Realization of Constant-Depth Fan-Out with Real-Time Feedforward on a Superconducting Quantum Processor

  1. Yongxin Song,
  2. Liberto Beltrán,
  3. Ilya Besedin,
  4. Michael Kerschbaum,
  5. Marek Pechal,
  6. François Swiadek,
  7. Christoph Hellings,
  8. Dante Colao Zanuz,
  9. Alexander Flasby,
  10. Jean-Claude Besse,
  11. and Andreas Wallraff
When using unitary gate sequences, the growth in depth of many quantum circuits with output size poses significant obstacles to practical quantum computation. The quantum fan-out operation,
which reduces the circuit depth of quantum algorithms such as the quantum Fourier transform and Shor’s algorithm, is an example that can be realized in constant depth independent of the output size. Here, we demonstrate a quantum fan-out gate with real-time feedforward on up to four output qubits using a superconducting quantum processor. By performing quantum state tomography on the output states, we benchmark our gate with input states spanning the entire Bloch sphere. We decompose the output-state error into a set of independently characterized error contributions. We extrapolate our constant-depth circuit to offer a scaling advantage compared to the unitary fan-out sequence beyond 25 output qubits with feedforward control, or beyond 17 output qubits if the classical feedforward latency is negligible. Our work highlights the potential of mid-circuit measurements combined with real-time conditional operations to improve the efficiency of complex quantum algorithms.

Deterministic generation of a 20-qubit two-dimensional photonic cluster state

  1. James O'Sullivan,
  2. Kevin Reuer,
  3. Aleksandr Grigorev,
  4. Xi Dai,
  5. Alonso Hernández-Antón,
  6. Manuel H. Muñoz-Arias,
  7. Christoph Hellings,
  8. Alexander Flasby,
  9. Dante Colao Zanuz,
  10. Jean-Claude Besse,
  11. Alexandre Blais,
  12. Daniel Malz,
  13. Christopher Eichler,
  14. and Andreas Wallraff
Multidimensional cluster states are a key resource for robust quantum communication, measurement-based quantum computing and quantum metrology. Here, we present a device capable of
emitting large-scale entangled microwave photonic states in a two dimensional ladder structure. The device consists of a pair of coupled superconducting transmon qubits which are each tuneably coupled to a common output waveguide. This architecture permits entanglement between each transmon and a deterministically emitted photonic qubit. By interleaving two-qubit gates with controlled photon emission, we generate 2 x n grids of time- and frequency-multiplexed cluster states of itinerant microwave photons. We measure a signature of localizable entanglement across up to 20 photonic qubits. We expect the device architecture to be capable of generating a wide range of other tensor network states such as tree graph states, repeater states or the ground state of the toric code, and to be readily scalable to generate larger and higher dimensional states.

Mitigating Losses of Superconducting Qubits Strongly Coupled to Defect Modes

  1. Dante Colao Zanuz,
  2. Quentin Ficheux,
  3. Laurent Michaud,
  4. Alexei Orekhov,
  5. Kilian Hanke,
  6. Alexander Flasby,
  7. Mohsen Bahrami Panah,
  8. Graham J. Norris,
  9. Michael Kerschbaum,
  10. Ants Remm,
  11. François Swiadek,
  12. Christoph Hellings,
  13. Stefania Lazăr,
  14. Colin Scarato,
  15. Nathan Lacroix,
  16. Sebastian Krinner,
  17. Christopher Eichler,
  18. Andreas Wallraff,
  19. and Jean-Claude Besse
The dominant contribution to the energy relaxation of state-of-the-art superconducting qubits is often attributed to their coupling to an ensemble of material defects which behave as
two-level systems. These defects have varying microscopic characteristics which result in a large range of observable defect properties such as resonant frequencies, coherence times and coupling rates to qubits g. Here, we investigate strategies to mitigate losses to the family of defects that strongly couple to qubits (g/2π≥ 0.5 MHz). Such strongly coupled defects are particularly detrimental to the coherence of qubits and to the fidelities of operations relying on frequency excursions, such as flux-activated two-qubit gates. To assess their impact, we perform swap spectroscopy on 92 frequency-tunable qubits and quantify the spectral density of these strongly coupled modes. We show that the frequency configuration of the defects is rearranged by warming up the sample to room temperature, whereas the total number of defects on a processor tends to remain constant. We then explore methods for fabricating qubits with a reduced number of strongly coupled defect modes by systematically measuring their spectral density for decreasing Josephson junction dimensions and for various surface cleaning methods. Our results provide insights into the properties of strongly coupled defect modes and show the benefits of minimizing Josephson junction dimensions to improve qubit properties.

Fast Flux-Activated Leakage Reduction for Superconducting Quantum Circuits

  1. Nathan Lacroix,
  2. Luca Hofele,
  3. Ants Remm,
  4. Othmane Benhayoune-Khadraoui,
  5. Alexander McDonald,
  6. Ross Shillito,
  7. Stefania Lazar,
  8. Christoph Hellings,
  9. Francois Swiadek,
  10. Dante Colao Zanuz,
  11. Alexander Flasby,
  12. Mohsen Bahrami Panah,
  13. Michael Kerschbaum,
  14. Graham J. Norris,
  15. Alexandre Blais,
  16. Andreas Wallraff,
  17. and Sebastian Krinner
Quantum computers will require quantum error correction to reach the low error rates necessary for solving problems that surpass the capabilities of conventional computers. One of the
dominant errors limiting the performance of quantum error correction codes across multiple technology platforms is leakage out of the computational subspace arising from the multi-level structure of qubit implementations. Here, we present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. This operation removes leakage down to our measurement accuracy of 7⋅10−4 in approximately 50ns with a low error of 2.5(1)⋅10−3 on the computational subspace, thereby reaching durations and fidelities comparable to those of single-qubit gates. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion to close to what can be achieved using leakage-rejection methods which do not scale. Our approach does neither require additional control electronics nor on-chip components and is applicable to both auxiliary and data qubits. These benefits make our method particularly attractive for mitigating leakage in large-scale quantum error correction circuits, a crucial requirement for the practical implementation of fault-tolerant quantum computation.

Enhancing Dispersive Readout of Superconducting Qubits Through Dynamic Control of the Dispersive Shift: Experiment and Theory

  1. François Swiadek,
  2. Ross Shillito,
  3. Paul Magnard,
  4. Ants Remm,
  5. Christoph Hellings,
  6. Nathan Lacroix,
  7. Quentin Ficheux,
  8. Dante Colao Zanuz,
  9. Graham J. Norris,
  10. Alexandre Blais,
  11. Sebastian Krinner,
  12. and Andreas Wallraff
The performance of a wide range of quantum computing algorithms and protocols depends critically on the fidelity and speed of the employed qubit readout. Examples include gate sequences
benefiting from mid-circuit, real-time, measurement-based feedback, such as qubit initialization, entanglement generation, teleportation, and perhaps most importantly, quantum error correction. A prominent and widely-used readout approach is based on the dispersive interaction of a superconducting qubit strongly coupled to a large-bandwidth readout resonator, frequently combined with a dedicated or shared Purcell filter protecting qubits from decay. By dynamically reducing the qubit-resonator detuning and thus increasing the dispersive shift, we demonstrate a beyond-state-of-the-art two-state-readout error of only 0.25% in 100 ns integration time. Maintaining low readout-drive strength, we nearly quadruple the signal-to-noise ratio of the readout by doubling the readout mode linewidth, which we quantify by considering the hybridization of the readout-resonator and its dedicated Purcell-filter. We find excellent agreement between our experimental data and our theoretical model. The presented results are expected to further boost the performance of new and existing algorithms and protocols critically depending on high-fidelity, fast, mid-circuit measurements.

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.

Intermodulation Distortion in a Josephson Traveling Wave Parametric Amplifier

  1. Ants Remm,
  2. Sebastian Krinner,
  3. Nathan Lacroix,
  4. Christoph Hellings,
  5. Francois Swiadek,
  6. Graham Norris,
  7. Christopher Eichler,
  8. and Andreas Wallraff
Josephson traveling wave parametric amplifiers enable the amplification of weak microwave signals close to the quantum limit with large bandwidth, which has a broad range of applications
in superconducting quantum computing and in the operation of single-photon detectors. While the large bandwidth allows for their use in frequency-multiplexed detection architectures, an increased number of readout tones per amplifier puts more stringent requirements on the dynamic range to avoid saturation. Here, we characterize the undesired mixing processes between the different frequency-multiplexed tones applied to a Josephson traveling wave parametric amplifier, a phenomenon also known as intermodulation distortion. The effect becomes particularly significant when the amplifier is operated close to its saturation power. Furthermore, we demonstrate that intermodulation distortion can lead to significant crosstalk and reduction of fidelity for multiplexed readout of superconducting qubits. We suggest using large detunings between the pump and signal frequencies to mitigate crosstalk. Our work provides insights into the limitations of current Josephson traveling wave parametric amplifiers and highlights the importance of performing further research on these devices.

Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code

  1. Sebastian Krinner,
  2. Nathan Lacroix,
  3. Ants Remm,
  4. Agustin Di Paolo,
  5. Elie Genois,
  6. Catherine Leroux,
  7. Christoph Hellings,
  8. Stefania Lazar,
  9. Francois Swiadek,
  10. Johannes Herrmann,
  11. Graham J. Norris,
  12. Christian Kraglund Andersen,
  13. Markus Müller,
  14. Alexandre Blais,
  15. Christopher Eichler,
  16. and Andreas Wallraff
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors
occurring due to unavoidable decoherence and limited control accuracy. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors. Using 17 physical qubits in a superconducting circuit we encode quantum information in a distance-three logical qubit building up on recent distance-two error detection experiments. In an error correction cycle taking only 1.1μs, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit- and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in postprocessing. We find a low error probability of 3% per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error correction cycles, together with recent advances in ion traps, support our understanding that fault-tolerant quantum computation will be practically realizable.

Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases

  1. Johannes Herrmann,
  2. Sergi Masot Llima,
  3. Ants Remm,
  4. Petr Zapletal,
  5. Nathan A. McMahon,
  6. Colin Scarato,
  7. Francois Swiadek,
  8. Christian Kraglund Andersen,
  9. Christoph Hellings,
  10. Sebastian Krinner,
  11. Nathan Lacroix,
  12. Stefania Lazar,
  13. Michael Kerschbaum,
  14. Dante Colao Zanuz,
  15. Graham J. Norris,
  16. Michael J. Hartmann,
  17. Andreas Wallraff,
  18. and Christopher Eichler
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct
measurements and classically computed correlations become computationally expensive when increasing the system size. Quantum neural networks tailored to recognize specific features of quantum states by combining unitary operations, measurements and feedforward promise to require fewer measurements and to tolerate errors. Here, we realize a quantum convolutional neural network (QCNN) on a 7-qubit superconducting quantum processor to identify symmetry-protected topological (SPT) phases of a spin model characterized by a non-zero string order parameter. We benchmark the performance of the QCNN based on approximate ground states of a family of cluster-Ising Hamiltonians which we prepare using a hardware-efficient, low-depth state preparation circuit. We find that, despite being composed of finite-fidelity gates itself, the QCNN recognizes the topological phase with higher fidelity than direct measurements of the string order parameter for the prepared states.

Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets

  1. Nathan Lacroix,
  2. Christoph Hellings,
  3. Christian Kraglund Andersen,
  4. Agustin Di Paolo,
  5. Ants Remm,
  6. Stefania Lazar,
  7. Sebastian Krinner,
  8. Graham J. Norris,
  9. Mihai Gabureac,
  10. Alexandre Blais,
  11. Christopher Eichler,
  12. and Andreas Wallraff
Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof
is the quantum approximate optimization algorithm (QAOA), an approach to solve combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from QAOA critically relies on the mitigation of errors during the execution of the algorithm, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two CZ-gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to 9 layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.