Recovering noise-free quantum observables

We introduce a technique for recovering noise-free observables in noisy quantum systems by combining the results of many slightly different experiments. Our approach is applicable to a variety of quantum systems, but we illustrate it with applications to quantum information and quantum sensing. The approach corresponds to repeating the same quantum evolution many times with known variations on the underlying systems' error properties, e.g., the spontaneous emission and dephasing times $T_1$ and $T_2$. As opposed to standard quantum error correction methods, which have an overhead in the number of qubits (many physical qubits must be added for each logical qubit), our method has only an overhead in the number of evaluations, allowing the overhead to, in principle, be hidden via parallelization. We show that the effective spontaneous emission $T_1$ and dephasing $T_2$ times can be increased using this method in both simulation and experiments on an actual quantum computer. We also show how to correct more complicated entangled states and how Ramsey fringes relevant to quantum sensing can be significantly extended in time.

Figure 1

Example of a “hypersurface” fit to many experiments with slightly different noise parameters ${\gamma }_1$ and ${\gamma }_2$. Black points are measurements of an observable with different noise rates. The “$\times$” is the noise-free result. Blue (lower), orange (middle), and green (upper) surfaces are first-, third-, and fourth-order fits, respectively. Many observable measurements are outside the region displayed.

Figure 2

Population recovery in a relaxation time experiment. (a) Simulated data from 450 simulations with random $T_1$ times. (b) Experimental results on Rigetti's eight-qubit quantum computer [13]. Some 45 repetitions are made at each time with experimentally determined $T_1$ times. The inset shows the comparison between our noise model run with the experimentally determined $T_1$ times and the experimental data.

Figure 3

Population recovery in Ramsey interferometry with no background magnetic field. (a) Simulated data from 450 simulations with random $T_1$ and $T_2^{*}$ times. (b) Experimental results on Rigetti's eight-qubit quantum computer [13]; 12 repetitions are included at each time with experimentally determined $T_1$ and $T_2^{*}$ times.

Figure 4

Ramsey fringe recovery from using 350 simulations of three entangled qubits with random $T_2^{*}$ times.

Figure 5

Single qubit Ramsey interferometry. Some 350 simulations with random $T_2^{*}$ times are used.