg gg I m (parity) I m is now blind to contents of ge, eg With/ appropriate initial state, outcome is Bell state w/ % success rate Q m encodes phase of Bell state

31 Back action of two qubit msmt creates entanglement Even parity states: = gg Q m = ee I m Odd parity states: = ge eg = ge + i eg = ge + eg = ge i eg I m gives info on even vs. odd parity (a bit too much, actually) Q m gives sign info for odd parity states

32 Q m σ Q m σ Q m σ Probability of ground Tomography of strong entangling msmt 4 1 Histogram I m σ ZZ c ZI c -1 XX c -1 I m σ 1-1 1

33 Q m σ Q m σ Q m σ Probability of ground Tomography of weak entangling msmt 3 Histogram ZZ c +1 - σ I m - ZI c - XX c - I m σ -

34 Q Q m m σ σ Bloch comp. value Signature of entangling operation 2. Average a strip along Q m XX YY ZZ - XX c - I m σ -. - Q m σ currently, too much information is lost correct dependence of qubit correlations expect to demonstrate entanglement soon (F >.)

35 Total efficiency η Evolution of single-qubit readout vs time 1 1. Compare with optical systems: η~1 3 due to collector/detector inefficiencies Year Conclusions Coherent states can be used as flying qubits Quantum mechanics goes through the amplifier New tools for building large-scale quantum entanglement