Quantum technology promises to revolutionize many fields, ranging from finding better materials, faster drug discovery, optimal routing, rock solid cryptography, and many more. This comes with a price, the quantum systems are incredibly sensitive, even a small perturbation can throw it off the whole computation, losing any advantage it has over classical methods.

The whole field of quantum technologies is highly invested in finding methods for accurate quantum control.

As noise stands out as a huge challenge, a lot of attention has been afforded to correcting errors in gate-based computations, recently shown to be paramount for any useful quantum advantage. One important source of errors not covered by gate-based error correction methods are readout errors, which have still received little attention.

Readout errors are broadly captured by misidentification of the measurement outcome. This could be as simple as misidentifying whether a value was 0 or 1, analogue to classical computers, or as complicated as having the state of a qubit influence the readout outcome of another qubit. 

The goal of our work was to develop a method that captures a general set of readout errors, while light-weight enough to be applied to system sizes of up to 6 qubits. We develop such a protocol and verify its utility experimentally with a superconducting qubits. 

Our method consists of two stages: First, a calibration stage, where the measurement setup itself is characterized. Here, we find out what imperfections there are and how they could affect the measured values. Second, we perform an experiment of interest, which in our case is quantum state tomography, an experiment that reconstructs the full quantum state of the system. 
The key insight of the procedure is that we directly integrate the information about the readout noise, gained in the first step, into the state estimator used in the second step. 

We characterize the performance of the new readout error mitigation method by varying important noise sources present in superconducting qubit systems.
These are non-optimal readout signal amplification, insufficient number of photons in the readout resonator, off-resonant qubit drive, and effectively shortened coherence times.
In doing so, we see a consistent ability to mitigate any added error by lowering the amplification and decreasing the readout power. Even with optimal experimental parameters, we see a large improvement. We identified noise sources for which readout error mitigation worked well and observed that the precision of state reconstruction is improved by a factor of up to 30, enabling us to reconstruct quantum states even in a very noisy quantum device.

Our method adds to the toolbox of readout error mitigation schemes and opens up new possibilities for systems with noisy readouts where accurate knowledge of the quantum state is required. As our developed method is not specific to any quantum computing architecture, one can also implement it on their qubits of choice, by using our code made publicly available on GitHub - check our publication for details.