Algorithmic cooling for resolving state preparation and measurement errors in quantum computing

State preparation and measurement errors are commonly regarded as indistinguishable. The problem of distinguishing state preparation errors from measurement errors is important to the field of characterizing quantum processors. In this work, we propose a method to separately characterize state preparation and measurement errors using a different type of algorithmic cooling protocol called measurement-based algorithmic cooling (MBAC). MBAC assumes the ability to perform (potentially imperfect) projective measurements on individual qubits, which is available on many modern quantum processors. We demonstrate that MBAC can significantly reduce state preparation error under realistic assumptions, with a small overhead that can be upper bounded by measurable quantities. Thus, MBAC can be a valuable tool not only for benchmarking near-term quantum processors but also for improving the performance of quantum processors in an algorithmic manner.

Figure 1

The circuit for three-qubit BCS aiming to cool down the target spin $s_t$. Within the box is a swap gate, which is controlled by spin $s_1$.

Figure 2

Two equivalent circuits where the order of two unitary gates are exchanged, and the second gate on the right-hand side is replaced by the original gate conjugated by the first gate. $C$ stands for the cnot gate in this case.

Figure 3

A circuit for two-qubit measurement-based algorithmic cooling which increases the bias of the target qubit $s_t$. The double-line notation means “controlled on classical outcome”; i.e., $s_t$ is kept for further computations when the measurement outcome is 0 and discarded if the outcome is 1.

Figure 4

Simulated evolution of ${\delta }_t$ between $\mathrm{MBAC}\text{−}k$ and SV-$k$, plotted on a semi-log scale. The initial errors (red: $\delta =0.45$; blue: $\delta =0.1$) are assumed to be the same on all qubits. The effect of decoherence is assumed negligible and gates are assumed to be ideal.

Figure 5

Upper bound $N_{\text{upper}}$ on the expected number of runs required for different values of $r$ [the improvement ratio defined in Eq. (20)] versus the initial SP error ${\delta }_{\text{SP}}$ (assumed to be the same on the target and all ancillary qubits). Solid and dashed lines represent the cases of ${\delta }_{\text{M},a}=0$ and ${\delta }_{\text{M},a}=0.1$, respectively.