Superconducting Qubit Single Flux Quantum Interface B L

Superconducting Qubit – Single Flux Quantum Interface B. L. T. Plourde R. Mc. Dermott, M. G. Vavilov Fermilab June 20, 2019 F. K. Wilhelm

Superconducting Qubit – Single Flux Quantum Interface Can we do high-fidelity qubit control and measurement without microwaves? B. L. T. Plourde R. Mc. Dermott, M. G. Vavilov Fermilab June 20, 2019 F. K. Wilhelm

Outline • Demands for scalable QC control and measurement • Single Flux Quantum (SFQ)-based qubit control • Photon counter-based qubit measurement • Outlook

Next-Generation Quantum Systems ? Unknown how to scale beyond ~102 -103 physical QB • • Is it possible to maintain coherence in ultralarge array? How to wire up? How to control? How to measure?

Classical Coprocessor for Scalable QC

Scalable Qubit Control Desirable to integrate as much control and measurement circuitry as possible into multi-qubit cryostat. Reduce: • Power consumption • Wiring heat load • Latency • Overall system footprint Single Flux Quantum (SFQ) digital logic an obvious candidate Advantages: • High speed • Low power • Cryogenic(!)

SFQ Classical Digital Logic IARPA C 3 program Applications: • High-speed DSP • High-speed ADC • Software-defined radio • Low-power, high-speed classical computing Possible end-of-roadmap successor to CMOS

Energy Coupled from SFQ Pulse width of SFQ pulse much less than oscillator period approximate as d-function V(t) = F 0 d(t) C’ = Cc + C For C = 100 f. F, Cc = 100 a. F, w 0/2 p = 5 GHz, only 6. 6 e-5 quanta per SFQ pulse

SFQ Excitation of a Qubit Mc. Dermott, Vavilov, PR Applied 2, 014007 (2014) Resonant pulse train: SFQ pulse induces discrete rotation about y-axis by angle

SFQ Excitation of a Qubit

Error of SFQ-based Gates Error due to qubit anharmonicity Error due to SFQ timing jitter w 10/2 p = 5 GHz w 21/2 p = 4. 8 GHz rms timing jitter of SFQ pulse generator

SCALable Leakage Optimized Pulse Sequenes (SCALLOPS) Li, Mc. Dermott, Vavilov, ar. Xiv: 1902. 02911 (to appear in PR Applied) • Nonuniform SFQ pulse spacing to reduce leakage errors • Efficient algorithm for generation of high-fidelity SFQ sequences

SCALable Leakage Optimized Pulse Sequenes (SCALLOPS) Li, Mc. Dermott, Vavilov, ar. Xiv: 1902. 02911 (to appear in PR Applied) • Control of many qubits with a single global SFQ clock • Repeated streaming of compact bit registers (35 -55 bits)

SCALable Leakage Optimized Pulse Sequenes (SCALLOPS) Li, Mc. Dermott, Vavilov, ar. Xiv: 1902. 02911 (to appear in PR Applied) • High density of high-fidelity (> 99. 99%) control sequences

SFQ-driven Qubit: Experiment Leonard et al. , PR Applied 11, 014009 (2019) v Collaborative fabrication combining high-Jc Nb/Al -Al. Ox/Nb JJs from UW and low-Jc Al/Al. Ox/Al JJs from SU

Layer Stack, QB Coherence

Rabi, Ramsey

Orthogonal Control with SFQ Pulses

Randomized Benchmarking of SFQ Gates

QP Poisoning

Multi-Chip Module (MCM) Circuit Layout (joint fab with Syracuse, HYPRES, Inc. ) In bumps Readout in/out SFQ Driver In bumps for ground connections; all other signals coupled capacitively or inductively QB Flux Bias Trigger

Classical Coprocessor for Scalable QC

Alternative approaches to dispersive readout …by Amplification: Coherent state discrimination …by Photon Counting: Intensity discrimination Josephson Photomultiplier (JPM) g. D energy g. J phase g. D Tunneling events produce easily-measured, unambiguous “clicks”.

0, 1 |0> + |1> QB

JPM Operation ● |1> ⇒ right well ● |0> ⇒ left well

JPM State Interrogation Map qubit state onto the question of right well or left well.

JPM-detected Rabi Oscillations Opremcak et al. , Science 361, 1239 (2018)

Measurement Backaction Opremcak et al. , Science 361, 1239 (2018) • Corresponds to qubit ground state • 50/50 population • Corresponds to qubit excited state

Update: JPM-Detected Rabi Oscillations Error budget: ● 98. 3% assignment fidelity. ● 135 ns measurement pulse and a T 1 = 2. 8 us ⇒ ~ 2. 4% relaxation error during readout. ● Unheralded ground state.

Integration of Q. Array with Large-scale SFQ Coprocessor SFQ PGU mstrip interconnect SFQ repeaters Q-C interface m. K quantum array dilute measurement results 3 K dense control sequences Quantum Sci. Technol. 3, 024004 (2018)

Integration of Q. Array with Large-scale SFQ Coprocessor Quantum Sci. Technol. 3, 024004 (2018) 3 K 108 x 103 -bit shift registers, Ic = 100 m. A 10 W @ 10% duty cycle 10 m 2 SFQ PGU 107 microstrip lines (Nb. Ti on Kapton) 1 ~ 0. 3 m. W 2 SFQ repeaters Q-C interface 2 e 8 SFQ JJs (MUX, Tx, Rx) Ic = 10 m. A 2 m. W @ 10% duty cycle 1 m 2 quantum array 108 QB 1 m 2 m. K 1 Cryogenics 2 Cryogenics 40, 203 (2000) 33, 729 (1993)

Personnel Wisconsin Syracuse Matt Beck (GS) JJ Nelson (PD) Ed Leonard (GS) Kenneth Dodge (GS) Vincent Liu (GS) Caleb Howington (GS) Alex Opremcak (GS) Ivan Pechenezhskiy (PD) Zhenyi Qi (GS) Guilhem Ribeill (GS)

Summary SFQ-based coherent control PR Applied 11, 014009 (2019) High-fidelity counter-based QB measurement Science 361, 1239 (2018) Prospect for integrated classical coprocessor QST 3, 024004 (2018) C Q