Decoherence predictions in a superconducting quantum processor using the steepest-entropy-ascent quantum thermodynamics framework

The current stage of quantum computing technology, called noisy intermediate-scale quantum technology, is characterized by large errors that prohibit it from being used for real applications. In these devices, decoherence, one of the main sources of error, is generally modeled by Markovian master equations such as the Lindblad master equation. In this paper, the decoherence phenomena are addressed from the perspective of the steepest-entropy-ascent quantum thermodynamics framework in which the noise is in part seen as internal to the system. The framework is as well used to describe changes in the energy associated with environmental interactions. Three scenarios, an inversion recovery demonstration, a Ramsey demonstration, and a two-qubit entanglement-disentanglement demonstration, are used to demonstrate the applicability of this framework, which provides good results relative to the demonstrations and the Lindblad equation; it does so, however, from a different perspective as to the cause of the decoherence. These demonstrations are conducted on the IBM superconducting quantum device $\mathrm{ibmq}\_\mathrm{bogota}$.

Figure 1

Schematic representation of an inversion recovery demonstration characterized by $T_1$: (a) the pulse in the $D_0$ channel is a $X_{\pi }$ gate, $M_0$ is the measurement, and (b) a pulse is applied in this channel to recover the state after the delay time. The demonstrations were conducted on the $\mathrm{ibmq}\_\mathrm{bogota}$ device from IBM, and using an open-pulse control in the qiskit python library.

Figure 2

Schematic representation of the Ramsey demonstration (a) circuit mode and (b) pulse mode to determine the coherence time $T_2^{*}$: The demonstration is conducted using the $\mathrm{ibmq}\_\mathrm{bogota}$ device and the pulse level control from IBMQ.

Figure 3

The circuit to create the entanglement and disentanglement sequence: here, $t_g/2$ is the width of the CR pulse and 0.1a corresponds to the amplitude of the pulse where “a” is the default amplitude of the CR pulse for a cnot gate. The channel $D_0$ represents the pulses on the control qubit, channel $D_1$ represents the pulses on the target qubit, and the brown and yellow pulses in $U_1$ represent the CR pulses that entangle both qubits.

Figure 4

Results from the inversion recovery demonstration for the time evolution of the $\langle \widehat{Z}\rangle$ component or observable: The demonstration results for all five qubits are compared with simulation results from the SEAQT and the Lindblad equations of motion. The error bars represent the standard deviation.

Figure 5

Evolution in time of ${\tau }_{D_R}$ for each qubit.

Figure 6

Results from the Ramsey demonstration for the time evolution of the $\langle \widehat{X}\rangle =\text{Tr}\left(\widehat{\rho }{\widehat{\sigma }}_x\right)$ component: The demonstration results are compared with the simulation results of the SEAQT and Lindblad equations of motion for all five $\mathrm{ibmq}\_\mathrm{bogota}$ qubits. The error bars represent the standard deviation.

Figure 7

Results from the Ramsey demonstration for the time evolution of the $\langle \widehat{Z}\rangle$ component: The demonstration results are compared with simulation results of the SEAQT and Lindblad equation of motion for all five $\mathrm{ibmq}\_\mathrm{bogota}$ qubits. The error bars represent the standard deviation.

Figure 8

Demonstration and model results for the two-qubit entanglement-disentanglement demonstration showing the time evolution of (a) the concurrence and (b) the fidelity.