qubits Michael Hatridge Department of Applied Physics, Yale - PowerPoint PPT Presentation

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

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

33 Remote entanglement with flying qubits How can we do this with a superconducting system? ALICE |𝐻 𝑆 𝑦 𝜌/2 , How well can we transmit our flying qubit? How do we entangle flying qubits? How do we build arnie efficient detector? 1/ 2 |𝐻𝐻 + |𝐹𝐹 |𝑕 measure or X 1/ 2 |𝐻𝐻 − |𝐹𝐹 1/ 2 |𝐻𝑕 + |𝐹𝑓 Instead of qubits (sign) or ⊗ use coherent states measure 1/ 2 |𝐻𝐹 + |𝐹𝐻 1/ 2 |𝐻𝑕 + |𝐹𝑓 Z bert or |𝑕 (parity) 1/ 2 |𝐻𝐹 − |𝐹𝐻 quantum-limited BOB amplification 𝑆 𝑦 𝜌/2 |𝐻 ,

32 Part 1: measurement with coherent states

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

30 Dispersive measurement: classical version |𝑕 |𝑓 microwave cavity transmission line phase meter dispersive cavity/pulse coherent interaction pulse

29 Now a wrinkle: finite phase uncertainty |𝑕 |𝑓 microwave cavity transmission line phase meter dispersive cavity/pulse coherent interaction pulse

28 Measurement with bad meter (still classical) noise added |𝑕 |𝑓 microwave by amp. AND cavity signal lost in transmission phase meter dispersive cavity/pulse • Each msmt tells us only a little coherent • interaction State after msmt not pure! pulse • This example optimistic, best commercial amp adds 20-30x noise • We fix this with quantum-limited amplification

27 Ideal phase-preserving amplifier • Phase-sensitive 180 ° hybrid 180 ° hybrid amps (beam splitter) (beam splitter) Signal Signal |𝛽 𝐻 ≫ 1     out in        𝜚 = 0       Idler Idler |0 𝐻 ≫ 1 in out 𝜚 = 𝜌 2 𝜍 𝑗 → 𝜍 𝑔 = 𝑈𝑠𝑉𝜍 𝑗 𝑉 † • 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. 𝑇 𝜍 𝑔 = 𝑇 𝜍 𝑗 We’ll use this for remote entanglement * 𝜏 𝑝𝑣𝑢2 = 2𝜏 𝑗𝑜2 (Caves’ Thm) Caves, Phys Rev D (1982)

26 Quantum-limited amplification: projective msmt microwave |𝑕 |𝑓 only quantum cavity fluctuations phase meter w/ P. P. pre-amp coherent superposition coherent pulse • state of qubit pure after each msmt • For unknown initial state 𝑑 𝑕 |𝑕 + 𝑑 𝑓 |𝑓 , repeat 2 , 𝑑 𝑓 2 many times to estimate 𝑑 𝑕

Quantum- limited amplification: ‘partial’ msmt 25 microwave |𝑕 |𝑓 only quantum cavity fluctuations phase meter w/ P. P. pre-amp coherent superposition WEAK coherent • state of qubit pure after each msmt • counter-intuitive, but is achievable pulse in the laboratory

24 Part 2: Partial measurement with transmon qubit and JPC

23 The Josephson tunnel junction C J 1nm 𝜚 𝐽 L J SUPERCONDUCTING TUNNEL JUNCTION 𝐽 = 𝐽 0 sin 𝜚 𝜒 0 nonlinear inductor shunted by capacitor   0 2 e Al/AlO x /Al 200 nm tunnel junction

22 Superconducting transmon qubit Josephson junction with shunting capacitor  anharmonic oscillator Potential energy |𝑔 |𝑓 |𝑕 f lowest two levels form qubit f ge ~ 5.025 GHz, f ef ~ 4.805 GHz Koch et al., Phys. Rev. A (2007)

21 Measurement configuration 𝑈 𝑛 𝑈 𝐽 𝑛 = 𝐽 𝑢 𝑒𝑢 𝑛 𝑅 𝑛 = 𝑅 𝑢 𝑒𝑢 𝑈 0 𝑛 HEMT readout Ref 𝐽 𝑛 = 𝐽 𝑢 𝑒𝑢 0 𝑈 𝑛 pulse at 𝑅 𝑛 = 𝑅 𝑢 𝑒𝑢 0 𝑔 0 𝑒    c JPC   Qubit + vacuum 50Ω Sig Idl resonator + qubit Pump pulses dispersive shift 𝜓 Readout |𝑓 amplitude |𝑕 2 + 𝑅 𝑛 2   𝐽 𝑛 𝑔 𝑔 𝑒 width 𝜆 𝜌 2 Readout 𝑏 𝑕 ⊗ 𝛽 𝑕 , 0 + 𝑐 𝑓 ⊗ 𝛽 𝑓 , 0 phase 𝜘 = 2 tan −1 𝜓 𝜆 |𝑓 tan −1 𝑅 𝑛 𝐽 𝑛 |𝑕 − 𝜌 2 𝑔

20 Isolating the transmon from the environment transmon output coupler waveguide-SMA input coupler adapter Purcell filter 10 mm 25 mm Cavity Qubit f c,g = 7.4817 GHz f Q =5.0252 GHz 1/  = 30 ns T 1 = 30  s T 2R = 8  s

19 The 8-junction Josephson Parametric Converter Signal Idler 10  m not a defect! quantum jumps of connected qubit 20 20 Direct G (dB) ~88% of output noise is 15 G (dB) quantum noise! 10 10 → quantum fluctuations ~100’s of MHz 5 on an oscilloscope 7.42 7.42 7.44 7.46 7.46 7.48 7.50 7.50 F 9 Bergeal et al Nature (2010) x10 Frequency (GHz) See also Roch et al PRL (2012)

18 Preparation by measurement + post-selection State preparation State preparation Confirm state Confirm state Rotate to z=0 Rotate to z=0 𝑆 𝑦 𝜌 𝑆 𝑦 𝜌/2 𝐽𝑒 or  11  11 𝑜 𝑜 𝑈 𝑛  320 ns 640 ns T rep = 20 µs M A |𝑕 |𝑕 10 10 |𝑓 |𝑓 10 4 𝑅 𝑛 /𝜏 𝑅 𝑛 /𝜏 5 5 8.6 σ 10 2 𝑔 , … 𝑔 , … 6000 0 0 1 0 -10 -5 0 5 10 -10 -5 0 5 10 𝐽 𝑛 /𝜏 𝐽 𝑛 /𝜏 See also Riste et al PRL (2012) Johnson et al PRL (2012)

17 Preparation by measurement + post-selection |𝑓 State preparation Confirm state Rotate to z=0 𝑆 𝑦 𝜌 𝑆 𝑦 𝜌/2 𝐽𝑒 or  11  11 𝑜 𝑜 𝑈 𝑛  320 ns M B |M A = |𝑕 640 ns T rep = 20 µs M A 𝐽𝑒 “ |𝑕 ” 𝑆 𝑦 𝜌 “ |𝑓 ” Now that we have outcomes M A = |𝑕 |𝑕 |𝑕 10 10 |𝑓 |𝑓 either do nothing to retain |𝑕 10 4 𝑅 𝑛 /𝜏 OR 𝑅 𝑛 /𝜏 5 5 rotate qubit by 𝑆 𝑦 𝜌 to create |𝑓 10 2 𝑔 , … 𝑔 , … 0 0 1 -10 -5 0 5 10 -10 -5 0 5 10 𝐽 𝑛 /𝜏 𝐽 𝑛 /𝜏

16 How ideal is this operation? |𝑓 𝐽𝑒 “ |𝑕 ” 𝑆 𝑦 𝜌 “ |𝑓 ” |𝑕 |𝑕 10 10 |𝑓 |𝑓 10 4 𝑅 𝑛 /𝜏 𝑅 𝑛 /𝜏 5 5 10 2 𝑔 , … 𝑔 , … 0 0 1 Say : “practically useful, but doesn’t tell us -10 -5 0 5 10 -10 -5 0 5 10 𝐽 𝑛 /𝜏 𝐽 𝑛 /𝜏 improvement in signal processing” Fidelity=0.994! Strong measurements allow rapid, high-fidelity state preparation and tomography

15 A picture is worth a thousand math symbols * : Mapping ( 𝐽 𝑛 , 𝑅 𝑛 ) to the bloch vector • 𝑅 𝑛 𝜏 𝑛 𝜏 2 𝜃 = • 𝑹 𝒏 𝑨 𝑱 𝒏 𝜽 < 𝟐 𝐽 𝑛 𝑧 𝑦 𝐽 𝑛 gives latitude information 𝑅 𝑛 gives longitude information The equator is a dangerous place: lost information pulls trajectory 𝑦 𝑔 , 𝑧 𝑔 • towards the z-axis * Gambetta, et al PRA (2008); Korotkov/Girvin, Les Houches (2011); M. Hatridge et al Science (2013) 𝑕 − 𝐽 𝑛 𝑓 𝜖𝑦 𝑔 = η 𝐽 𝑛 𝜖𝑅 𝑛 2 𝐽 𝑛 ,𝑅 𝑛 =0

14 Back-action characterization protocol Variable Tomography State preparation strength 𝑆 𝑦 𝜌/2 measurement , 𝑆 𝑧 𝜌/2 , 𝑆 𝑦 𝜌/2 𝐽𝑒 or    c   qubit  11 variable 𝑜  11 𝑜 𝑜 𝑈 𝑛  320 ns cavity ( 𝐽 𝑛 , 𝑅 𝑛 ) 700ns 𝑨   𝑧 X =  1 𝑦 or 𝑦 𝑔 , 𝑧 𝑔 , 𝑨 𝑔 Y =  1 or Z =  1

𝒏 𝝉 13 Measurement with 𝑱 = 0.4 histogram of measurement after p /2 pulse tomography along X, Y and Z after measurement 6 6 6 𝐽 𝑛 𝑅 𝑛 /𝜏 𝑅 𝑛 /𝜏 𝜏 0 0 0 𝑌 𝑑 𝑍 𝑑 -6 0 6 -6 0 6 -6 0 6 𝐽 𝑛 /𝜏 𝐽 𝑛 /𝜏 6 1 Counts Probability of ground 0 0 Max 0 𝑎 𝑑 -1 -6 0 6

𝒏 𝝉 12 Measurement with 𝑱 = 1.0 histogram of measurement after p /2 pulse tomography along X, Y and Z after measurement 6 6 6 𝐽 𝑛 𝑅 𝑛 /𝜏 𝑅 𝑛 /𝜏 𝜏 0 0 0 𝑌 𝑑 𝑍 𝑑 -6 0 6 -6 0 6 -6 0 6 𝐽 𝑛 /𝜏 𝐽 𝑛 /𝜏 6 1 Counts Probability of ground 0 0 Max 0 𝑎 𝑑 -1 -6 0 6

𝒏 𝝉 11 Measurement with 𝑱 = 2.8 histogram of measurement after p /2 pulse tomography along X, Y and Z after measurement 6 6 6 𝜏 𝑅 𝑛 /𝜏 𝑅 𝑛 /𝜏 𝐽 𝑛 0 0 0 𝑌 𝑑 𝑍 𝑑 -6 0 6 -6 0 6 -6 0 6 𝐽 𝑛 /𝜏 𝐽 𝑛 /𝜏 6 1 𝑔 , … show at Counts ~10 -4 contamination Probability of ground 0 0 Max 0 𝑎 𝑑 -1 -6 0 6

𝑜 𝑜 x- and y-component along 𝑱 𝒏 = 𝟏 10 1 𝒏 𝝉 𝑱 = 0.82 𝑌 𝑑 , 𝑍 𝑑 𝑅 𝑛 /𝜏 0 𝑌 𝑑 𝐽 𝑛 = 0 -1 𝑅 𝑛 /𝜏 -6 0 6 2 1 − 𝜃 𝑌 𝑑 = sin 𝑅 𝑛 𝐽 𝜏 + 𝜄 exp − 𝐽 𝑛 𝑛 𝑅 𝑛 /𝜏 𝜏 𝜏 𝜃 2 1 − 𝜃 𝑍 𝑑 = cos 𝑅 𝑛 𝐽 𝜏 + 𝜄 exp − 𝐽 𝑛 𝑛 𝜏 𝜏 𝜃 Amplitude determined by one fit parameter: 𝜽 = 0.57 ± 0.02 𝑍 𝑑 𝐽 𝑛 = 0 𝜽 ≥ 𝟏. 𝟔 → 3 body entanglement (qubit, signal, idler) 𝐽 𝑛 /𝜏 𝐽 𝑛 /𝜏

9 Part 3: remote entanglement experiment