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.

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.

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.

Hybrid Quantum Error Correction in Qubit Architectures

  1. Lasse Bjørn Kristensen,
  2. Morten Kjaergaard,
  3. Christian Kraglund Andersen,
  4. and Nikolaj Thomas Zinner
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors
on quantum information. Here, we present such a quantum error correcting scheme for correcting the dominant error sources, phase decoherence and energy relaxation, in qubit architectures, using a hybrid approach combining autonomous correction based on engineered dissipation with traditional measurement-based quantum error correction. Using numerical simulations with realistic device parameters for superconducting circuits, we show that this scheme can achieve a 5- to 10-fold increase in storage-time while using only six qubits for the encoding and two ancillary qubits for the operation of the autonomous part of the scheme, providing a potentially large reduction of qubit overhead compared to typical measurement-based error correction schemes. Furthermore, the scheme relies on standard interactions and qubit driving available in most major quantum computing platforms, making it implementable in a wide range of architectures.

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.

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.

Low-Latency Digital Signal Processing for Feedback and Feedforward in Quantum Computing and Communication

  1. Yves Salathé,
  2. Philipp Kurpiers,
  3. Thomas Karg,
  4. Christian Lang,
  5. Christian Kraglund Andersen,
  6. Abdulkadir Akin,
  7. Christopher Eichler,
  8. and Andreas Wallraff
Quantum computing architectures rely on classical electronics for control and readout. Employing classical electronics in a feedback loop with the quantum system allows to stabilize
states, correct errors and to realize specific feedforward-based quantum computing and communication schemes such as deterministic quantum teleportation. These feedback and feedforward operations are required to be fast compared to the coherence time of the quantum system to minimize the probability of errors. We present a field programmable gate array (FPGA) based digital signal processing system capable of real-time quadrature demodulation, determination of the qubit state and generation of state-dependent feedback trigger signals. The feedback trigger is generated with a latency of 110ns with respect to the timing of the analog input signal. We characterize the performance of the system for an active qubit initialization protocol based on dispersive readout of a superconducting qubit and discuss potential applications in feedback and feedforward algorithms.

Strong Coupling Cavity QED with Gate-Defined Double Quantum Dots Enabled by a High Impedance Resonator

  1. Anna Stockklauser,
  2. Pasquale Scarlino,
  3. Jonne Koski,
  4. Simone Gasparinetti,
  5. Christian Kraglund Andersen,
  6. Christian Reichl,
  7. Werner Wegscheider,
  8. Thomas Ihn,
  9. Klaus Ensslin,
  10. and Andreas Wallraff
The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single
photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-detuned GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices (SQUIDs). In the resonant regime, we resolve the vacuum Rabi mode splitting of size 2g/2π=238 MHz at a resonator linewidth κ/2π=12 MHz and a DQD charge qubit dephasing rate of γ2/2π=80 MHz extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit based cavity QED for quantum information processing in semiconductor nano-structures.

Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators

  1. Shruti Puri,
  2. Christian Kraglund Andersen,
  3. Arne L. Grimsmo,
  4. and Alexandre Blais
Quantum annealing aims to solve combinatorial optimization problems mapped on to Ising interactions between quantum spins. A critical factor that limits the success of a quantum annealer
is its sensitivity to noise, and intensive research is consequently focussed towards developing noise-resilient annealers. Here we propose a new paradigm for quantum annealing with a scalable network of all-to-all connected, two-photon driven Kerr-nonlinear resonators. Each of these resonators encode an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. The fully-connected optimization problem is mapped onto local fields driving the resonators, which are themselves connected by local four-body interactions. We describe an adiabatic annealing protocol in this system and analyze its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, making it a promising platform for implementing a large scale quantum Ising machine. Finally, we propose a realistic implementation of this scheme in circuit QED.