Quantum Control of an Oscillator with a Kerr-cat Qubit

  1. Andy Z. Ding,
  2. Benjamin L. Brock,
  3. Alec Eickbusch,
  4. Akshay Koottandavida,
  5. Nicholas E. Frattini,
  6. Rodrigo G. Cortinas,
  7. Vidul R. Joshi,
  8. Stijn J. de Graaf,
  9. Benjamin J. Chapman,
  10. Suhas Ganjam,
  11. Luigi Frunzio,
  12. Robert J. Schoelkopf,
  13. and Michel H. Devoret
Bosonic codes offer a hardware-efficient strategy for quantum error correction by redundantly encoding quantum information in the large Hilbert space of a harmonic oscillator. However,
experimental realizations of these codes are often limited by ancilla errors propagating to the encoded logical qubit during syndrome measurements. The Kerr-cat qubit has been proposed as an ancilla for these codes due to its theoretically-exponential noise bias, which would enable fault-tolerant error syndrome measurements, but the coupling required to perform these syndrome measurements has not yet been demonstrated. In this work, we experimentally realize driven parametric coupling of a Kerr-cat qubit to a high-quality-factor microwave cavity and demonstrate a gate set enabling universal quantum control of the cavity. We measure the decoherence of the cavity in the presence of the Kerr-cat and discover excess dephasing due to heating of the Kerr-cat to excited states. By engineering frequency-selective dissipation to counteract this heating, we are able to eliminate this dephasing, thereby demonstrating a high on-off ratio of control. Our results pave the way toward using the Kerr-cat to fault-tolerantly measure error syndromes of bosonic codes.

A mid-circuit erasure check on a dual-rail cavity qubit using the joint-photon number-splitting regime of circuit QED

  1. Stijn J. de Graaf,
  2. Sophia H. Xue,
  3. Benjamin J. Chapman,
  4. James D. Teoh,
  5. Takahiro Tsunoda,
  6. Patrick Winkel,
  7. John W.O. Garmon,
  8. Kathleen M. Chang,
  9. Luigi Frunzio,
  10. Shruti Puri,
  11. and Robert J. Schoelkopf
Quantum control of a linear oscillator using a static dispersive coupling to a nonlinear ancilla underpins a wide variety of experiments in circuit QED. Extending this control to more
than one oscillator while minimizing the required connectivity to the ancilla would enable hardware-efficient multi-mode entanglement and measurements. We show that the spectrum of an ancilla statically coupled to a single mode can be made to depend on the joint photon number in two modes by applying a strong parametric beamsplitter coupling between them. This `joint-photon number-splitting‘ regime extends single-oscillator techniques to two-oscillator control, which we use to realize a hardware-efficient erasure check for a dual-rail qubit encoded in two superconducting cavities. By leveraging the beamsplitter coupling already required for single-qubit gates, this scheme permits minimal connectivity between circuit elements. Furthermore, the flexibility to choose the pulse shape allows us to limit the susceptibility to different error channels. We use this scheme to detect leakage errors with a missed erasure fraction of (9.0±0.5)×10−4, while incurring an erasure rate of 2.92±0.01% and a Pauli error rate of 0.31±0.01%, both of which are dominated by cavity errors.

A high on-off ratio beamsplitter interaction for gates on bosonically encoded qubits

  1. Benjamin J. Chapman,
  2. Stijn J. de Graaf,
  3. Sophia H. Xue,
  4. Yaxing Zhang,
  5. James Teoh,
  6. Jacob C. Curtis,
  7. Takahiro Tsunoda,
  8. Alec Eickbusch,
  9. Alexander P. Read,
  10. Akshay Koottandavida,
  11. Shantanu O. Mundhada,
  12. Luigi Frunzio,
  13. M. H. Devoret,
  14. S. M. Girvin,
  15. and R. J. Schoelkopf
Encoding a qubit in a high quality superconducting microwave cavity offers the opportunity to perform the first layer of error correction in a single device, but presents a challenge:
how can quantum oscillators be controlled while introducing a minimal number of additional error channels? We focus on the two-qubit portion of this control problem by using a 3-wave mixing coupling element to engineer a programmable beamsplitter interaction between two bosonic modes separated by more than an octave in frequency, without introducing major additional sources of decoherence. Combining this with single-oscillator control provided by a dispersively coupled transmon provides a framework for quantum control of multiple encoded qubits. The beamsplitter interaction gbs is fast relative to the timescale of oscillator decoherence, enabling over 103 beamsplitter operations per coherence time, and approaching the typical rate of the dispersive coupling χ used for individual oscillator control. Further, the programmable coupling is engineered without adding unwanted interactions between the oscillators, as evidenced by the high on-off ratio of the operations, which can exceed 105. We then introduce a new protocol to realize a hybrid controlled-SWAP operation in the regime gbs≈χ, in which a transmon provides the control bit for the SWAP of two bosonic modes. Finally, we use this gate in a SWAP test to project a pair of bosonic qubits into a Bell state with measurement-corrected fidelity of 95.5%±0.2%.

Dual-rail encoding with superconducting cavities

  1. James D. Teoh,
  2. Patrick Winkel,
  3. Harshvardhan K. Babla,
  4. Benjamin J. Chapman,
  5. Jahan Claes,
  6. Stijn J. de Graaf,
  7. John W.O. Garmon,
  8. William D. Kalfus,
  9. Yao Lu,
  10. Aniket Maiti,
  11. Kaavya Sahay,
  12. Neel Thakur,
  13. Takahiro Tsunoda,
  14. Sophia H. Xue,
  15. Luigi Frunzio,
  16. Steven M. Girvin,
  17. Shruti Puri,
  18. and Robert J. Schoelkopf
The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computations. To this end, we introduce
the circuit-QED dual-rail qubit in which our physical qubit is encoded in the single-photon subspace of two superconducting cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers completely new capabilities. Using a single transmon ancilla, we describe a universal gate set that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors due to the cavity and transmon in all of these operations can be detected and converted to erasure errors, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit delivers an optimal hierarchy of errors and rates, and is expected to be well below the relevant QEC thresholds with today’s devices.

Error-detectable bosonic entangling gates with a noisy ancilla

  1. Takahiro Tsunoda,
  2. James D. Teoh,
  3. William D. Kalfus,
  4. Stijn J. de Graaf,
  5. Benjamin J. Chapman,
  6. Jacob C. Curtis,
  7. Neel Thakur,
  8. Steven M. Girvin,
  9. and Robert J. Schoelkopf
Bosonic quantum error correction has proven to be a successful approach for extending the coherence of quantum memories, but to execute deep quantum circuits, high-fidelity gates between
encoded qubits are needed. To that end, we present a family of error-detectable two-qubit gates for a variety of bosonic encodings. From a new geometric framework based on a „Bloch sphere“ of bosonic operators, we construct ZZL(θ) and eSWAP(θ) gates for the binomial, 4-legged cat, dual-rail and several other bosonic codes. The gate Hamiltonian is simple to engineer, requiring only a programmable beamsplitter between two bosonic qubits and an ancilla dispersively coupled to one qubit. This Hamiltonian can be realized in circuit QED hardware with ancilla transmons and microwave cavities. The proposed theoretical framework was developed for circuit QED but is generalizable to any platform that can effectively generate this Hamiltonian. Crucially, one can also detect first-order errors in the ancilla and the bosonic qubits during the gates. We show that this allows one to reach error-detected gate fidelities at the 10−4 level with today’s hardware, limited only by second-order hardware errors.

The squeezed Kerr oscillator: spectral kissing and phase-flip robustness

  1. Nicholas E. Frattini,
  2. Rodrigo G. Cortiñas,
  3. Jayameenakshi Venkatraman,
  4. Xu Xiao,
  5. Qile Su,
  6. Chan U Lei,
  7. Benjamin J. Chapman,
  8. Vidul R. Joshi,
  9. S. M. Girvin,
  10. Robert J. Schoelkopf,
  11. Shruti Puri,
  12. and Michel H. Devoret
By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as the
squeezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schrödinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.

Precision measurement of the microwave dielectric loss of sapphire in the quantum regime with parts-per-billion sensitivity

  1. Alexander P. Read,
  2. Benjamin J. Chapman,
  3. Chan U Lei,
  4. Jacob C. Curtis,
  5. Suhas Ganjam,
  6. Lev Krayzman,
  7. Luigi Frunzio,
  8. and Robert J. Schoelkopf
Dielectric loss is known to limit state-of-the-art superconducting qubit lifetimes. Recent experiments imply upper bounds on bulk dielectric loss tangents on the order of 100 parts-per-billion,
but because these inferences are drawn from fully fabricated devices with many loss channels, they do not definitively implicate or exonerate the dielectric. To resolve this ambiguity, we have devised a measurement method capable of separating and resolving bulk dielectric loss with a sensitivity at the level of 5 parts-per-billion. The method, which we call the dielectric dipper, involves the in-situ insertion of a dielectric sample into a high-quality microwave cavity mode. Smoothly varying the sample’s participation in the cavity mode enables a differential measurement of the sample’s dielectric loss tangent. The dielectric dipper can probe the low-power behavior of dielectrics at cryogenic temperatures, and does so without the need for any lithographic process, enabling controlled comparisons of substrate materials and processing techniques. We demonstrate the method with measurements of EFG sapphire, from which we infer a bulk loss tangent of 62(7)×10−9 and a substrate-air interface loss tangent of 12(2)×10−4. For a typical transmon, this bulk loss tangent would limit device quality factors to less than 20 million, suggesting that bulk loss is likely the dominant loss mechanism in the longest-lived transmons on sapphire. We also demonstrate this method on HEMEX sapphire and bound its bulk loss tangent to be less than 15(5)×10−9. As this bound is about four times smaller than the bulk loss tangent of EFG sapphire, use of HEMEX sapphire as a substrate would lift the bulk dielectric coherence limit of a typical transmon qubit to several milliseconds.

Observation of wave-packet branching through an engineered conical intersection

  1. Christopher S. Wang,
  2. Nicholas E. Frattini,
  3. Benjamin J. Chapman,
  4. Shruti Puri,
  5. Steven M. Girvin,
  6. Michel H. Devoret,
  7. and Robert J. Schoelkopf
In chemical reactions, the interplay between coherent evolution and dissipation is central to determining key properties such as the rate and yield. Of particular interest are cases
where two potential energy surfaces cross at features known as conical intersections (CIs), resulting in nonadiabatic dynamics that may promote ultrafast and highly efficient reactions when rovibrational damping is present. A prominent chemical reaction that involves a CI is the cis-trans isomerization reaction in rhodopsin, which is crucial to vision. CIs in real molecular systems are typically investigated via optical pump-probe spectroscopy, which has demanding spectral bandwidth and temporal resolution requirements, and where precise control of the environment is challenging. A complementary approach for understanding chemical reactions is to use quantum simulators that can provide access to a wider range of observables, though thus far combining strongly interacting linear (rovibrational) and nonlinear (electronic) degrees of freedom with engineered dissipation has yet to be demonstrated. Here, we create a tunable CI in a hybrid qubit-oscillator circuit QED processor and simultaneously track both a reactive wave-packet and electronic qubit in the time-domain. We identify dephasing of the electronic qubit as the mechanism that drives wave-packet branching along the reactive coordinate in our model. Furthermore, we directly observe enhanced branching when the wave-packet passes through the CI. Thus, the forces that influence a chemical reaction can be viewed as an effective measurement induced dephasing rate that depends on the position of the wave-packet relative to the CI. Our results set the groundwork for more complex simulations of chemical dynamics, offering deeper insight into the role of dissipation in determining macroscopic quantities of interest such as the quantum yield of a chemical reaction.

Efficient and low-backaction quantum measurement using a chip-scale detector

  1. Eric I. Rosenthal,
  2. Christian M. F. Schneider,
  3. Maxime Malnou,
  4. Ziyi Zhao,
  5. Felix Leditzky,
  6. Benjamin J. Chapman,
  7. Waltraut Wustmann,
  8. Xizheng Ma,
  9. Daniel A. Palken,
  10. Maximilian F. Zanner,
  11. Leila R. Vale,
  12. Gene C. Hilton,
  13. Jiansong Gao,
  14. Graeme Smith,
  15. Gerhard Kirchmair,
  16. and K. W. Lehnert
Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction. One feature of this platform is the ability to perform projective measurements
orders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators – magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Because these non-reciprocal elements have limited performance and are not easily integrated on-chip, it has been a longstanding goal to replace them with a scalable alternative. Here, we demonstrate a solution to this problem by using a superconducting switch to control the coupling between a qubit and amplifier. Doing so, we measure a transmon qubit using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and has 70% efficiency, comparable to the best that has been reported in any superconducting qubit measurement. As such, this work constitutes a high-quality platform for the scalable measurement of superconducting qubits.

Design of an on-chip superconducting microwave circulator with octave bandwidth

  1. Benjamin J. Chapman,
  2. Eric I. Rosenthal,
  3. and K. W. Lehnert
We present a design for a superconducting, on-chip circulator composed of dynamically modulated transfer switches and delays. Design goals are set for the multiplexed readout of superconducting
qubits. Simulations of the device show that it allows for low-loss circulation (insertion loss < 0.35 dB and isolation >20 dB) over an instantaneous bandwidth of 2.3 GHz. As the device is estimated to be linear for input powers up to -65 dBm, this design improves on the bandwidth and power-handling of previous superconducting circulators by over a factor of 50, making it ideal for integration with broadband quantum limited amplifiers.