Versatile parametric coupling between two statically decoupled transmon qubits

  1. X. Y. Jin,
  2. K. Cicak,
  3. Z. Parrott,
  4. S. Kotler,
  5. F. Lecocq,
  6. J. Teufel,
  7. J. Aumentado,
  8. E. Kapit,
  9. and R. W. Simmonds
Parametric coupling is a powerful technique for generating tunable interactions between superconducting circuits using only microwave tones. Here, we present a highly flexible parametric
coupling scheme demonstrated with two transmon qubits, which can be employed for multiple purposes, including the removal of residual ZZ coupling and the implementation of driven swap or swap-free controlled-Z (cZ) gates. Our fully integrated coupler design is only weakly flux tunable, cancels static linear coupling between the qubits, avoids internal coupler dynamics or excitations, and operates with rf-pulses. We show that residual ZZ coupling can be reduced with a parametric dispersive tone down to an experimental uncertainty of 5.5 kHz. Additionally, randomized benchmarking reveals that the parametric swap cZ gate achieves a fidelity of 99.4% in a gate duration of 60 ns, while the dispersive parametric swap-free cZ gate attains a fidelity of 99.5% in only 30 ns. We believe this is the fastest and highest fidelity gate achieved with on-chip parametric coupling to date. We further explore the dependence of gate fidelity on gate duration for both p-swap and p-swap-free cZ gates, providing insights into the possible error sources for these gates. Overall, our findings demonstrate a versatility, precision, speed, and high performance not seen in previous parametric approaches. Finally, our design opens up new possibilities for creating larger, modular systems of superconducting qubits.

Strong parametric dispersive shifts in a statically decoupled multi-qubit cavity QED system

  1. T. Noh,
  2. Z. Xiao,
  3. K. Cicak,
  4. X. Y. Jin,
  5. E. Doucet,
  6. J. Teufel,
  7. J. Aumentado,
  8. L. C. G. Govia,
  9. L. Ranzani,
  10. A. Kamal,
  11. and R. W. Simmonds
Cavity quantum electrodynamics (QED) with in-situ tunable interactions is important for developing novel systems for quantum simulation and computing. The ability to tune the dispersive
shifts of a cavity QED system provides more functionality for performing either quantum measurements or logical manipulations. Here, we couple two transmon qubits to a lumped-element cavity through a shared dc-SQUID. Our design balances the mutual capacitive and inductive circuit components so that both qubits are highly decoupled from the cavity, offering protection from decoherence processes. We show that by parametrically driving the SQUID with an oscillating flux it is possible to independently tune the interactions between either of the qubits and the cavity dynamically. The strength and detuning of this cavity QED interaction can be fully controlled through the choice of the parametric pump frequency and amplitude. As a practical demonstration, we perform pulsed parametric dispersive readout of both qubits while statically decoupled from the cavity. The dispersive frequency shifts of the cavity mode follow the expected magnitude and sign based on simple theory that is supported by a more thorough theoretical investigation. This parametric approach creates a new tunable cavity QED framework for developing quantum information systems with various future applications, such as entanglement and error correction via multi-qubit parity readout, state and entanglement stabilization, and parametric logical gates.

Efficient qubit measurement with a nonreciprocal microwave amplifier

  1. F. Lecocq,
  2. L. Ranzani,
  3. G. A. Peterson,
  4. K. Cicak,
  5. X. Y. Jin,
  6. R. W. Simmonds,
  7. J. D. Teufel,
  8. and J. Aumentado
The act of observing a quantum object fundamentally perturbs its state, resulting in a random walk toward an eigenstate of the measurement operator. Ideally, the measurement is responsible
for all dephasing of the quantum state. In practice, imperfections in the measurement apparatus limit or corrupt the flow of information required for quantum feedback protocols, an effect quantified by the measurement efficiency. Here we demonstrate the efficient measurement of a superconducting qubit using a nonreciprocal parametric amplifier to directly monitor the microwave field of a readout cavity. By mitigating the losses between the cavity and the amplifier we achieve a measurement efficiency of 72%. The directionality of the amplifier protects the readout cavity and qubit from excess backaction caused by amplified vacuum fluctuations. In addition to providing tools for further improving the fidelity of strong projective measurement, this work creates a testbed for the experimental study of ideal weak measurements, and it opens the way towards quantum feedback protocols based on weak measurement such as state stabilization or error correction.

Microwave measurement beyond the quantum limit with a nonreciprocal amplifier

  1. F. Lecocq,
  2. L. Ranzani,
  3. G. A. Peterson,
  4. K. Cicak,
  5. A. Metelmann,
  6. S. Kotler,
  7. R. W. Simmonds,
  8. J. D. Teufel,
  9. and J. Aumentado
The measurement of a quantum system is often performed by encoding its state in a single observable of a light field. The measurement efficiency of this observable can be reduced by
loss or excess noise on the way to the detector. Even a \textit{quantum-limited} detector that simultaneously measures a second non-commuting observable would double the output noise, therefore limiting the efficiency to 50%. At microwave frequencies, an ideal measurement efficiency can be achieved by noiselessly amplifying the information-carrying quadrature of the light field, but this has remained an experimental challenge. Indeed, while state-of-the-art Josephson-junction based parametric amplifiers can perform an ideal single-quadrature measurement, they require lossy ferrite circulators in the signal path, drastically decreasing the overall efficiency. In this paper, we present a nonreciprocal parametric amplifier that combines single-quadrature measurement and directionality without the use of strong external magnetic fields. We extract a measurement efficiency of 62+17−9% that exceeds the quantum limit and that is not limited by fundamental factors. The amplifier can be readily integrated with superconducting devices, creating a path for ideal measurements of quantum bits and mechanical oscillators.

Ultrastrong parametric coupling between a superconducting cavity and a mechanical resonator

  1. G. A. Peterson,
  2. S. Kotler,
  3. F. Lecocq,
  4. K. Cicak,
  5. X. Y. Jin,
  6. R. W. Simmonds,
  7. J. Aumentado,
  8. and J. D. Teufel
We present a new optomechanical device where the motion of a micromechanical membrane couples to a microwave resonance of a three-dimensional superconducting cavity. With this architecture,
we realize ultrastrong parametric coupling, where the coupling rate not only exceeds the dissipation rates in the system but also rivals the mechanical frequency itself. In this regime, the optomechanical interaction induces a frequency splitting between the hybridized normal modes that reaches 88% of the bare mechanical frequency, limited by the fundamental parametric instability. The coupling also exceeds the mechanical thermal decoherence rate, enabling new applications in ultrafast quantum state transfer and entanglement generation.

Demonstration of efficient nonreciprocity in a microwave optomechanical circuit

  1. G. A. Peterson,
  2. F. Lecocq,
  3. K. Cicak,
  4. R. W. Simmonds,
  5. J. Aumentado,
  6. and J. D. Teufel
The ability to engineer nonreciprocal interactions is an essential tool in modern communication technology as well as a powerful resource for building quantum networks. Aside from large
reverse isolation, a nonreciprocal device suitable for applications must also have high efficiency (low insertion loss) and low output noise. Recent theoretical and experimental studies have shown that nonreciprocal behavior can be achieved in optomechanical systems, but performance in these last two attributes has been limited. Here we demonstrate an efficient, frequency-converting microwave isolator based on the optomechanical interactions between electromagnetic fields and a mechanically compliant vacuum gap capacitor. We achieve simultaneous reverse isolation of more than 20 dB and insertion loss less than 1.5 dB over a bandwidth of 5 kHz. We characterize the nonreciprocal noise performance of the device, observing that the residual thermal noise from the mechanical environments is routed solely to the input of the isolator. Our measurements show quantitative agreement with a general coupled-mode theory. Unlike conventional isolators and circulators, these compact nonreciprocal devices do not require a static magnetic field, and they allow for dynamic control of the direction of isolation. With these advantages, similar devices could enable programmable, high-efficiency connections between disparate nodes of quantum networks, even efficiently bridging the microwave and optical domains.

Nonreciprocal microwave signal processing with a Field-Programmable Josephson Amplifier

  1. F. Lecocq,
  2. L. Ranzani,
  3. G. A. Peterson,
  4. K. Cicak,
  5. R. W. Simmonds,
  6. J. D. Teufel,
  7. and J. Aumentado
We report on the design and implementation of a Field Programmable Josephson Amplifier (FPJA) – a compact and lossless superconducting circuit that can be programmed extit{in
situ} by a set of microwave drives to perform reciprocal and nonreciprocal frequency conversion and amplification. In this work we demonstrate four modes of operation: frequency conversion (−0.5 dB transmission, −30 dB reflection), circulation (−0.5 dB transmission, −30 dB reflection, 30 dB isolation), phase-preserving amplification (gain >20 dB, 1 photon of added noise) and directional phase-preserving amplification (−10 dB reflection, 18 dB forward gain, 8 dB reverse isolation, 1 photon of added noise). The system exhibits quantitative agreement with theoretical prediction. Based on a gradiometric Superconducting Quantum Interference Device (SQUID) with Nb/Al-AlOx/Nb Josephson junctions, the FPJA is first-order insensitive to flux noise and can be operated without magnetic shielding at low temperature. Due to its flexible design and compatibility with existing superconducting fabrication techniques, the FPJA offers a straightforward route toward on-chip integration with superconducting quantum circuits such as qubits or microwave optomechanical systems.

Tunable-Cavity QED with Phase Qubits

  1. J. D. Whittaker,
  2. F. C. S. da Silva,
  3. M. S. Allman,
  4. F. Lecocq,
  5. K. Cicak,
  6. A. J. Sirois,
  7. J. D. Teufel,
  8. J. Aumentado,
  9. and R. W. Simmonds
We describe a tunable-cavity QED architecture with an rf SQUID phase qubit inductively coupled to a single-mode, resonant cavity with a tunable frequency that allows for both microwave
readout of tunneling and dispersive measurements of the qubit. Dispersive measurement is well characterized by a three-level model, strongly dependent on qubit anharmonicity, qubit-cavity coupling and detuning. A tunable cavity frequency provides a way to strongly vary both the qubit-cavity detuning and coupling strength, which can reduce Purcell losses, cavity-induced dephasing of the qubit, and residual bus coupling for a system with multiple qubits. With our qubit-cavity system, we show that dynamic control over the cavity frequency enables one to avoid Purcell losses during coherent qubit evolutions and optimize state readout during qubit measurements. The maximum qubit decay time T1 = 1.5 μs is found to be limited by surface dielectric losses from a design geometry similar to planar transmon qubits.

State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime

  1. T. A. Palomaki,
  2. J. W. Harlow,
  3. J. D. Teufel,
  4. R. W. Simmonds,
  5. and K. W. Lehnert
or a combination of refrigeration and laser-like cooling"][2, 3]. This exciting result has encouraged notions that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits [1, 4-7], either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems [8, 9]. As yet, the transfer of an itinerant state or propagating mode of a microwave field to and from a mechanical oscillator has not been demonstrated owing to the inability to agilely turn on and off the interaction between microwave electricity and mechanical motion. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in, and retrieved from a mechanical oscillator with amplitudes at the single quanta level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store and transduce quantum information.