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.

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.

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.

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.

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.

Engineering cryogenic setups for 100-qubit scale superconducting circuit systems

  1. Sebastian Krinner,
  2. Simon Storz,
  3. Philipp Kurpiers,
  4. Paul Magnard,
  5. Johannes Heinsoo,
  6. Raphael Keller,
  7. Janis Luetolf,
  8. Christopher Eichler,
  9. and Andreas Wallraff
A robust cryogenic infrastructure in form of a wired, thermally optimized dilution refrigerator is essential for present and future solid-state based quantum processors. Here, we engineer
an extensible cryogenic setup, which minimizes passive and active heat loads, while guaranteeing rapid qubit control and readout. We review design criteria for qubit drive lines, flux lines, and output lines used in typical experiments with superconducting circuits and describe each type of line in detail. The passive heat load of stainless steel and NbTi coaxial cables and the active load due to signal dissipation are measured, validating our robust and extensible concept for thermal anchoring of attenuators, cables, and other microwave components. Our results are important for managing the heat budget of future large-scale quantum computers based on superconducting circuits.

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.