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-defined 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.In the strong coupling limit, cavity QED realizes the coherent exchange of a single quantum of energy between a nonlinear quantum system with two or more energy levels, e.g. a qubit, and a single mode of a high quality cavity capable of storing individual photons [1]. The distinguishing feature of strong coupling is a coherent coupling rate g, determined by the product of the dipole moment of the multi-level system and the vacuum field of the cavity, which exceeds both the cavity mode linewidth κ, determining the photon life time, and the qubit linewidth γ 2 = γ 1 /2 + γ ϕ , set by its energy relaxation and pure dephasing rates, γ 1 and γ ϕ , respectively.The strong coupling limit of Cavity QED has been reached with a multitude of physical systems including alkali atoms [2], Rydberg atoms [3], superconducting circuits [4,5] and optical transitions in semiconductor quantum dots [6,7]. Of particular interest is the use of this concept in quantum information processing with supercondcuting circuits where it is known as circuit QED [4,8,9].Motivated by the ability to suppress the spontaneous emission of qubits beyond the free space limit [10], to perform quantum non-demolition (QND) qubit read-out [11,12], to couple distant qubits through microwave photons coherently [13,14] and to convert quantum information stored in stationary qubits to photons [15,16], research towards reaching the strong coupling limit of cavity QED is pursued for the charge and spin degrees of freedom in semiconductor nano-structures [17][18][19][20][21][22]. Recently, in parallel with the work discussed here, independent efforts to reach this goal have come to fruition with gate defined DQDs in silicon [23] and carbon nanotubes [24].The essence of our approach to reach the strong coupling limit with individual electronic charges in GaAs DQDs is rooted in the enhancement of the electric component of the vacuum fluctuations ∝ √ Z r [25] by increas-ing the resonator impedance Z r beyond the typical 50 Ω of a standard copl...

No abstract

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.

Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine.

No abstract

No abstract

Variational quantum algorithms are believed to be promising for solving computationally hard problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from these algorithms critically relies on the mitigation of errors during their execution, 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 for the quantum approximate optimization algorithm (QAOA) 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 nine 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.

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.The inevitable interaction of quantum mechanical systems with their environment renders quantum information vulnerable to decoherence [1][2][3]. Quantum error correction aims to overcome this challenge by redundantly encoding logical quantum states into a larger-dimensional Hilbert space and performing repeated measurements to detect and correct for errors [4][5][6][7]. For sufficiently small error probabilities of individual operations, logical errors are expected to become increasingly unlikely when scaling up the number of physical qubits per logical qubit [8,9]. As the concept of quantum error correction provides a clear path toward fault tolerant quantum computing [10], it has been explored in a variety of physical systems ranging from nuclear magnetic resonance [11], to trapped ions [12-15] and superconducting circuits, both for conventional [16][17][18][19] and for continuous variable based encoding schemes [20].Quantum error correction typically relies on the measurement of a set of commuting multi-qubit parity operators, which ideally project the state of the data qubits onto a subspace of their Hilbert space -known as the code space -without extracting information about the logical qubit state [7]. A change in the outcome of repeated parity measurements signals the occurrence of an error, which brings the state of the qubits out of the code space. Such errors can either be corrected for in real-time by applying conditional feedback, or by keeping track of the measurement outcomes in a classical register to reconstruct the quantum state evolution in post-processing. The latter approach -also known as Pauli frame updating [21] -has the advantage of avoiding errors introduced by imperfect feedback and additional decoherence due to feedback latency. Real-time feedback, on the other hand, could be beneficial in the presence of * These authors contributed equally to this work. asymmetric relaxation e...