Combatting noise in near-term quantum data centres

TL;DR

This work tackles the challenge of mitigating entanglement-induced noise in near-term distributed quantum computing by comparing localized quantum error detection (QED) against entanglement-distillation techniques for remote gates. Using circuit-level, discrete-event simulations with realistic hardware parameters, it analyzes remote CNOT gates implemented via unencoded, QED-augmented, and entanglement-distillation schemes, including 3QRC, 4QED/SS, and LNCY 412_subcode encodings, as well as BBPSSW and DEJMPS distillation—with nested DEJMPS rounds. The results show that four-qubit QED schemes and DEJMPS4 consistently improve average fidelity over the unencoded baseline, while two-qubit distillation schemes offer smaller gains; importantly, DEJMPS generally provides lower latency than equivalent QED protocols under comparable conditions. Overall, entanglement distillation emerges as the most practical near-term strategy for improving remote-gate fidelity in resource-constrained QDCs, though localized QED remains a valuable bridge toward fault-tolerant architectures, especially when encoding choices balance qubit cost and latency. The findings inform design trade-offs for QDCs and offer concrete guidance on employing distillation versus error-detection-based mitigation in early scalable quantum networks.

Abstract

We analyse the performance of different error handling methods in the quantum data centre paradigm of distributed quantum computing. We compare the impact of quantum error detection, using the three-qubit repetition code and the [[4, 1, 2]] Leung-Nielsen-Chuang-Yamamoto code, on remote gates with that of conventional entanglement distillation techniques. Detailed classical simulation is used to obtain results for realistic near-term hardware.

Figures (8)

• Figure 1: A remote CNOT gate between qubits $\mathrm{A_{p_0}}$ and $\mathrm{B_{p_0}}$ implemented using the 1TP protocol. Zigzag lines indicate the distribution of an ebit, which, ideally, in the absence of noise, has the state $| \Phi^+ \rangle = \frac{1}{\sqrt{2}} ( | 00 \rangle + | 11 \rangle)$. Double lines indicate classical communication. The subscript $\mathrm{c}_i$ indicates a communication qubit with index $i$ and $\mathrm{p}_i$ is a processing qubit with index $i$.
• Figure 2: 1TP remote CNOT gate using (a) fully-coded 1TP (FC-1TP) and (b) partially-coded 1TP (PC-1TP). The subscript L refers to a logical version of the operation or state. We omit the L for the measurements in (a) but both measurements are logical measurements. Double lines refer to classical communication, squiggly lines to the distribution of an ebit and squiggly arrows to quantum teleportations from the tail of the arrow to its head. $| c \rangle$ and $| t \rangle$ are arbitrary quantum states, which we assume to be separable from each other and pure in this work. If an error is detected during the decoding step then the final CNOT is not done and the entire process must be restarted.
• Figure 3: Encoding circuits for (a) the three-qubit repetition code, (b) the Leung-Nielsen-Chuang-Yamamoto (LNCY) code 412_subcode code using the encoder from QuantumErrorCorrectionIntroductoryGuide, (c) a simpler encoding of the LNCY. $| \psi \rangle$ is an arbitrary quantum state.
• Figure 4: Decoding/error detection circuits for (a) 3QRC, (b) 4QED, and (c) SS. The X and Z stabiliser measurements indicated in (c) are identical to those explicitly shown in (b). Qubits labelled 'anc.' are ancilla qubits. Everything after the Z stabiliser measurement in (b) and (c) is only done if no error was detected during the X and Z stabiliser measurements. If an error is detected, the result is discarded and the entire operation must be discarded.
• Figure 5: The (a) BBPSSW, (b) DEJMPS and (c) general two-round entanglement distillation schemes. BBPSSW assumes a Werner state input, which can be enforced with local operations, although this is not done here, while DEJMPS allows a more general input. For both schemes, the circuit is run repeatedly until both of the measurements shown give the same result. The squiggly lines indicate the distribution of the state $| \Phi^+ \rangle = \frac{1}{\sqrt{2}} ( | 00 \rangle + | 11 \rangle)$, in the ideal case where no noise is present. In reality, noise will be present and for BBPSSW, it is assumed that this noise has the Werner form, as discussed in the main text. For DEJMPS, no such assumptions are made and the state $\rho_{\mathrm{M}}$ can instead be distributed, which is an arbitrary mixture of the different Bell states $| \Phi^{\pm} \rangle = \frac{1}{\sqrt{2}}(| 00 \rangle \pm | 11 \rangle)$, $| \Psi^{\pm} = \frac{1}{\sqrt{2}}(| 01 \rangle \pm | 10 \rangle) \rangle$. $R_x$ is a $\frac{\pi}{2}$ rotation about the $x$ axis and $R_x^{\dagger}$ is the $-\frac{\pi}{2}$ rotation. (a) and (b) show just one round of entanglement distillation here, but the fidelity can be further improved by further distilling the outcome as illustrated in (c).