Decoherence in Josephson-junction qubits due to critical-current fluctuations

Abstract

We compute the decoherence caused by 1/f fluctuations at low frequency f in the critical current I0 of Josephson junctions incorporated into flux, phase, charge and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time τ φ scales as I0/ΩΛS 1/2 I 0(1 Hz), where Ω/2π is the energy level splitting frequency, SI 0 (1 Hz) is the spectral density of the critical current noise at 1 Hz, and Λ ≡ |I0dΩ/ΩdI0| is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time t scales as exp(−t 2 /2τ 2 φ ) when the dephasing due to critical current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in I0 and A, and show that their values of SI 0 (1 Hz) scale to within a factor of three of 144 (I0/µA) 2 / A/µmWe empirically extrapolate S 1/2 I 0(1 Hz) to lower temperatures using a scaling T (K)/4.2. Using this result, we find that the predicted values of τ φ at 100 mK range from 0.8 to 12 µs, and are usually substantially longer than values measured experimentally at lower temperatures.

Spectroscopy of low-frequency noise and its temperature dependence in a superconducting qubit

“…These expressions reproduce the noise spectrum, with the use of correction factors, as explained in the following section (Eqs. [18][19][20][21][22][23][24].…”

“…This noise may originate in the critical-current fluctuations of the Josephson junctions [19][20][21][22] , and/or fluctuating offset charges, due to, e.g., charge traps located in the oxides of the junction, metal-insulator interfaces, or surfaces. Charge noise can lead to dephasing even in the flux qubit, even though the junctions have a relatively high ratio of Josephson-tunneling to Coulomb-charging energies (E J /E C ≈ 50 in our device).…”

Relaxation and decoherence in a resonantly driven qubit

“…(19) to (21). However, such conditions can not be fulfilled in reality for a resonantly driven qubit starting from a pure state.…”

“…According to Eqs. (19) to (21), for the resonantly driven qubit, the relaxation time is T 1 = τ 1 and the field-dependent decoherence time is T 2,2 = τ 22 . For comparison, we have calculated the relaxation and field-dependent decoherence times using the analytical expressions given by Eq.…”

“…For this reason, environment-induced decoherence has been and is still a main obstacle to the practical application of superconducting qubits in quantum computation. [2,13,14,15,16] The environment-induced decoherence of superconducting qubits has been extensively studied both theoretically [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33] and experimentally [2,8,13,21,25,34,35,36,37,38,39,40] in the absence of ac driving fields (free decay). Quite a few proposals, such as dynamical decoupling, [41,42,43,44,45,46,47,48] decoherence free subspaces, [49,50,51,52] spin echoes, …”