Readout Error Mitigation
◐ Design-level API
This page documents qalgora-Q API design, architecture, or adaptation workflows. Code examples illustrate intended usage and are not guaranteed to run in the current reference implementation.Correct biased measurement counts by inverting a confusion matrix calibrated from known input states.
Calibrate & correct
import qalgora
import numpy as np
# 1. characterize the readout with calibration circuits
confusion = qalgora.experimental.measure_confusion_matrix(n_qubits=2,
noise_model=noise)
# 2. invert it
correction = np.linalg.inv(confusion)
# 3. apply to raw counts (normalize counts to a probability vector first)
raw = qalgora.sample(kernel, shots_count=10000, noise_model=noise)
corrected = correction @ raw.to_vector()Specification API — not in the open reference build yet
This example shows a qalgora-Q specification API (or a third-party library) that the open reference build does not bundle today. It documents the intended interface; to run code now, use the reference build’s supported core API.Inversion and normalization caveats
Directly inverting the confusion matrix amplifies statistical noise and can produce negative
probabilities or a total that drifts from 1. In practice one uses a pseudo-inverse, constrained
least squares, regularization, or clips negative entries and renormalizes. Note too that
raw.to_vector() should be normalized from counts into a probability vector, and the
corrected vector is typically truncated to non-negative values and renormalized afterwards.
Strategies
- Full confusion matrix — captures all correlated readout errors, but 2N×2N; small systems only.
- Tensored / k-local — assume independent qubit errors. An independent single-qubit model calibrates with cost growing linearly in qubit count; a k-local model's cost grows exponentially in the block size and roughly linearly in the number of blocks.
- Single-qubit — cheapest approximation for weakly-correlated readout.
读出误差缓解
◐ 设计接口
本页描述的是 qalgora-Q 的接口设计、架构设计或适配工作流。相关代码用于说明预期用法，当前参考实现不保证可以直接运行。通过对已知输入态标定混淆矩阵，再对其求逆，修正带偏差的测量计数。
标定与校正
import qalgora
import numpy as np
# 1. characterize the readout with calibration circuits
confusion = qalgora.experimental.measure_confusion_matrix(n_qubits=2,
noise_model=noise)
# 2. invert it
correction = np.linalg.inv(confusion)
# 3. apply to raw counts（先把计数归一化为概率向量）
raw = qalgora.sample(kernel, shots_count=10000, noise_model=noise)
corrected = correction @ raw.to_vector()规范接口 · 参考实现暂未包含
此示例展示的是 qalgora-Q 规范中的接口（或第三方库），开放参考实现目前尚未内置，仅用于说明预期用法；如需立即运行，请使用参考实现已支持的核心 API。求逆与归一化注意事项
直接矩阵求逆会放大统计噪声，可能产生负概率或总概率偏离 1；实际常用伪逆、约束最小二乘、正则化、截断负值并重新归一化。此外 raw.to_vector() 应先把计数归一化为概率向量，校正后的向量通常再做截断负值与重新归一化处理。
策略
- 完整混淆矩阵 — 能捕捉全部关联读出误差，但规模为 2N×2N，仅适用于小规模系统。
- 张量积 / k-局域 — 假设各量子比特读出误差独立。独立单比特模型标定规模随量子比特数线性增长；k-局域模型开销随块大小指数增长、随块数近似线性增长。
- 单量子比特 — 最低开销的近似，适用于弱关联读出场景。