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-qubitparity 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.
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 measurementor 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.
Quantum computing architectures rely on classical electronics for control and readout. Employing classical electronics in a feedback loop with the quantum system allows to stabilizestates, 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.
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 singlephoton 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 aims to solve combinatorial optimization problems mapped on to Ising interactions between quantum spins. A critical factor that limits the success of a quantum annealeris 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.
We study an implementation of the open GRAPE (Gradient Ascent Pulse Engineering) algorithm well suited for large open quantum systems. While typical implementations of optimal controlalgorithms for open quantum systems rely on a transformation to Liouville space, our implementation avoid this transformation which leads to a polynomial speed-up of the open GRAPE algorithm in cases of interest. As an example, we apply our implementation to active reset of a readout resonator in circuit QED. In this problem, the shape of a microwave pulse is optimized to steer the cavity state towards its ground state as fast as possible. Using our open GRAPE implementation, we obtain pulse shapes leading to a reset time over four times faster than typical passive reset.
We present a method to identify the coupled, normal modes of a superconducting transmission-line with an embedded lumped element circuit. We evaluate the effective transmission-linenon-linearities in the case of Kerr-like Josephson interactions in the circuit and in the case where the embedded circuit constitutes a qubit degree of freedom, which is Rabi coupled to the field in the transmission-line. Our theory quantitatively accounts for the very high and positive Kerr non-linearities observed in a recent experiment [M. Reh\’ak et.al., Appl. Phys. Lett. 104, 162604], and we can evaluate the accomplishments of modified versions of the experimental circuit.
The interaction of light and matter is often described by the exchange of single excitations. When the coupling strength is a significant fraction of the system frequencies, the numberof excitations are no longer preserved and that simple picture breaks down. This regime is known as the ultrastrong coupling regime and is characterized by non-trivial light-matter eigenstates and complex dynamics. In this work, we propose to use a an array Josephson junctions to increase the impedance of the light mode enabling ultrastrong coupling to a transmon qubit. We show that the resulting dynamics can be generated and probed by taking advantage of the multi-mode structure of the junction array. This proposal relies on the frequency tunability of the transmon and, crucially, on the use of a low frequency mode of the array, which allows for non-adiabatic changes of the ground state.
We propose to use a cryogenic nonlinear resonator for the projective readout, classical memory, and feedback for a superconducting qubit. This approach sidesteps many of the inefficienciesinherent in two-way communication between temperature stages in typical systems with room temperature controllers, and avoids increasing the cryogenic heat load. This controller may find a broad range of uses in multi-qubit systems, but here we analyze two specific demonstrative cases in single qubit-control. In the first case, the nonlinear controller is used to initialize the qubit in a definite eigenstate. And in the second case, the qubit’s state is read into the controller’s classical memory, where it is stored for an indefinite period of time, and then used to reinstate the measured state after the qubit has decayed. We analyze the properties of this system and we show simulations of the time evolution for the full system dynamics.
A Superconducting Quantum Interference Device (SQUID) inserted in a superconducting waveguide resonator imposes current and voltage boundary conditions that makes it suitable as a tuningelement for the resonator modes. If such a SQUID element is subject to a periodically varying magnetic flux, the resonator modes acquire frequency side bands. In this work we calculate the multi-frequency eigenmodes of resonators coupled to periodically driven SQUIDs and we use the Lagrange formalism to propose a theory for their quantization. The elementary excitations of a multi-frequency mode can couple resonantly to physical systems with different transition frequencies and this makes the resonator an efficient quantum bus for state transfer and coherent quantum operations in hybrid quantum systems. As an example of the application of our multi-frequency modes, we determine their coupling to transmon qubits with different frequencies and we present a bi-chromatic scheme for entanglement and gate operations.