Coherence properties of the 0-πqubit

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...

Control and coherence time enhancement of the 0–π qubit

“…any low-degree polynomials in {f, θ, q f , q θ }. Equations (6), (7) lead together to the remarkably long coherence times expected for the qubit in the deep 0-π regime, as recently confirmed quantitatively in [22]. (a) Effective one-dimensional potential (black) and wave functions for the two lowest lying energy states (color), extracted using a Born-Oppenheimer approach (see appendix B).…”

“…Using this approach, we predict coherence time enhancements between one and three orders of magnitude, depending on parameter regime. ζ-mode) [22]. Nevertheless, we found that the 0-π qubit still has the potential to outperform state-of-the-art superconducting devices.…”

“…where J(t) is the tunable Josephson-energy of the coupling element, and f r the resonator phase operator. We have previously shown that the ζ-mode frequency goes to zero in the deep 0-π regime leading to diverging thermal occupation of this mode [22], something which was not taken into account in [20]. The impact of thermal fluctuations due to the 0-π circuit internal modes thus requires further study and we propose in section 6 a cooling scheme that can help approximate the ideal behavior considered in [20].…”

“…As mentioned above, in the limit  ¥ L , moderate variations of the external flux through the qubit loop do not break the 0-π symmetry, such that mutual inductive coupling can potentially be a symmetry-preserving coupling mechanism. However, for precisely the same reason that the qubit is highly insensitive to flux noise [22], control and readout strategies based on mutual inductive coupling are ineffective. Large external flux excursions, in contrast, can be used to move between regimes where the logical states are localized in different potential wells, to a regime where they are in a superposition of both wells.…”

“…With a set of non-overlapping logical wave functions and very low flux and charge dispersion, the 0-π qubit displays exponential suppression of relaxation and dephasing. It has been shown that the 0-π qubit can be used to encode quantum information in a protected subspace [20][21][22][23], but in a regime of parameters that is challenging to realize with current superconducting quantum circuits. In fact, the fully protected regime of this device exploits a degree of freedom with large quantum fluctuations, something which requires an effective impedance surpassing the quantum of resistance by orders of magnitude.…”