Distilled remote entanglement between superconducting qubits across optical channels

Abstract

A promising quantum computing architecture comprises modules of superconducting quantum processors linked via optical channels using quantum transducers. As quantum transducer hardware improves, a need has arisen to understand the quantitative relationship between transducer-device characteristics and the strength of the resulting remote entanglement. Using Monte Carlo simulations that incorporate 2-to-1 and 3-to-1 entanglement distillation methods, our model maps transducer device performance up to system-level channel performance, thereby allowing the performance of remote entanglement approaches to be compared and optimized. We find the extreme photon loss (EPL) distillation protocol to be particularly high performing. Moreover, even without distillation, present-day transducers with added noise of photons are at the threshold of enabling remote Bell pairs with fidelities exceeding 50%. If the next generation of transducers can improve by 3 orders of magnitude in added noise, efficiency, and repetition rates, then they would allow for remote two-qubit gates achieving 99.7% fidelities at MHz rates. These results set practical targets for transducers to be ready for deployment into modular quantum computing systems.

Figures (9)

• Figure 1: Circuit diagrams for different remote entanglement procedures. (a) The 1-click protocol using four superconducting qubits (Q1-Q4). Q1 and Q4 are the data qubits that are to be remotely entangled. Q2 and Q3 are the interface qubits that are swapped to optical photon channels O1 and O2 via the quantum transducer (denoted $\chi^{(2)}$). After upconversion, the optical photons are sent to detectors D1 and D2 through a 50:50 beamsplitter. (b) The 2-click protocol comprises two 1-click protocols with with an intervening $\pi$-pulse. The dashed boxes are instances of the 1-click protocol from (a). (c) Remote entanglement with the EPL distillation protocol. A Bell pair is heralded and swapped to memory qubits Q0 and Q5. After creation of second Bell pair, an interference measurement is applied between the memory qubits and data qubits, and a measurement of $\ket{11}$ on the memory qubits heralds successfully distilled entanglement of Q1 and Q4.
• Figure 2: The fraction of heralded events corresponding to the scenarios shown in Table \ref{['table:monte']} at (a) $p_e=0.5$ and (b) the $p_e$ value that maximizes fidelity of the 1-click protocol. (c) The $p_e$ value that maximizes the fidelity of the 1-click protocol. (d) The fidelity and (e) entanglement rate of the 1-click, 2-click and EPL protocols as a function of $\eta$, with $N_{add}$ = 0.1 and the attempt rate = 1 MHz.
• Figure 3: The fidelity and e-bit rate as a function of $N_{add}$. (a) The fidelity of the 1-click protocol as a function of $N_{add}$ and $p_e$, with $\eta$ = 0.1. The solid white line corresponds to maximum fidelity line cut. (b) Fidelity vs. $N_{add}$ line-cuts of (a) at maximum fidelity (solid line), maximum e-bit rate (dashed-dotted line), and minimal near-0 values of $p_e$ (dashed line). (c) E-bit rate as a function $N_{add}$ and $p_e$, with the attempt rate (AR) = 1 MHz. (d) Fidelity of the EPL protocol as a function of $N_{add}$ and $p_e$, with $\eta$ = 0.1. (e) Fidelity and infidelity of the 1-click, 2-click, and EPL protocols as a function of $N_{add}$ , with $p_e$ chosen to maximize fidelity for the 1-click protocol. (f) Entanglement rate of the EPL protocol, with AR = 1 MHz, as before.
• Figure 4: A comparison of e-bit rate vs. (a) fidelity and (b) infidelity for the 1-click, 2-click, EPL 2-to-1 distillation, and Chi 3-to-1 distillation protocols. To generate these curves, we vary $N_{add}$ (from $10^{-3}$ to $10^{-1}$) and $\eta$ (from $10^{-2}$ to 1) together, while fixing the ratio $\eta / N_{add} = 10$, and setting the attempt rate to 1 MHz. For the 1-click protocol, $p_{e}$ can be chosen to maximize either fidelity or entanglement rate.
• Figure 5: A comparison of entanglement rate and fidelity for the 1-click, 2-click, and EPL protocols under five different scenarios. "Present" is the approximate state-of-the-art. "Present w/o $T_1$" is the same specifications except the memory qubit's $T_1$ time is set to be infinity. For this scenario, only the EPL protocol's metrics are shown, as the others do not use a memory. S1-S3 are three improvement scenarios. The solid lines connecting the open and closed squares represent points on the fidelity vs. entanglement rate that can be achieved by the 1-click protocol through the choice of $p_e$.