No abstract

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...

No abstract

We characterize a fluxonium qubit consisting of a Josephson junction inductively shunted with a NbTiN nanowire superinductance. We explain the measured energy spectrum by means of a multimode theory accounting for the distributed nature of the superinductance and the effect of the circuit nonlinearity to all orders in the Josephson potential. Using multiphoton Raman spectroscopy, we address multiple fluxonium transitions, observe multilevel Autler-Townes splitting and measure an excited state lifetime of T1 = 20 µs. By measuring T1 at different magnetic flux values, we find a crossover in the lifetime limiting mechanism from capacitive to inductive losses.The development of superinductors [1-5] has received significant interest due to their potential to provide noise protection in superconducting qubits [6][7][8]. Moreover, inductively shunted Josephson junction based superconducting circuits are known to be immune to charge noise [1], and to flux noise in the limit of large inductances [9][10][11][12]. Despite remarkable progress, the superinductances that have been so far reported in the literature are still small compared to those needed for qubit protection [7,8,11,12].A thin-film nanowire built from a disordered superconductor constitutes an alternative approach to reach the required superinductance regime. High-kinetic inductance superconducting materials, such as NbTiN and TiN, have been studied in the context of microwave detectors [13][14][15], parametric amplifiers [16][17][18], and rfSQUID qubits [19,20]. In a nanowire, the inertia of the Cooper pair condensate is manifested as the kinetic inductance of the superconducting wire, and can be expressed aswhere m is the free electron mass, e is the electron charge and n s is the density of Cooper pairs [14,21]. The second bracketed term in Eq. (1) is a geometric factor dependent on the length l, width w, and thickness d of the nanowire. By choosing a disordered superconductor with a low n s and fabricating a sufficiently long and thin wire, the kinetic inductance can be made large enough to reach the superinductance regime. In this regime, the presence of stray ground capacitance and the large kinetic inductance lower the frequencies of the self-resonant modes of the device. As is the case of long junction arrays [2], the multimode structure of the device needs to be taken into account to produce an accurate theoretical description [22,23].In this Letter, we demonstrate a fluxonium circuit integrating a NbTiN nanowire superinductance. We charac- * These authors contributed equally to this work.terize the effect of the nanowire modes on the qubit spectrum with a multimode circuit theory accounting for the distributed nature of the superinductance. Importantly, and in contrast to previous approaches tailored to weakly anharmonic qubits [24,25], our theory incorporates the circuit nonlinearity to all orders in the Josephson potential. Such difference allows us to treat the strong anharmonicity of the fluxonium qubit efficiently, and to retain the effect of ch...

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.