Mitigating measurement errors in multi-qubit experiments (2006.14044v2)

Abstract: Reducing measurement errors in multi-qubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical post-processing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parameterizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error mitigation overhead, including the the number of measurements and the cost of the classical post-processing, is exponential in $\epsilon n$, where $\epsilon$ is the maximum error rate and $n$ is the number of qubits. We report experimental demonstration of our error mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\le 12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.

• The paper introduces noise mitigation techniques using tensor product and correlated Markovian (CTMP) models to improve quantum measurement accuracy.
• It validates these methods on IBM Quantum devices, showing significant error reduction such as lower total variation distance in 20-qubit experiments.
• The study offers scalable post-processing strategies that enhance the reliability of quantum simulations and NISQ-era multi-qubit computations.

Mitigating Measurement Errors in Multi-Qubit Experiments

The paper "Mitigating Measurement Errors in Multi-Qubit Experiments," authored by Sergey Bravyi et al., proposes methods for addressing measurement errors in quantum computing, particularly those that arise in multi-qubit quantum processing units. The paper primarily focuses on noise mitigation using classical post-processing techniques and offers frameworks that enhance the fidelity of quantum state readouts, which are crucial for executing reliable quantum algorithms.

Main Contributions

The authors propose error mitigation schemes based on tensor product and correlated Markovian noise models. These models are instrumental in processing the outcomes of quantum measurements and reducing the intrinsic errors encountered in multi-qubit systems:

1. Tensor Product Noise Model: This model assumes that noise affecting each qubit during measurement is independent of others. It simplifies the noise matrix to a tensor product of single-qubit noise matrices. The error rates corresponding to bit-flips ($0 \to 1$ and $1 \to 0$) for each qubit are extracted from calibration data.
2. Correlated Markovian Noise Model (CTMP): Unlike the tensor product model, the CTMP accounts for cross-talk errors occurring in real-world multi-qubit setups, where noise is not strictly independent. This model expresses the full noise matrix as an exponential of a generator matrix consisting of local operators that define rates of specific error processes. The CTMP model provides a better approximation to the readout noise observed in practice, especially when two-qubit and correlated errors are significant.
3. Noise Matrix Inversion: Error mitigation is implemented by applying the inverse of the noise matrix to a probability vector representing the noisy measurement outcomes. Importantly, the authors bypass a direct computation of the inverse (which could be prohibitive) by employing techniques from quasi-probability decompositions, allowing scalability to larger systems.

Experimental Validation

The paper reports on experimental validations using IBM Quantum devices. Specific graph states and entangled states prepared by low-depth random Clifford circuits were used to test and compare the proposed models:

• Graph States: The fidelity of these highly entangled states was measured, and the mitigation techniques were demonstrated to effectively recover the mean values of stabilizers even in the presence of noise. The CTMP model, in particular, showed a significant reduction in total variation distance (TVD) from the full noise matrix, indicating better accuracy over the tensor product model.
• 20-Qubit Experiment: The authors demonstrate the practicality of their methods on a 20-qubit IBM Quantum device. The CTMP model, though computationally demanding, offers robust readout error mitigation without the need for quantum error-correcting codes.

Implications and Future Directions

The findings have substantial implications for near-term quantum computing, particularly in enhancing the precision of quantum simulations and variational quantum eigensolver (VQE) algorithms. The techniques outlined in the paper enable significant error suppression without increasing the complexity of quantum circuits, thus improving the feasibility of quantum computations on noisy intermediate-scale quantum (NISQ) devices.

Moving forward, this research opens pathways for further improvements in noise modeling, specifically incorporating more complexities such as time-dependent noise or device-specific irregularities. Additionally, as quantum processors scale up in qubit count and connectivity, refining these error models to maintain efficiency and scalability will be crucial. Future developments might involve hybrid models or machine learning techniques to dynamically adapt noise models to changing conditions in quantum hardware.

In conclusion, this paper contributes significantly to the field of quantum error mitigation by providing scalable solutions to one of the critical challenges in quantum computation, thus laying groundwork for more reliable quantum information processing in the NISQ era.