Fusion-based quantum computation (2101.09310v1)

Abstract: We introduce fusion-based quantum computing (FBQC) - a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant-sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computing, such as photonics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, requiring an extremely low depth of operations on each physical qubit and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a hardware agnostic fusion error model including both erasure and Pauli error. We also study an error model of linear optical quantum computing with probabilistic fusion and photon loss. In FBQC the non-determinism of fusion is directly dealt with by the quantum error correction protocol, along with other errors. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.4% probability of suffering photon loss in each fusion.

• The paper introduces a universal quantum computation model leveraging entangling fusion measurements on constant, small resource states.
• It demonstrates robust fault tolerance with a 10.4% photon loss threshold per fusion and establishes error thresholds using a stabilizer formalism.
• The methodology simplifies classical processing and is tailored for photonic systems, paving the way for scalable quantum architectures.

Insights into Fusion-Based Quantum Computation

The paper "Fusion-based quantum computation (FBQC)" authored by Sara Bartolucci, Patrick Birchall, and colleagues, introduces an innovative model of universal quantum computation. This model leverages the concept of entangling measurements, termed as "fusions", performed on qubits of small, constant-sized entangled resource states. FBQC distinguishes itself by proposing a framework inherently aligned with the error structures and physical constraints relevant to specific quantum systems such as photonics. This essay provides an overview of the key contributions, methodology, and implications of FBQC for quantum computing.

Overview of Fusion-Based Quantum Computation

At the heart of FBQC is the construction of fusion networks. These networks define configurations of fusion measurements applied to a collection of resource states. The FBQC model naturally results in architectural simplifications by utilizing identical modules, requiring minimal operational depth on each qubit, and reducing classical processing needs. A stabilizer formalism is developed within FBQC to analyze fault tolerance and computation.

Strong numerical evidence is presented for fault-tolerance capability within FBQC, demonstrated through pedagogical examples. These examples show that FBQC can yield considerable improvements over existing fault-tolerant schemes. A significant yield is presented with a ballistic scheme showing a 10.4% photon loss tolerance per fusion, which surpasses previous results reported in quantum computing literature. A threshold of 11.98% against erasure under a hardware agnostic model and 1.07% against Pauli error is also established.

Methodological Innovations

FBQC employs fusion networks as an approach to executing quantum computations. These networks allow for projective measurements — fusions that contribute to constructing fault-tolerant quantum memories and implementing logical operations using topological features. Critically, FBQC builds large-scale entanglement from physical primitives, significantly avoiding mapping inefficiencies associated with other computational paradigms like circuit-based or MBQC.

The proposed framework is particularly advantageous for systems with native operations characterized by multi-qubit projective measurements, such as photonics, where linear optical fusion can be probabilistically implemented. The use of constant-sized resource states, controlled-depth operations, and an emphasis on fault tolerance are paramount features. FBQC simplifies classical controlling requirements and decouples classical computation from the physical qubit operation timescale.

Implications for Quantum Computing

FBQC's distinctiveness lies not only in its theoretical contributions but also in its practical implications for quantum architectures. It establishes a tightly knit relationship between physical operations and topological quantum error correction, which can lead to more efficient hardware designs. The proposed model effectively supports universal logic operations through resource states and fusion, potentially enabling more robust and scalable quantum systems.

Future developments could include exploring FBQC's adaptability to different quantum hardware platforms and optimizing resource states for better error suppression. Moreover, the flexibility FBQC offers in handling non-deterministic operations without extensive classical processing presents exciting opportunities for advancing quantum photonics and hybrid classical-quantum systems.

Overall, the insights provided by FBQC represent a significant step forward in the pursuit of scalable, efficient, and robust quantum computing. It underscores a pivotal shift towards integrating computation directly into the fault-tolerant framework, offering potential pathways for innovations in quantum architectural design and implementation.