Reducing quantum error correction overhead using soft information

Abstract

Imperfect measurements are a prevalent source of error across quantum computing platforms, significantly degrading the logical error rates achievable on current hardware. To mitigate this issue, rich measurement data referred to as soft information has been proposed to efficiently identify and correct measurement errors as they occur. In this work, we model soft information decoding across a variety of physical qubit platforms and decoders and showcase how soft information can make error correction viable at lower code distances and higher physical error rates than is otherwise possible. We simulate the effects of soft information decoding on quantum memories for surface codes and bivariate bicycle codes, and evaluate the error suppression performance of soft decoders against traditional decoders. Our simulations show that soft information decoding on near-term devices can provide up to 11% higher error suppression on superconducting qubits and up to 20% stronger error suppression on neutral atom qubits. These accuracy gains correspond to 13% and 33% reductions in the physical qubit footprint of superconducting and neutral atom devices respectively when operating at a logical error rate of $10^{-6}$, showcasing that soft information is a powerful tool for reducing the cost and complexity of large-scale fault-tolerant quantum computers.

Figures (7)

• Figure 1: Readout model for superconducting and neutral atom qubits. I. Superconducting readout, a) showing example IQ voltages from a repeated state-preparation and measurement routine for states $\ket{0}$ (in purple) and $\ket{1}$ (in orange), b) the resulting probability density functions when projected along the axis connecting the 0- and 1-centroids, and c) the posterior probability of a measurement outcome $\mu$ given the initial state preparation $\ket{0}$ or $\ket{1}$. II. Neutral atom readout, a) showing photon counts $\mu$ for a bright state $\ket{1}$ (in orange) and a dark state $\ket{0}$ (in purple), and b) the posterior probability of a measurement outcome $\mu$ given either a 0- or 1-state preparation.
• Figure 2: LCD on superconducting qubits: error suppression rate $\Lambda$ versus physical qubit fidelity $\mathcal{F}=1 - p$. Data from a simulated quantum memory experiment with $T=10$ rounds of syndrome extraction and $N=10^6$ shots per data point. In panel a), we show $\Lambda$ for a noise regime where soft flips are sub-dominant $p_\textrm{S}/p = 1$, and in panel b) we show $\Lambda$ when soft flips are a significant component of the error model $p_\textrm{S}/p=5$. Error bars in each plot correspond to hypotheses with a likelihood within a factor of 10 of the maximum likelihood hypothesis, given the sampled data.
• Figure 3: LCD on neutral atom qubits: error suppression rate $\Lambda$ versus physical qubit fidelity $\mathcal{F}=1 - p$. Data from a simulated quantum memory experiment with $T=10$ rounds of syndrome extraction and $N=10^7$ shots per data point in panel a) and $N=10^6$ in panel b). In panel a), we show $\Lambda$ for a noise regime where soft flips are sub-dominant $p_\textrm{S}/p = 1$, and in panel b) we show $\Lambda$ when soft flips are a significant component of the error model $p_\textrm{S}/p=5$. Error bars in each plot correspond to hypotheses with a likelihood within a factor of 10 of the maximum likelihood hypothesis, given the sampled data.
• Figure 4: LCD: error suppression rate $\Lambda$ versus measurement time $\tau_{\textrm{M}}$. $\Lambda$ is obtained from simulations of rotated planar code quantum memory experiments with $T=10$ rounds of syndrome extraction. In panel a) we plot $\Lambda$ for superconducting qubits under physical error rate $p=0.3\%$, classification error rate $p_\textrm{S}=5p$ at $\tau_{\textrm{M}}=500~\textrm{ns}$ and $\textrm{T}_1=100~\mu\textrm{s}$. In panel b), we plot $\Lambda$ for neutral atom qubits, with $p=1\%$ and $Z$-bias $100$. The soft flip probability $p_\textrm{S}$ varies based on $\tau_{\textrm{M}}$. On both qubit platforms, a higher $\Lambda$ is reached with soft compared to hard decoding. Error bars in each plot correspond to hypotheses with a likelihood within a factor of 10 of the maximum likelihood hypothesis, given the sampled data.
• Figure 5: BM on superconducting qubits: error suppression rate $\Lambda$ versus physical qubit fidelity $\mathcal{F}=1 - p$. Data from a simulated quantum memory experiment with $T=10$ rounds of syndrome extraction. Sample size is limited to $N=5\times10^5$ due to slow decoder throughput, causing significant uncertainty in $\Lambda$ at low error rates. In panel a), we show $\Lambda$ for a noise regime where soft flips are sub-dominant $p_\textrm{S}/p = 1$, and in panel b) we show $\Lambda$ when soft flips are a significant component of the error model $p_\textrm{S}/p=5$. Error bars in each plot correspond to hypotheses with a likelihood within a factor of 10 of the maximum likelihood hypothesis, given the sampled data.