Basic entanglement distillation with realistic noise

Abstract

Entanglement distillation is a key component of modular quantum computing and long-range quantum communications. However, this powerful tool to reduce noise in entangled states is difficult to realize in practice for two main reasons. First, operations used to carry out distillation inject noise they seek to remove. Second, the extent to which distillation can work under realistic device noise is less well studied. In this work, we both simulate distillation using a variety of device noise models and perform distillation experiments on fixed-frequency IBM devices. We find reasonable agreement between experimental data and simulation done using Pauli and non-Pauli noise models. In our data, we find broad improvement when the metric of success for distillation is to improve average Bell fidelity under effective global depolarizing noise, remove coherent errors, or improve the Bell fidelity of mildly degraded Bell pairs. We pave the way to obtain broad improvement from distillation under a stricter, but practically relevant, metric: distill (physically) nonlocal Bell pairs with higher fidelity than possible to obtain with other available methods. Our results also help understand metrics and requirements for quantum devices to use entanglement distillation as a primitive for modular computing.

Figures (19)

• Figure 1: Basic circuits for entanglement distillation
• Figure 2: Algebraically obtained increase in Bell fidelity by different distillation protocols. The $x$ and $y$ axes represent the Bell fidelity of the states prior to distillation while the color corresponds to the increase (if any) in fidelity upon distillation.
• Figure 3: Circuits for entanglement distillation with depolarizing channels $\Lambda _p$ and $\Lambda _q$ inserted at various stages.
• Figure 4: Results from simulation of recurrence with circuit noise described in Fig. \ref{['fig:TwoToOne']}. Plots \ref{['fig:2To1Plot1']} and \ref{['fig:2To1Plot2']} show fractional change in Bell fidelity, $r$ (see eq. \ref{['eq:ratio']}), plotted against initial Bell fidelity, $F_b$ (defined below \ref{['eq:ratio']}), for various gate and measurement errors, $g$ and $m$, respectively. The region where the plot remain above $r=1$ indicates where the noisy distillation circuit is beneficial. Plots \ref{['fig:2To1Plot3']} and \ref{['fig:2To1Plot4']} focus on high fidelity Bell pairs and show the percentage decrease in Bell infidelity, $\epsilon_d$ (defined in eq. \ref{['eq:errDec']}), plotted against initial fidelity $F_b$ for various gate and measurement errors.
• Figure 5: Results from simulation of $ZX_{3B}$ distillation with circuit noise given in Fig. \ref{['fig:ThreeToOne']}. Plots \ref{['fig:3To1Plot1']} and \ref{['fig:3To1Plot2']} show fractional change in Bell fidelity, $r$ (see eq. \ref{['eq:ratio']}), plotted against initial Bell fidelity, $F_b$ (defined below \ref{['eq:ratio']}), for various gate and measurement errors. The region of the plot above $r=1$ indicates where the noisy distillation circuit is beneficial. Plots \ref{['fig:3To1Plot3']} and \ref{['fig:3To1Plot4']} focus on low noise Bell pairs and show the percentage decrease in Bell infidelity, $\epsilon_d$ (defined in eq. \ref{['eq:errDec']}), plotted against initial fidelity $F_b$ for various gate and measurement errors.