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.

Correlations and entanglement of microwave photons emitted in a cascade decay

  1. Simone Gasparinetti,
  2. Marek Pechal,
  3. Jean-Claude Besse,
  4. Mintu Mondal,
  5. Christopher Eichler,
  6. and Andreas Wallraff
An excited emitter decays by radiating a photon into a quantized mode of the electromagnetic field, a process known as spontaneous emission. If the emitter is driven to a higher excited
state, it radiates multiple photons in a cascade decay. Atomic and biexciton cascades have been exploited as sources of polarization-entangled photon pairs. Because the photons are emitted sequentially, their intensities are strongly correlated in time, as measured in a double-beam coincidence experiment. Perhaps less intuitively, their phases can also be correlated, provided a single emitter is deterministically prepared into a superposition state, and the emitted radiation is detected in a phase-sensitive manner and with high efficiency. Here we have met these requirements by using a superconducting artificial atom, coherently driven to its second-excited state and decaying into a well-defined microwave mode. Our results highlight the coherent nature of cascade decay and demonstrate a novel protocol to generate entanglement between itinerant field modes.

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.

A Superconducting Quantum Simulator for Topological Order and the Toric Code

  1. Mahdi Sameti,
  2. Anton Potocnik,
  3. Dan E. Browne,
  4. Andreas Wallraff,
  5. and Michael J. Hartmann
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based
on symmetries. Fractional quantum Hall systems and quantum spin liquids are receiving substantial interest because of their intriguing quantum correlations, their exotic excitations and prospects for protecting stored quantum information against errors. Here we show that the Hamiltonian of the central model of this class of systems, the Toric Code, can be directly implemented as an analog quantum simulator in lattices of superconducting circuits. The four-body interactions, which lie at its heart, are in our concept realized via Superconducting Quantum Interference Devices (SQUIDs) that are driven by a suitably oscillating flux bias. All physical qubits and coupling SQUIDs can be individually controlled with high precision. Topologically ordered states can be prepared via an adiabatic ramp of the stabilizer interactions. Strings of qubit operators, including the stabilizers and correlations along non-contractible loops, can be read out via a capacitive coupling to read-out resonators. Moreover, the available single qubit operations allow to create and propagate elementary excitations of the Toric Code and to verify their fractional statistics. The architecture we propose allows to implement a large variety of many-body interactions and thus provides a versatile analog quantum simulator for topological order and lattice gauge theories.

Contextuality without nonlocality in a superconducting quantum system

  1. Markus Jerger,
  2. Yarema Reshitnyk,
  3. Markus Oppliger,
  4. Anton Potočnik,
  5. Mintu Mondal,
  6. Andreas Wallraff,
  7. Kenneth Goodenough,
  8. Stephanie Wehner,
  9. Kristinn Juliusson,
  10. Nathan K. Langford,
  11. and Arkady Fedorov
Quantum physics cannot be reconciled with the classical philosophy of noncontextual realism. Realism demands that system properties exist independently of whether they are measured,
while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell-Kochen-Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such models experimentally, since imperfections may introduce loopholes that enable a realist interpretation. Using a superconducting qutrit with deterministic, binary-outcome readouts, we violate a noncontextuality inequality while addressing the detection, individual-existence and compatibility loopholes. Noncontextuality tests have been carried out in a range of different physical systems and dimensionalities, including neutrons, trapped ions and single photons, but no experiment addressing all three loopholes has been performed in the qutrit scenario where entanglement cannot play a role. Demonstrating state-dependent contextuality of a solid-state system is also an important conceptual ingredient for universal quantum computation in surface-code architectures, currently the most promising route to scalable quantum computing.

Photon-mediated interactions between distant artificial atoms

  1. Arjan F. van Loo,
  2. Arkady Fedorov,
  3. Kevin Lalumière,
  4. Barry C. Sanders,
  5. Alexandre Blais,
  6. and Andreas Wallraff
Photon-mediated interactions between atoms are of fundamental importance in quantum optics, quantum simulations and quantum information processing. The exchange of real and virtual
photons between atoms gives rise to non-trivial interactions the strength of which decreases rapidly with distance in three dimensions. Here we study much stronger photon mediated interactions using two superconducting qubits in an open onedimensional transmission line. Making use of the unique possibility to tune these qubits by more than a quarter of their transition frequency we observe both coherent exchange interactions at an effective separation of 3λ/4 and the creation of super- and sub-radiant states at a separation of one photon wavelength λ. This system is highly suitable for exploring collective atom/photon interactions and applications in quantum communication technology.

Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms

  1. Kevin Lalumière,
  2. Barry C. Sanders,
  3. Arjan F. van Loo,
  4. Arkady Fedorov,
  5. Andreas Wallraff,
  6. and Alexandre Blais
We study the collective effects that emerge in waveguide quantum electrodynamics where several (artificial) atoms are coupled to a one-dimensional (1D) superconducting transmission
line. Since single microwave photons can travel without loss for a long distance along the line, real and virtual photons emitted by one atom can be reabsorbed or scattered by a second atom. Depending on the distance between the atoms, this collective effect can lead to super- and subradiance or to a coherent exchange-type interaction between the atoms. Changing the artificial atoms transition frequencies, something which can be easily done with superconducting qubits (two levels artificial atoms), is equivalent to changing the atom-atom separation and thereby opens the possibility to study the characteristics of these collective effects. To study this waveguide quantum electrodynamics system, we extend previous work and present an effective master equation valid for an ensemble of inhomogeneous atoms. Using input-output theory, we compute analytically and numerically the elastic and inelastic scattering and show how these quantities reveal information about collective effects. These theoretical results are compatible with recent experimental results using transmon qubits coupled to a superconducting one-dimensional transmission line [A.F. van Loo {\it et al.} (2013)].

Collective Suppression of Linewidths in Circuit QED

  1. Felix Nissen,
  2. Johannes M. Fink,
  3. Jonas A. Mlynek,
  4. Andreas Wallraff,
  5. and Jonathan Keeling
We report the experimental observation, and a theoretical explanation, of collective suppression of linewidths for multiple superconducting qubits coupled to a good cavity. This demonstrates
how strong qubit-cavity coupling can significantly modify the dephasing and dissipation processes that might be expected for individual qubits, and can potentially improve coherence times in many-body circuit QED.

Demonstrating W-type Entanglement of Dicke-States in Resonant Cavity Quantum Electrodynamics

  1. Jonas A. Mlynek,
  2. Abdufarrukh A. Abdumalikov Jr,
  3. Johannes M. Fink,
  4. Lars Steffen,
  5. Matthias Baur,
  6. Christian Lang,
  7. Arjan F. van Loo,
  8. and Andreas Wallraff
Nonlinearity and entanglement are two important properties by which physical systems can be identified as non-classical. We study the dynamics of the resonant interaction of up to N=3
two-level systems and a single mode of the electromagnetic field sharing a single excitation dynamically. We observe coherent vacuum Rabi oscillations and their nonlinear speed up by tracking the populations of all qubits and the resonator in time. We use quantum state tomography to show explicitly that the dynamics generates maximally entangled states of the W class in a time limited only by the collective interaction rate. We use an entanglement witness and the threetangle to characterize the state whose fidelity F=78% is limited in our experiments by crosstalk arising during the simultaneous qubit manipulations which is absent in a sequential approach with F=91%.