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arXiv:2207.06805 · npj Quantum Information

Parity-encoding-based quantum computing with Bayesian error tracking

Seok-Hyung Lee, S. Omkar, Yong Siah Teo, Hyunseok Jeong

Published Apr 24, 2023• 9 citations
arXivHTMLPDF

Abstract

Abstract Measurement-based quantum computing (MBQC) in linear optical systems is promising for near-future quantum computing architecture. However, the nondeterministic nature of entangling operations and photon losses hinder the large-scale generation of graph states and introduce logical errors. In this work, we propose a linear optical topological MBQC protocol employing multiphoton qubits based on the parity encoding, which turns out to be highly photon-loss tolerant and resource-efficient even under the effects of nonideal entangling operations that unavoidably corrupt nearby qubits. For the realistic error analysis, we introduce a Bayesian methodology, in conjunction with the stabilizer formalism, to track errors caused by such detrimental effects. We additionally suggest a graph-theoretical optimization scheme for the process of constructing an arbitrary graph state, which greatly reduces its resource overhead. Notably, we show that our protocol is advantageous over several other existing approaches in terms of the fault-tolerance and resource overhead.

DOI
10.1038/s41534-023-00705-9

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Abstract Measurement-based quantum computing (MBQC) in linear optical systems is promising for near-future quantum computing architecture. However, the nondeterministic nature of entangling operations and photon losses hinder the large-scale generation of graph states and introduce logical errors. In this work, we propose a linear optical topological MBQC protocol employing multiphoton qubits based on the parity encoding, which turns out to be highly photon-loss tolerant and resource-efficient even under the effects of nonideal entangling operations that unavoidably corrupt nearby qubits. For the realistic error analysis, we introduce a Bayesian methodology, in conjunction with the stabilizer formalism, to track errors caused by such detrimental effects. We additionally suggest a graph-theoretical optimization scheme for the process of constructing an arbitrary graph state, which greatly reduces its resource overhead. Notably, we show that our protocol is advantageous over several other existing approaches in terms of the fault-tolerance and resource overhead.
We propose an all-linear-optical scheme to ballistically generate a cluster state for measurement-based topological fault-tolerant quantum computation using hybrid photonic qubits entangled in a continuous-discrete domain. Availability of near-deterministic Bell-state measurements on hybrid qubits is exploited for this purpose. In the presence of photon losses, we show that our scheme leads to a significant enhancement in both tolerable photon-loss rate and resource overheads. More specifically, we report a photon-loss threshold of $\ensuremath{\sim}3.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which is higher than those of known optical schemes under a reasonable error model. Furthermore, resource overheads to achieve logical error rate of ${10}^{\ensuremath{-}6}({10}^{\ensuremath{-}15})$ is estimated to be $\ensuremath{\sim}8.5\ifmmode\times\else\texttimes\fi{}{10}^{5}(1.7\ifmmode\times\else\texttimes\fi{}{10}^{7})$, which is significantly less by multiple orders of magnitude compared to other reported values in the literature.
Fault-tolerant photonic quantum computing schemes have suffered low photon-loss thresholds and heavy resource requirements particularly when using single-photon qubits. Recently, several approaches utilizing both discrete and continuous variables of light have been proposed to reach high photon-loss thresholds with relatively low resource requirements. Here we present two schemes that outperform known previous schemes in terms of photon-loss thresholds and resource overheads. The first one is a hybrid scheme that combines discrete-variable (DV) and continuous-variable (CV) states of light. This scheme is nearly ballistic in the sense that passive measurements with hybrid entangled states are sufficient with little feedforwards. The second scheme is based on the parity-based encoding and Bayesian error tracking that enables one to reach a significantly high photon-loss threshold of ~8.5% with moderate resource requirements compared to previous known schemes.
Photonic quantum computing provides a promising route toward quantum computation by naturally supporting the measurement-based quantum computation (MBQC) model. In MBQC, programs are executed through measurements on a pre-generated graph state, whose construction largely depends on probabilistic fusion operations. However, fusion operations in PQC are vulnerable to two major error sources: fusion failure and fusion erasure. As a result, MBQC compilation must account for both error mechanisms to generate reliable and efficient photonic executions. Prior state-of-the-art MBQC compilation, represented by OneAdapt, is designed for all-photonic architectures and mainly focuses on handling fusion failures. Nevertheless, it does not explicitly model fusion erasures induced by photon loss, which can be substantially more damaging than fusion failures. To mitigate fusion erasure errors, we introduce a new MBQC compilation scheme built upon the spin qubit quantum memory. We propose tree-encoded fusion, an encoding strategy that suppresses erasure errors during graph-state generation. We further incorporate this scheme into a compiler framework with algorithms that reduce the execution overhead of quantum programs. We evaluate the proposed framework using a realistic PQC simulator on six representative quantum algorithm benchmarks across multiple program scales. The results show that tree-encoded fusion achieves better robustness than alternative fusion-encoding strategies, and that our compiler provides exponential improvement over OneAdapt. In addition, we validate the feasibility of our approach through a proof-of-concept demonstration on real PQC hardware.
Linear optical quantum computing in the dual-rail representation offers the practical advantage of room-temperature operation, with quantum gates implemented through beam splitters and phase shifters. Despite its appeal, this approach is fundamentally constrained by the nondeterministic nature of entangling gates, which limits scalability within the circuit-based paradigm. Measurement-based quantum computation (MBQC) addresses this issue by employing pre-generated cluster states and single-qubit projective measurements, but both frameworks remain highly susceptible to photon loss, the dominant error in photonic systems. In this work, we investigate the effects of photon loss on single-qubit gates, heralded two-qubit entangling gates, the two-qubit Grover algorithm, and the preparation of a three-qubit cluster state. By employing simplified photon-loss models, we quantify both the success probability and fidelity degradation of the resulting states. These results provide practical insight into the limitations of current photonic architectures and highlight pathways toward efficient error mitigation in near-term quantum technologies.
Fault tolerance is essential for scalable quantum technologies and is enabled by quantum error-correction codes. Bell-state measurements (BSMs) are a fundamental building block for modern quantum technologies such as measurement-based quantum computation and fusion-based quantum computation, as well as quantum networks. Therefore, performing BSMs on error-corrected qubits is a necessary step for achieving fault tolerance in these applications. In this work, we realise a logical BSM using linear optics, based on a two-qubit repetition code, an instance of a quantum parity code that allows detection of bit-flip errors, and experimentally achieve a mean success probability of (70.8 +/- 0.4)%. While standard linear-optical BSMs are fundamentally limited to a maximum success probability of 50%, this increased success probability enables higher secure key rates in quantum communication and facilitates the generation of large graph states for quantum computation. Since fault-tolerant schemes require error-correction codes regardless, this improvement comes at no additional resource overhead. Our results demonstrate that error-correction codes can be used to surpass the linear-optics limit of BSMs, which is an important step towards practical, fault-tolerant, and scalable photonic quantum technologies.
Photonic measurement-based quantum computation (MBQC) is a promising route towards fault-tolerant universal quantum computing. A central challenge in this effort is the huge overhead in the resources required for the construction of large photonic clusters using probabilistic linear-optics gates. Although strong single-photon nonlinearity ideally enables deterministic construction of such clusters, it is challenging to realise in a scalable way. Here we explore the prospects of using moderate nonlinearity (with conditional phase shifts smaller than $\ensuremath{\pi}$) to boost photonic quantum computing and significantly reduce its resources' overhead. The key element in our scheme is a nonlinear router that preferentially directs photonic wavepackets to different output ports depending on their intensity. As a relevant example, we analyze the nonlinearity provided by Rydberg blockade in atomic ensembles, in which the trade-off between the nonlinearity and the accompanying loss is well understood. We present protocols for efficient Bell measurement and GHZ-state preparation---both key elements in the construction of cluster states, as well as for the cnot gate and quantum factorization. Given the large number of entangling operations involved in fault-tolerant MBQC, the increase in success probability provided by our protocols already at moderate nonlinearities can result in a significant reduction in the required resources.