Calibration of Drive Non-Linearity for Arbitrary-Angle Single-Qubit Gates Using Error Amplification

  1. Stefania Lazăr,
  2. Quentin Ficheux,
  3. Johannes Herrmann,
  4. Ants Remm,
  5. Nathan Lacroix,
  6. Christoph Hellings,
  7. Francois Swiadek,
  8. Dante Colao Zanuz,
  9. Graham J. Norris,
  10. Mohsen Bahrami Panah,
  11. Alexander Flasby,
  12. Michael Kerschbaum,
  13. Jean-Claude Besse,
  14. Christopher Eichler,
  15. and Andreas Wallraff
The ability to execute high-fidelity operations is crucial to scaling up quantum devices to large numbers of qubits. However, signal distortions originating from non-linear components
in the control lines can limit the performance of single-qubit gates. In this work, we use a measurement based on error amplification to characterize and correct the small single-qubit rotation errors originating from the non-linear scaling of the qubit drive rate with the amplitude of the programmed pulse. With our hardware, and for a 15-ns pulse, the rotation angles deviate by up to several degrees from a linear model. Using purity benchmarking, we find that control errors reach 2×10−4, which accounts for half of the total gate error. Using cross-entropy benchmarking, we demonstrate arbitrary-angle single-qubit gates with coherence-limited errors of 2×10−4 and leakage below 6×10−5. While the exact magnitude of these errors is specific to our setup, the presented method is applicable to any source of non-linearity. Our work shows that the non-linearity of qubit drive line components imposes a limit on the fidelity of single-qubit gates, independent of improvements in coherence times, circuit design, or leakage mitigation when not corrected for.

Realization of a Universal Quantum Gate Set for Itinerant Microwave Photons

  1. Kevin Reuer,
  2. Jean-Claude Besse,
  3. Lucien Wernli,
  4. Paul Magnard,
  5. Philipp Kurpiers,
  6. Graham J. Norris,
  7. Andreas Wallraff,
  8. and Christopher Eichler
Deterministic photon-photon gates enable the controlled generation of entanglement between mobile carriers of quantum information. Such gates have thus far been exclusively realized
in the optical domain and by relying on post-selection. Here, we present a non-post-selected, deterministic, photon-photon gate in the microwave frequency range realized using superconducting circuits. We emit photonic qubits from a source chip and route those qubits to a gate chip with which we realize a universal gate set by combining controlled absorption and re-emission with single-qubit gates and qubit-photon controlled-phase gates. We measure quantum process fidelities of 75% for single- and of 57% for two-qubit gates, limited mainly by radiation loss and decoherence. This universal gate set has a wide range of potential applications in superconducting quantum networks.

Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems

  1. Paul Magnard,
  2. Simon Storz,
  3. Philipp Kurpiers,
  4. Josua Schär,
  5. Fabian Marxer,
  6. Janis Luetolf,
  7. Jean-Claude Besse,
  8. Mihai Gabureac,
  9. Kevin Reuer,
  10. Abdulkadir Akin,
  11. Baptiste Royer,
  12. Alexandre Blais,
  13. and Andreas Wallraff
Superconducting circuits are a strong contender for realizing quantum computing systems, and are also successfully used to study quantum optics and hybrid quantum systems. However,
their cryogenic operation temperatures and the current lack of coherence-preserving microwave-to-optical conversion solutions have hindered the realization of superconducting quantum networks either spanning different cryogenics systems or larger distances. Here, we report the successful operation of a cryogenic waveguide coherently linking transmon qubits located in two dilution refrigerators separated by a physical distance of five meters. We transfer qubit states and generate entanglement on-demand with average transfer and target state fidelities of 85.8 % and 79.5 %, respectively, between the two nodes of this elementary network. Cryogenic microwave links do provide an opportunity to scale up systems for quantum computing and create local area quantum communication networks over length scales of at least tens of meters.

Implementation of Conditional-Phase Gates based on tunable ZZ-Interactions

  1. Michele C. Collodo,
  2. Johannes Herrmann,
  3. Nathan Lacroix,
  4. Christian Kraglund Andersen,
  5. Ants Remm,
  6. Stefania Lazar,
  7. Jean-Claude Besse,
  8. Theo Walter,
  9. Andreas Wallraff,
  10. and Christopher Eichler
High fidelity two-qubit gates exhibiting low crosstalk are essential building blocks for gate-based quantum information processing. In superconducting circuits two-qubit gates are typically
based either on RF-controlled interactions or on the in-situ tunability of qubit frequencies. Here, we present an alternative approach using a tunable cross-Kerr-type ZZ-interaction between two qubits, which we realize by a flux-tunable coupler element. We control the ZZ-coupling rate over three orders of magnitude to perform a rapid (38 ns), high-contrast, low leakage (0.14 %) conditional-phase CZ gate with a fidelity of 97.9 % without relying on the resonant interaction with a non-computational state. Furthermore, by exploiting the direct nature of the ZZ-coupling, we easily access the entire conditional-phase gate family by adjusting only a single control parameter.

Realizing a Deterministic Source of Multipartite-Entangled Photonic Qubits

  1. Jean-Claude Besse,
  2. Kevin Reuer,
  3. Michele C. Collodo,
  4. Arne Wulff,
  5. Lucien Wernli,
  6. Adrian Copetudo,
  7. Daniel Malz,
  8. Paul Magnard,
  9. Abdulkadir Akin,
  10. Mihai Gabureac,
  11. Graham J. Norris,
  12. J. Ignacio Cirac,
  13. Andreas Wallraff,
  14. and Christopher Eichler
Sources of entangled electromagnetic radiation are a cornerstone in quantum information processing and offer unique opportunities for the study of quantum many-body physics in a controlled
experimental setting. While multi-mode entangled states of radiation have been generated in various platforms, all previous experiments are either probabilistic or restricted to generate specific types of states with a moderate entanglement length. Here, we demonstrate the fully deterministic generation of purely photonic entangled states such as the cluster, GHZ, and W state by sequentially emitting microwave photons from a controlled auxiliary system into a waveguide. We tomographically reconstruct the entire quantum many-body state for up to N=4 photonic modes and infer the quantum state for even larger N from process tomography. We estimate that localizable entanglement persists over a distance of approximately ten photonic qubits, outperforming any previous deterministic scheme.

Primary thermometry of propagating microwaves in the quantum regime

  1. Marco Scigliuzzo,
  2. Andreas Bengtsson,
  3. Jean-Claude Besse,
  4. Andreas Wallraff,
  5. Per Delsing,
  6. and Simone Gasparinetti
The ability to control and measure the temperature of propagating microwave modes down to very low temperatures is indispensable for quantum information processing, and may open opportunities
for studies of heat transport at the nanoscale, also in the quantum regime. Here we propose and experimentally demonstrate primary thermometry of propagating microwaves using a transmon-type superconducting circuit. Our device operates continuously, with a sensitivity down to 4×10−4 photons/Hz−−−√ and a bandwidth of 40 MHz. We measure the thermal occupation of the modes of a highly attenuated coaxial cable in a range of 0.001 to 0.4 thermal photons, corresponding to a temperature range from 35 mK to 210 mK at a frequency around 5 GHz. To increase the radiation temperature in a controlled fashion, we either inject calibrated, wideband digital noise, or heat the device and its environment. This thermometry scheme can find applications in benchmarking and characterization of cryogenic microwave setups, temperature measurements in hybrid quantum systems, and quantum thermodynamics.

Parity Detection of Propagating Microwave Fields

  1. Jean-Claude Besse,
  2. Simone Gasparinetti,
  3. Michele C. Collodo,
  4. Theo Walter,
  5. Ants Remm,
  6. Jonas Krause,
  7. Christopher Eichler,
  8. and Andreas Wallraff
The parity of the number of elementary excitations present in a quantum system provides important insights into its physical properties. Parity measurements are used, for example, to
tomographically reconstruct quantum states or to determine if a decay of an excitation has occurred, information which can be used for quantum error correction in computation or communication protocols. Here we demonstrate a versatile parity detector for propagating microwaves, which distinguishes between radiation fields containing an even or odd number n of photons, both in a single-shot measurement and without perturbing the parity of the detected field. We showcase applications of the detector for direct Wigner tomography of propagating microwaves and heralded generation of Schrödinger cat states. This parity detection scheme is applicable over a broad frequency range and may prove useful, for example, for heralded or fault-tolerant quantum communication protocols.

Entanglement Stabilization using Parity Detection and Real-Time Feedback in Superconducting Circuits

  1. Christian Kraglund Andersen,
  2. Ants Remm,
  3. Stefania Balasiu,
  4. Sebastian Krinner,
  5. Johannes Heinsoo,
  6. Jean-Claude Besse,
  7. Mihai Gabureac,
  8. Andreas Wallraff,
  9. and Christopher Eichler
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit
parity operators and by conditioning operations on the observed error syndromes. Here, we experimentally demonstrate the use of an ancillary qubit to repeatedly measure the ZZ and XX parity operators of two data qubits and to thereby project their joint state into the respective parity subspaces. By applying feedback operations conditioned on the outcomes of individual parity measurements, we demonstrate the real-time stabilization of a Bell state with a fidelity of F≈74% in up to 12 cycles of the feedback loop. We also perform the protocol using Pauli frame updating and, in contrast to the case of real-time stabilization, observe a steady decrease in fidelity from cycle to cycle. The ability to stabilize parity over multiple feedback rounds with no reduction in fidelity provides strong evidence for the feasibility of executing stabilizer codes on timescales much longer than the intrinsic coherence times of the constituent qubits.

Quantum communication with time-bin encoded microwave photons

  1. Philipp Kurpiers,
  2. Marek Pechal,
  3. Baptiste Royer,
  4. Paul Magnard,
  5. Theo Walter,
  6. Johannes Heinsoo,
  7. Yves Salathé,
  8. Abdulkadir Akin,
  9. Simon Storz,
  10. Jean-Claude Besse,
  11. Simone Gasparinetti,
  12. Alexandre Blais,
  13. and Andreas Wallraff
Heralding techniques are useful in quantum communication to circumvent losses without resorting to error correction schemes or quantum repeaters. Such techniques are realized, for example,
by monitoring for photon loss at the receiving end of the quantum link while not disturbing the transmitted quantum state. We describe and experimentally benchmark a scheme that incorporates error detection in a quantum channel connecting two transmon qubits using traveling microwave photons. This is achieved by encoding the quantum information as a time-bin superposition of a single photon, which simultaneously realizes high communication rates and high fidelities. The presented scheme is straightforward to implement in circuit QED and is fully microwave-controlled, making it an interesting candidate for future modular quantum computing architectures.

Rapid high-fidelity multiplexed readout of superconducting qubits

  1. Johannes Heinsoo,
  2. Christian Kraglund Andersen,
  3. Ants Remm,
  4. Sebastian Krinner,
  5. Theodore Walter,
  6. Yves Salathé,
  7. Simone Gasperinetti,
  8. Jean-Claude Besse,
  9. Anton Potočnik,
  10. Christopher Eichler,
  11. and Andreas Wallraff
The duration and fidelity of qubit readout is a critical factor for applications in quantum information processing as it limits the fidelity of algorithms which reuse qubits after measurement
or apply feedback based on the measurement result. Here we present fast multiplexed readout of five qubits in a single 1.2 GHz wide readout channel. Using a readout pulse length of 80 ns and populating readout resonators for less than 250 ns we find an average correct assignment probability for the five measured qubits to be 97%. The differences between the individual readout errors and those found when measuring the qubits simultaneously are within 1%. We employ individual Purcell filters for each readout resonator to suppress off-resonant driving, which we characterize by the dephasing imposed on unintentionally measured qubits. We expect the here presented readout scheme to become particularly useful for the selective readout of individual qubits in multi-qubit quantum processors.