Pitch and Catch of Non-Classical Microwaves PI’s: Rob Schoelkopf Liang Jiang Michel Devoret Students/postdocs: Wolfgang Pfaff Chris Axline Luke Burkhart Jianming Wen Changling Zhou Linshu Li Phil Reinhold Marius Constantin Chris Wang Menghen Zhang Disclosure: RS and MD are co-founders, consultants, and equity holders at Quantum Circuits, Inc.

Wiring up quantum systems with mechanical oscillators

Quantum state transfer between transmon qubits and microwave circuits Roles in collaboration: Assist w/ SC qubit + mechanics integration Develop source of on-demand, non-classical propagating m-wave states Demonstrate all m-wave state transfer Perform error-corrected state transfer Demo transduction of non-classical states

Quantum state transfer between transmon qubits and microwave circuits Roles in collaboration: Assist w/ SC qubit + mechanics integration Develop source of on-demand, non-classical propagating m-wave states Demonstrate all m-wave state transfer Perform error-corrected state transfer Demo transduction of non-classical states W. Pfaff et al., in preparation!

Overview Intro to “Pitch and Catch” for quantum state transfer Using a microwave-driven transmon as a Q-switch Collecting flying quantum states with a JPC amplifier Demonstration of high-fidelity conversion of standing to flying states Future plans for pitch and catch

Vision: Cavity QED Quantum Network Goal: Transfer and route interesting cavity states. Two-level system required for state preparation and tomography. (J. Kimble, 2008)

Near-term Goal: ”Pitch & Catch”

Expts. Towards P&C with SC Circuits Princeton: Houck group UCSB: Martinis/Cleland group Srinivasan et al., PRA 2014 Wenner et al., PRL 2014 Tunable coupling qubit (double transmon): adjust dipole moment to shape emission Zurich: Wallraff group Flux-tunable resonator coupling (Q) adjust absorption to catch Pechal et al., arXiv 1308.4094 No actual transfer of non-classical states demonstrated so far … All-RF shaping of emission using higher levels of transmon

Desired Characteristics of Quantum Source Launches complex quantum states on demand Control over temporal waveform Match to converter bandwidth: 104 – 106 Hz Applicable to a variety of non-classical states Fock states, cats for error correction, … High contrast (on/off ratio) High fidelity – preserves coherences

3D cavities for module-based scaling seamless modules, integration of ms-coherence memory cavities combines 3D cavities with qubit/stripline chips versions in use with ~ 5 qubits and ~ 10 cavities Axline et. al., APL 109 (4), 042601 (2016)

Complex Ops. thru Optimal Control (Heeres, et al., arXiv 1608.02430) GRAPE Realize | 6 0| to make Fock state | 6 ? Cavity Transmon

Implementing a Node in cQED Qubit = artificial Kerr medium* * as in many JJ parametric amplifiers “controllable beam-splitter or converter”

Implementing a Node in cQED 0.64 MHz means decay time of b mode is 250 nanoseconds Idea: Switch coupling on/off w/ RF signals turning on parametric conversion using the non-linearity of the qubit. During/after conversion, the field leaks from the low-Q mode into the transmission line.

First Milestone: Pitch Cavity States JPC amplifier courtesy of Devoret group First, use this chain to measure qubit and monitor the state remaining in storage cavity…

Evacuation of the Memory Cavity

Evacuation of the Memory Cavity

3 Orders of Magnitude Tuning Range Exact model (no free params, independent calibrations of g) Approximation: g large enough to see onset of non-exponential decay Fastest evacuation rate achieved so far ~ 1/500 ns, close to being limited by the low-Q resonator

Evacuation is State-Independent Solid lines: theory with independently calibrated g m = 2 n = 0 n = 2 n = 1 Time (ms) 40

Evacuation is State-Independent Solid lines: theory with independently calibrated g m = 2 m = 5 n = 0 n = 2 n = 1 n = 3 n = 4 n = 5

First Milestone: Pitch Cavity States Analyze flying states out using JPC courtesy Devoret group

Cavity Field is Emitted Coherently

Cavity Field is Emitted Coherently

Cavity Field is Emitted Coherently

Cavity Field is Emitted Coherently Q-functions of flying states Detection efficiency here ~ 47% raw data sim.

Fock-State Superpositions 0+n Intra-cavity Wigner functions n = 1 n = 2 n = 3 n = 4 n = 5 Detected propagating fields aw data Radial integral clearly shows n-fold symmetry. Solid line: theory, only assuming loss.

Entanglement by Half-Pitching 1) Pitch half the energy in the cavity. 2) Correlate the traveling field with measurement of standing state remaining. Cavity found in 0 Cavity found in 1 Cavity found in 0+1 Cavity found in 0-1 Pump Pump

Summary Two cavity/one qubit modules as generator/analyzers of quantum states Demonstrated RF-activated “Q-switching” to pitch states On/off ratio now almost 1,000x Pitching preserves coherence Estimated efficiency is of order unity. Damping is photon independent. Pitching works even for complex multiphoton states Future plans: shaping temporal wavepacket full microwave pitch and catch between two modules use a source to measure efficiency of optical transducer pitching an encoded logical qubit?

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Fidelity of Logical Qubit Operations Interleaved randomized benchmarking Heeres, et al., arXiv 1608.02430 data! data! data! Gate Fidelity (%) <all> 99.1 I 99.5 X90 99.2 -X90 X180 98.9 Y90 -Y90 Y180 98.7 H Dec/enc 98.3 X90 X90