Preserving phase coherence and linearity in cat qubits with exponential bit-flip suppression

  1. Harald Putterman,
  2. Kyungjoo Noh,
  3. Rishi N. Patel,
  4. Gregory A. Peairs,
  5. Gregory S. MacCabe,
  6. Menyoung Lee,
  7. Shahriar Aghaeimeibodi,
  8. Connor T. Hann,
  9. Ignace Jarrige,
  10. Guillaume Marcaud,
  11. Yuan He,
  12. Hesam Moradinejad,
  13. John Clai Owens,
  14. Thomas Scaffidi,
  15. Patricio Arrangoiz-Arriola,
  16. Joe Iverson,
  17. Harry Levine,
  18. Fernando G.S.L. Brandão,
  19. Matthew H. Matheny,
  20. and Oskar Painter
Cat qubits, a type of bosonic qubit encoded in a harmonic oscillator, can exhibit an exponential noise bias against bit-flip errors with increasing mean photon number. Here, we focus
on cat qubits stabilized by two-photon dissipation, where pairs of photons are added and removed from a harmonic oscillator by an auxiliary, lossy buffer mode. This process requires a large loss rate and strong nonlinearities of the buffer mode that must not degrade the coherence and linearity of the oscillator. In this work, we show how to overcome this challenge by coloring the loss environment of the buffer mode with a multi-pole filter and optimizing the circuit to take into account additional inductances in the buffer mode. Using these techniques, we achieve near-ideal enhancement of cat-qubit bit-flip times with increasing photon number, reaching over 0.1 seconds with a mean photon number of only 4. Concurrently, our cat qubit remains highly phase coherent, with phase-flip times corresponding to an effective lifetime of T1,eff≃70 μs, comparable with the bare oscillator lifetime. We achieve this performance even in the presence of an ancilla transmon, used for reading out the cat qubit states, by engineering a tunable oscillator-ancilla dispersive coupling. Furthermore, the low nonlinearity of the harmonic oscillator mode allows us to perform pulsed cat-qubit stabilization, an important control primitive, where the stabilization can remain off for a significant fraction (e.g., two thirds) of a 3 μs cycle without degrading bit-flip times. These advances are important for the realization of scalable error-correction with cat qubits, where large noise bias and low phase-flip error rate enable the use of hardware-efficient outer error-correcting codes.

Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons

  1. Harry Levine,
  2. Arbel Haim,
  3. Jimmy S.C. Hung,
  4. Nasser Alidoust,
  5. Mahmoud Kalaee,
  6. Laura DeLorenzo,
  7. E. Alex Wollack,
  8. Patricio Arrangoiz-Arriola,
  9. Amirhossein Khalajhedayati,
  10. Yotam Vaknin,
  11. Aleksander Kubica,
  12. Aashish A. Clerk,
  13. David Hover,
  14. Fernando Brandão,
  15. Alex Retzker,
  16. and Oskar Painter
Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantagein practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We experimentally demonstrate that a „dual-rail qubit“ consisting of a pair of resonantly-coupled transmons can form a highly coherent erasure qubit, where the erasure error rate is given by the transmon T1 but for which residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability perasure=2.19(2)×10−3 per gate while the residual errors are ∼40 times lower. We further demonstrate mid-circuit detection of erasure errors while introducing <0.1% dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction.[/expand]

Building a fault-tolerant quantum computer using concatenated cat codes

  1. Christopher Chamberland,
  2. Kyungjoo Noh,
  3. Patricio Arrangoiz-Arriola,
  4. Earl T. Campbell,
  5. Connor T. Hann,
  6. Joseph Iverson,
  7. Harald Putterman,
  8. Thomas C. Bohdanowicz,
  9. Steven T. Flammia,
  10. Andrew Keller,
  11. Gil Refael,
  12. John Preskill,
  13. Liang Jiang,
  14. Amir H. Safavi-Naeini,
  15. Oskar Painter,
  16. and Fernando G.S.L. Brandão
We present a comprehensive architectural analysis for a fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware,
we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated near-term physical parameters for electro-acoustic systems, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic-state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are intractable for classical supercomputers. Hardware with 32,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.

Loss channels affecting lithium niobate phononic crystal resonators at cryogenic temperature

  1. E. Alex Wollack,
  2. Agnetta Y. Cleland,
  3. Patricio Arrangoiz-Arriola,
  4. Timothy P. McKenna,
  5. Rachel G. Gruenke,
  6. Rishi N. Patel,
  7. Wentao Jiang,
  8. Christopher J. Sarabalis,
  9. and Amir H. Safavi-Naeini
We investigate the performance of microwave-frequency phononic crystal resonators fabricated on thin-film lithium niobate for integration with superconducting quantum circuits. For
different design geometries at millikelvin temperatures, we achieve mechanical internal quality factors Qi above 105−106 at high microwave drive power, corresponding to 5×106 phonons inside the resonator. By sweeping the defect size of resonators with identical mirror cell designs, we are able to indirectly observe signatures of the complete phononic bandgap via the resonators‘ internal quality factors. Examination of quality factors‘ temperature dependence shows how superconducting and two-level system (TLS) loss channels impact device performance. Finally, we observe an anomalous low-temperature frequency shift consistent with resonant TLS decay and find that material choice can help to mitigate these losses.

Cryogenic microwave-to-optical conversion using a triply-resonant lithium niobate on sapphire transducer

  1. Timothy P. McKenna,
  2. Jeremy D. Witmer,
  3. Rishi N. Patel,
  4. Wentao Jiang,
  5. Raphaël Van Laer,
  6. Patricio Arrangoiz-Arriola,
  7. E. Alex Wollack,
  8. Jason F. Herrmann,
  9. and Amir H. Safavi-Naeini
Quantum networks are likely to have a profound impact on the way we compute and communicate in the future. In order to wire together superconducting quantum processors over kilometer-scale
distances, we need transducers that can generate entanglement between the microwave and optical domains with high fidelity. We present an integrated electro-optic transducer that combines low-loss lithium niobate photonics with superconducting microwave resonators on a sapphire substrate. Our triply-resonant device operates in a dilution refrigerator and converts microwave photons to optical photons with an on-chip efficiency of 6.6×10−6 and a conversion bandwidth of 20 MHz. We discuss design trade-offs in this device, including strategies to manage acoustic loss, and outline ways to increase the conversion efficiency in the future.

Electric fields for light: Propagation of microwave photons along a synthetic dimension

  1. Nathan R. A. Lee,
  2. Marek Pechal,
  3. E. Alex Wollack,
  4. Patricio Arrangoiz-Arriola,
  5. Zhaoyou Wang,
  6. and Amir H. Safavi-Naeini
The evenly-spaced modes of an electromagnetic resonator are coupled to each other by appropriate time-modulation, leading to dynamics analogous to those of particles hopping between
different sites of a lattice. This substitution of a real spatial dimension of a lattice with a „synthetic'“ dimension in frequency space greatly reduces the hardware complexity of an analog quantum simulator. Complex control and read-out of a highly multi-moded structure can thus be accomplished with very few physical control lines. We demonstrate this concept with microwave photons in a superconducting transmission line resonator by modulating the system parameters at frequencies near the resonator’s free spectral range and observing propagation of photon wavepackets in time domain. The linear propagation dynamics are equivalent to a tight-binding model, which we probe by measuring scattering parameters between frequency sites. We extract an approximate tight-binding dispersion relation for the synthetic lattice and initialize photon wavepackets with well-defined quasimomenta and group velocities. As an example application of this platform in simulating a physical system, we demonstrate Bloch oscillations associated with a particle in a periodic potential and subject to a constant external field. The simulated field strongly affects the photon dynamics despite photons having zero charge. Our observation of photon dynamics along a synthetic frequency dimension generalizes immediately to topological photonics and single-photon power levels, and expands the range of physical systems addressable by quantum simulation.

Superconducting circuit quantum computing with nanomechanical resonators as storage

  1. Marek Pechal,
  2. Patricio Arrangoiz-Arriola,
  3. and Amir H. Safavi-Naeini
We analyze the quantum information processing capability of a superconducting transmon circuit used to mediate interactions between quantum information stored in a collection of phononic
crystal cavity resonators. Having only a single processing element to be controlled externally makes this approach significantly less hardware-intensive than traditional architectures with individual control of each qubit. Moreover, when compared with the commonly considered alternative approach using coplanar waveguide or 3d cavity microwave resonators for storage, the nanomechanical resonators offer both very long lifetime and small size — two conflicting requirements for microwave resonators. A detailed gate error analysis leads to an optimal value for the qubit-resonator coupling rate as a function of the number of mechanical resonators in the system. For a given set of system parameters, a specific amount of coupling and number of resonators is found to optimize the quantum volume, an approximate measure for the computational capacity of a system. We see this volume is higher in the proposed hybrid nanomechanical architecture than in the competing on-chip electromagnetic approach.