Demonstration of Fidelity Improvement Using Dynamical Decoupling with Superconducting Qubits

Quantum computers must be able to function in the presence of decoherence. The simplest strategy for decoherence reduction is dynamical decoupling (DD), which requires no encoding overhead and works by converting quantum gates into decoupling pulses. Here, using the IBM and Rigetti platforms, we demonstrate that the DD method is suitable for implementation in today’s relatively noisy and small-scale cloud-based quantum computers. Using DD, we achieve substantial fidelity gains relative to unprotected, free evolution of individual superconducting transmon qubits. To a lesser degree, DD is also capable of protecting entangled two-qubit states. We show that dephasing and spontaneous emission errors are dominant in these systems, and that different DD sequences are capable of mitigating both effects. Unlike previous work demonstrating the use of quantum error correcting codes on the same platforms, we make no use of postselection and hence report unconditional fidelity improvements against natural decoherence.

Figure 1

Mean fidelity over 16 qubits of IBMQX5 and 15 qubits of Acorn, for initial states $|\psi ⟩=-i[\cos (\theta /2)|0⟩+\sin (\theta /2)|1⟩]$. Results shown are under DD using XY4 and under free evolution. IBMQX5: after $N=40$ pulses, i.e., 10 repetitions of the base $XY4$ sequence. DD improves the fidelity only for states with $\theta \gtrsim \pi /3$. Acorn: after $N=192$ pulses, i.e., 48 repetitions of the base $XY4$ sequence. DD improves the fidelity only for states with $\theta \gtrsim \pi /4$. Throughout, we report $2\sigma$ error bars (95% confidence intervals) calculated using the bootstrap method (for more details see Ref. [20], Sec. C).

Figure 2

Mean fidelity, after averaging over all qubits, and all 36 initial conditions in type 2 preparation, as a function of the number of pulses for IBMQX5 (bottom axis) and Acorn (top axis). The pulse interval is the shortest possible: 90 ns for IBMQX5, and 50 ns for Acorn. Solid lines are fits to Eq. (1), with fit parameters as per Table 1.

Figure 3

DD performance as a function of pulse interval $\tau$ for IBMQX5 (in units of 90 ns). The intersection time $t_{\mathrm{int}}$ of the fidelity curves under free evolution and DD, and the decay-time exponent $\lambda$, as a function of the pulse spacing $\tau$. Linear fits yield $t_{\mathrm{int}}=-3.5(\tau /90\mathrm{ns})+108$ and $\lambda =-4.3(\tau /90\mathrm{ns})+88.0$.

Figure 4

Probabilities of different computational basis states after DD for initially prepared Bell states $|{\mathrm{\Phi }}^{+}⟩=(1/\sqrt{2})(|00⟩+|11⟩)$ and $|{\mathrm{\Psi }}^{+}⟩=(1/\sqrt{2})(|01⟩+|10⟩)$, as a function of the number of pulses, for both IBMQX5 and Acorn. Top row: free evolution. Bottom row: evolution under DD. The $|00⟩$ state is favored under free evolution. The solid horizontal line indicates $p=0.25$, the limit of a fully mixed state. For $|{\mathrm{\Psi }}^{+}⟩$ there is no noticeable difference in the performance with or without DD. For $|{\mathrm{\Phi }}^{+}⟩$ on IBMQX5, after $N\approx 20$, $p_{11}\approx 0.25$, suggesting that at this point all information has essentially been scrambled. On Acorn, complete scrambling of $|{\mathrm{\Phi }}^{+}⟩$ occurs after $N\sim 30$. Overall, DD is more effective at slowing down the decay to the fully mixed state for Acorn than for IBMQX5.