Demonstrating a superconducting dual-rail cavity qubit with erasure-detected logical measurements

  1. Kevin S. Chou,
  2. Tali Shemma,
  3. Heather McCarrick,
  4. Tzu-Chiao Chien,
  5. James D. Teoh,
  6. Patrick Winkel,
  7. Amos Anderson,
  8. Jonathan Chen,
  9. Jacob Curtis,
  10. Stijn J. de Graaf,
  11. John W.O. Garmon,
  12. Benjamin Gudlewski,
  13. William D. Kalfus,
  14. Trevor Keen,
  15. Nishaad Khedkar,
  16. Chan U Lei,
  17. Gangqiang Liu,
  18. Pinlei Lu,
  19. Yao Lu,
  20. Aniket Maiti,
  21. Luke Mastalli-Kelly,
  22. Nitish Mehta,
  23. Shantanu O. Mundhada,
  24. Anirudh Narla,
  25. Taewan Noh,
  26. Takahiro Tsunoda,
  27. Sophia H. Xue,
  28. Joseph O. Yuan,
  29. Luigi Frunzio,
  30. Jose Aumentado,
  31. Shruti Puri,
  32. Steven M. Girvin,
  33. S. Harvey Moseley Jr.,
  34. and Robert J. Schoelkopf
A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is to
design a system where errors can be detected and converted into erasures. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. In this work, we implement such a dual-rail cavity qubit and use it to demonstrate a projective logical measurement with erasure detection. We measure logical state preparation and measurement errors at the 0.01%-level and detect over 99% of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability ∼0.2% per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 170 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.

A high-fidelity microwave beamsplitter with a parity-protected converter

  1. Yao Lu,
  2. Aniket Maiti,
  3. John W.O. Garmon,
  4. Suhas Ganjam,
  5. Yaxing Zhang,
  6. Jahan Claes,
  7. Luigi Frunzio,
  8. S. M. Girvin,
  9. and Robert J. Schoelkopf
Fast, high-fidelity operations between microwave resonators are an important tool for bosonic quantum computation and simulation with superconducting circuits. An attractive approach
for implementing these operations is to couple these resonators via a nonlinear converter and actuate parametric processes with RF drives. It can be challenging to make these processes simultaneously fast and high fidelity, since this requires introducing strong drives without activating parasitic processes or introducing additional decoherence channels. We show that in addition to a careful management of drive frequencies and the spectrum of environmental noise, leveraging the inbuilt symmetries of the converter Hamiltonian can suppress unwanted nonlinear interactions, preventing converter-induced decoherence. We demonstrate these principles using a differentially-driven DC-SQUID as our converter, coupled to two high-Q microwave cavities. Using this architecture, we engineer a highly-coherent beamsplitter and fast (∼ 100 ns) swaps between the cavities, limited primarily by their intrinsic single-photon loss. We characterize this beamsplitter in the cavities‘ joint single-photon subspace, and show that we can detect and post-select photon loss events to achieve a beamsplitter gate fidelity exceeding 99.98%, which to our knowledge far surpasses the current state of the art.

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.

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.

Distinguishing parity-switching mechanisms in a superconducting qubit

  1. Spencer Diamond,
  2. Valla Fatemi,
  3. Max Hays,
  4. Heekun Nho,
  5. Pavel D. Kurilovich,
  6. Thomas Connolly,
  7. Vidul R. Joshi,
  8. Kyle Serniak,
  9. Luigi Frunzio,
  10. Leonid I. Glazman,
  11. and Michel H. Devoret
Single-charge tunneling is a decoherence mechanism affecting superconducting qubits, yet the origin of excess quasiparticle excitations (QPs) responsible for this tunneling in superconducting
devices is not fully understood. We measure the flux dependence of charge-parity (or simply, „parity“) switching in an offset-charge-sensitive transmon qubit to identify the contributions of photon-assisted parity switching and QP generation to the overall parity-switching rate. The parity-switching rate exhibits a qubit-state-dependent peak in the flux dependence, indicating a cold distribution of excess QPs which are predominantly trapped in the low-gap film of the device. Moreover, we find that the photon-assisted process contributes significantly to both parity switching and the generation of excess QPs by fitting to a model that self-consistently incorporates photon-assisted parity switching as well as inter-film QP dynamics.

Single-shot number-resolved detection of microwave photons with error mitigation

  1. Jacob C. Curtis,
  2. Connor T. Hann,
  3. Salvatore S. Elder,
  4. Christopher S. Wang,
  5. Luigi Frunzio,
  6. Liang Jiang,
  7. and Robert J. Schoelkopf
Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, however, require not only detecting
the presence of any photons, but distinguishing the number present with a single shot. Here, we implement a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators which make up the bits in the binary decomposition of the photon number. Our protocol consists of successive, independent measurements of each bit by entangling the ancilla with the cavity, then reading out and resetting the ancilla. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in the measurement result, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from 13.5% to 1.3%. We also show that the mitigation is efficiently scalable to an M-mode system provided that the errors are independent and sufficiently small. Our work motivates the development of new algorithms that utilize single-shot, high-fidelity PNR detectors.

Error-detected state transfer and entanglement in a superconducting quantum network

  1. Luke D Burkhart,
  2. James Teoh,
  3. Yaxing Zhang,
  4. Christopher J Axline,
  5. Luigi Frunzio,
  6. M.H. Devoret,
  7. Liang Jiang,
  8. S.M. Girvin,
  9. and R. J. Schoelkopf
Modular networks are a promising paradigm for increasingly complex quantum devices based on the ability to transfer qubits and generate entanglement between modules. These tasks require
a low-loss, high-speed intermodule link that enables extensible network connectivity. Satisfying these demands simultaneously remains an outstanding goal for long-range optical quantum networks as well as modular superconducting processors within a single cryostat. We demonstrate communication and entanglement in a superconducting network with a microwave-actuated beamsplitter transformation between two bosonic qubits, which are housed in separate modules and joined by a demountable coaxial bus resonator. We transfer a qubit in a multi-photon encoding and track photon loss events to improve the fidelity, making it as high as in a single-photon encoding. Furthermore, generating entanglement with two-photon interference and postselection against loss errors produces a Bell state with success probability 79% and fidelity 0.94, halving the error obtained with a single photon. These capabilities demonstrate several promising methods for faithful operations between modules, including novel possibilities for resource-efficient direct gates.

High coherence superconducting microwave cavities with indium bump bonding

  1. Chan U Lei,
  2. Lev Krayzman,
  3. Suhas Ganjam,
  4. Luigi Frunzio,
  5. and Robert J. Schoelkopf
Low-loss cavities are important in building high-coherence superconducting quantum computers. Generating high quality joints between parts is crucial to the realization of a scalable
quantum computer using the circuit quantum electrodynamics (cQED) framework. In this paper, we adapt the technique of indium bump bonding to the cQED architecture to realize high quality superconducting microwave joints between chips. We use this technique to fabricate compact superconducting cavities in the multilayer microwave integrated quantum circuits (MMIQC) architecture and achieve single photon quality factor over 300 million or single-photon lifetimes approaching 5 ms. To quantify the performance of the resulting seam, we fabricate microwave stripline resonators in multiple sections connected by different numbers of bonds, resulting in a wide range of seam admittances. The measured quality factors combined with the designed seam admittances allow us to bound the conductance of the seam at gseam≥2×1010/(Ωm). Such a conductance should enable construction of micromachined superconducting cavities with quality factor of at least a billion. These results demonstrate the capability to construct very high quality microwave structures within the MMIQC architecture.

Quantum simulation of molecular vibronic spectra on a superconducting bosonic processor

  1. Christopher S. Wang,
  2. Jacob C. Curtis,
  3. Brian J. Lester,
  4. Yaxing Zhang,
  5. Yvonne Y. Gao,
  6. Jessica Freeze,
  7. Victor S. Batista,
  8. Patrick H. Vaccaro,
  9. Isaac L. Chuang,
  10. Luigi Frunzio,
  11. Liang Jiang,
  12. S. M. Girvin,
  13. and Robert J. Schoelkopf
The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. A controllable bosonic machine is naturally suited for simulating
systems with underlying bosonic structure, exploiting both quantum interference and an intrinsically large Hilbert space. Here, we experimentally realize a bosonic superconducting processor that combines arbitrary state preparation, a complete set of Gaussian operations, plus an essential non-Gaussian resource – a novel single-shot photon number resolving measurement scheme – all in one device. We utilize these controls to simulate the bosonic problem of molecular vibronic spectra, extracting the corresponding Franck-Condon factors for photoelectron processes in H2O, O3, NO2, and SO2. Our results demonstrate the versatile capabilities of the circuit QED platform, which can be extended to include non-Gaussian operations for simulating an even wider class of bosonic systems.