We present a comprehensive and self-contained simplified review of the quantum computing scheme of [1,2], which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction and low overhead, arbitrarily long-range logical gates. These features make it by far the best and most practical quantum computing scheme devised to date. We restrict the discussion to direct manipulation of the surface code using the stabilizer formalism, both of which we also briefly review, to make the scheme accessible to a broad audience.

Erratum: High-threshold universal quantum computation on the surface code [Phys. Rev. A 80, 052312 (2009)]

Superconducting circuits rank among some of the most interesting architectures for the implementation of quantum information processing devices. The recently proposed 0-π qubit (Brooks et al 2013 Phys. Rev. A 87 52306) promises increased protection from spontaneous relaxation and dephasing. In this paper we present a detailed theoretical study of the coherence properties of the 0-π device, investigate relevant decoherence channels, and show estimates for achievable coherence times in multiple parameter regimes. In our analysis, we include disorder in circuit parameters, which results in the coupling of the qubit to a low-energy, spurious harmonic mode. We analyze the effects of such coupling on decoherence, in particular dephasing due to photon shot noise, and outline how such a noise channel can be mitigated by appropriate parameter choices. In the end we find that the 0-π qubit performs well and may become an attractive candidate for the implementation of the next-generation superconducting devices for uses in quantum computing and information.Conceptually, the 0-π circuit exhibits a rudimentary form of topological protection that combines exponential suppression of noise-induced transitions (dissipation) with exponential suppression of dephasing, see figure 1. The former is achieved by engineering qubit states with disjoint support, the latter by rendering qubit states (nearly) degenerate and exponentially suppressing the sensitivity of the corresponding energies to lowfrequency environmental noise.The circuit underlying the 0-π qubit consists of four nodes connected by a pair of linear inductors, a pair of capacitors, and a pair of Josephson junctions as shown in figure 2. Two issues pose challenges to the implementation of the 0-π design: first, to achieve the desired regime it is necessary to simultaneously realize large superinductances, large shunting capacitors, and high junction charging energies (very low stray capacitances); second, circuit elements should ideally be pairwise identical (no disorder in circuit element parameters) in order to prevent coupling of the qubit to a spurious circuit mode [14], which we will refer to as the ζ-mode 6 .While notable increases in accessible inductance values by means of junction-array based superinductances may partially address the first issue [15][16][17][18][19], some amount of circuit parameter disorder and hence residual coupling to the ζ-mode is unavoidable. In the present work, we theoretically assess the coherence properties of 0-π devices, ones that are possible to realize with todayʼs state-of-the art fabrication techniques, as well as those that will require technological advances. Specifically, we present calculations of relevant decoherence rates resulting from the qubitʼs coupling to known noise sources, including both intrinsic sources, such as flux, charge and critical current noise, which couple directly to the qubitʼs degree of freedom, as well as noise mediated by the coupling to the spurious ζ-mode. We concentrate our study on three representa...

We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved with a tunable coupling design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasistatic tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single-photon exchange in 6 ns. Qubit coherence times exceeding 20  μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon nonconserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80%.

Qubit connectivity is an important property of a quantum processor, with an ideal processor having random access—the ability of arbitrary qubit pairs to interact directly. This a challenge with superconducting circuits, as state-of-the-art architectures rely on only nearest-neighbor coupling. Here, we implement a random access superconducting quantum information processor, demonstrating universal operations on a nine-qubit memory, with a Josephson junction transmon circuit serving as the central processor. The quantum memory uses the eigenmodes of a linear array of coupled superconducting resonators. We selectively stimulate vacuum Rabi oscillations between the transmon and individual eigenmodes through parametric flux modulation of the transmon frequency. Utilizing these oscillations, we perform a universal set of quantum gates on 38 arbitrary pairs of modes and prepare multimode entangled states, all using only two control lines. We thus achieve hardware-efficient random access multi-qubit control in an architecture compatible with long-lived microwave cavity-based quantum memories.