Nonlinear photonic architecture for fault-tolerant quantum computing

TL;DR

This work addresses fault-tolerant quantum computing with photons by replacing probabilistic linear-optical primitives with strong photon–photon nonlinearities realized via atomic ensembles in cavities. It develops a GHZ-measurement-based MBQC framework using small encoded resource states (2-chains) and QPC$(n,m)_r$ encodings, enabling near-deterministic resource generation and improved loss tolerance. The approach integrates a nonlinear CZ gate to deterministically generate seed states, reduces multiplexing overhead, and employs a foliated RHG lattice for error correction, achieving higher loss thresholds and smaller hardware footprints. The results suggest a path to scalable, room-temperature photonic quantum computers with modular networking capabilities and substantially lower component counts than traditional linear-optical schemes.

Abstract

We propose a novel architecture for fault-tolerant quantum computing that incorporates strong single-photon nonlinearities into a photonic GHZ-measurement-based architecture. The nonlinearities substantially reduce resource overheads compared to conventional linear-optics-based architectures, which require significant redundancy to accommodate probabilistic photon generation and probabilistic entangling operations. By removing linear-optical failure modes, our nonlinear architecture can also tolerate much higher optical losses than linear approaches, with a baseline loss tolerance of $\sim$12\% using a 32-photon resource state and a foliated surface code. Our results show how introducing a nonlinear primitive enables dramatic improvements in practical implementations of fault-tolerant quantum computing.

Figures (10)

• Figure 1: Resource states and measurements in the GHZ-measurement-based architecture. (a) We use encoded doubled 2-chains as our resource states and these are sent to a measurement module. (b) The measurement module performs a 4-GHZ measurement (blue) on four input qubits. (c) Measurement operators associated with the 4-GHZ measurement. Each input qubit is encoded in a 2-qubit repetition code (doubled 2-chain) to perform the 4-GHZ measurement in terms of physical Bell state measurements (d) which measure the operators $X_1X_2$ and $Z_1Z_2$ (green).
• Figure 2: Qubit gates and state preparation using nonlinearities. CZ gate in (a) the qubit picture, (b) using a ZX-diagram, and (c) implemented on dual-rail photonic qubits using balanced beam splitters (vertical black lines) and nonlinearities (yellow triangles). This nonlinear photonic CZ gate can be used to directly generate small seed states, such as (d) Bell states or (e) 3-GHZ states, as depicted using equivalent ZX-diagrams and optical circuits.
• Figure 3: Schematic of a resource state generator. A subset of photons from each seed state is routed to an entangling circuit. Upon successful detection of photons within this circuit, the photons in the resource branch are projected into an encoded 2-chain state. Losses in the entangling branch decrease the success probability of resource state generation and losses in the resource branch directly impact the loss threshold relevant to computation and error correction.
• Figure 4: Entangling gates based on the nonlinear photonic CZ gate. (a) 2-to-1-qubit entangling gate and (b) 2-qubit entangling gate (Bell state measurement). These are used in the entangling circuit for resource state generation. The circuit shown in (b) is also used in the measurement module.
• Figure 5: (a) Fault-tolerant base module comprising resource state generators (RSGs) and a measurement module. The RSGs are multiplexed to make the generation near-deterministic. Classical information from the measurement module is routed to a classical processor which handles decoding, Pauli frame tracking, feed-forward and change of measurement basis to implement logic. (b) Copies of this base module can be connected to generate the RHG lattice, with a representative cell shown here. Encoded 2-chains are combined using entangling operations (circles around nodes connected by thicker lines) which are 4-GHZ measurements in the bulk of the lattice and measurements on smaller numbers of qubits (e.g., Bell measurements) at the boundaries.