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.

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.

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.

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.

Repeated Quantum Error Detection in a Surface Code

  1. Christian Kraglund Andersen,
  2. Ants Remm,
  3. Stefania Lazar,
  4. Sebastian Krinner,
  5. Nathan Lacroix,
  6. Graham J. Norris,
  7. Mihai Gabureac,
  8. Christopher Eichler,
  9. and Andreas Wallraff
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes,
logical qubits can be redundantly encoded in a set of physical qubits. One such scalable approach is based on the surface code. Here we experimentally implement its smallest viable instance, capable of repeatedly detecting any single error using seven superconducting qubits, four data qubits and three ancilla qubits. Using high-fidelity ancilla-based stabilizer measurements we initialize the cardinal states of the encoded logical qubit with an average logical fidelity of 96.1%. We then repeatedly check for errors using the stabilizer readout and observe that the logical quantum state is preserved with a lifetime and coherence time longer than those of any of the constituent qubits when no errors are detected. Our demonstration of error detection with its resulting enhancement of the conditioned logical qubit coherence times in a 7-qubit surface code is an important step indicating a promising route towards the realization of quantum error correction in the surface code.