# Compilation-informed probabilistic logical-error cancellation

## TL;DR

This paper presents a quantum error mitigation scheme that reduces resource requirements for high-precision quantum computations by leveraging compilation information, circuit-agnostic methods, and linear programming, aiding near-term quantum hardware.

## Contribution

It introduces a compilation-informed, circuit-agnostic quantum error mitigation method that achieves unbiased estimates with constant overhead, independent of circuit size and code distance.

## Key findings

- Significantly reduces quantum resource needs for high-precision tasks.
- Demonstrates effectiveness through numerical simulations and knot polynomial estimation.
- Provides a practical approach for fault-tolerant quantum computation in the near term.

## Abstract

The potential of quantum computers to outperform classical ones in practically useful tasks remains challenging in the near term due to scaling limitations and high error rates of current quantum hardware. While quantum error correction (QEC) offers a clear path towards fault tolerance, overcoming the scalability issues will take time. Early applications will likely rely on QEC combined with quantum error mitigation (QEM). We introduce a QEM scheme against both compilation errors and logical-gate noise that is circuit-, QEC code-, and compiler-agnostic. The scheme builds on quasi-probability methods and uses information about the circuit's gates' compilations to attain an unbiased estimation of noiseless expectation values incurring a constant sample-complexity overhead. Moreover, it features maximal circuit size and code distance both independent of the target precision, in contrast to strategies based on QEC alone. We formulate the mitigation procedure as a linear program, demonstrate its efficacy through numerical simulations, and illustrate it for estimating the Jones polynomials of knots. Our method significantly reduces quantum resource requirements for high-precision estimations, offering a practical route towards fault-tolerant quantum computation with precision-independent overheads for fixed circuit complexity and code distance.