Integrated photonic source of Gottesman-Kitaev-Preskill qubits

Abstract

Building a useful photonic quantum computer requires robust techniques to synthesize optical states that can encode qubits. Gottesman-Kitaev-Preskill (GKP) states¹ offer one of the most attractive classes of such qubit encodings, as they enable the implementation of universal gate sets with straightforward, deterministic and room temperature-compatible Gaussian operations². Existing pioneering demonstrations generating optical GKP states³ and other complex non-Gaussian states^4-11 have relied on free-space optical components, hindering the scaling eventually required for a utility-scale system. Here we use an ultra-low-loss integrated photonic chip fabricated on a customized multilayer silicon nitride 300-mm wafer platform, coupled over fibre with high-efficiency photon number resolving detectors, to generate GKP qubit states. These states show critical mode-level features necessary for fault tolerance, including at least four resolvable peaks in both p and q quadratures, and a clear lattice structure of negative Wigner function regions, in this case a 3 × 3 grid. We also show that our GKP states show sufficient structure to indicate that the devices used to make them could, after further reduction in optical losses, yield states for the fault-tolerant regime. This experiment validates a key pillar of bosonic architectures for photonic quantum computing^2,12, paving the way for arrays of GKP sources that will supply future fault-tolerant machines.

Fig. 1. Three stages of the cluster state resource preparation for measurement-based quantum computation.

GKP qubits are generated using GBS sources. Many GBS outputs are combined at a refinery to boost the overall quality and probability of GKP sources. Arbitrary cluster states can be synthesized from these states deterministically using a network of beamsplitters. The need for scalable fabrication of GBS sources is evident for a scalable and high-quality cluster state.

Fig. 2. Schematic of experiment and simplified chip layout.

A series of pump and reference laser fields are sent over fibre to the input of an optically and electrically packaged chip. The strong classical fields are filtered and distributed (1) to an array of four squeezers based on a two-resonator photonic molecule design (2). The generated pulsed, nearly single-temporal-mode, squeezed vacuum states are separated from the pump laser light by on-chip optical filters (3), before being entangled by a programmable linear interferometer or unitary (4). Another array of integrated filters further suppresses the pump light (5). Three of the optical modes are sent to PNR detectors that, when the correct detection pattern is observed, herald the production of a GKP qubit state in the remaining optical mode, which is then analysed using homodyne detection (HD).

Fig. 3. Experimental result.

a, Wigner function heralded by the (n₁, n₂, n₃) = (3, 3, 3) PNR outcome with position, q, and momentum, p, quadrature probability (prob) distributions and symmetric, p and q effective squeezing (${\Delta }_{\text{sym}}^2$, ${\Delta }_p^2$, and ${\Delta }_q^2$, respectively) shown. White and grey homodyne bins corresponding to a rectangular GKP lattice indicating probability overlap with obtaining 0/1 and +/– outcomes. The state generated is a GKP $\mid 1⟩$ state on a rectangular lattice. b, Wigner functions of a subset of heralded states for different PNR heralding pattern, (n₁, n₂, n₃): (1, 1, 1) shows a heralded cat state; (1, 3, 3), a GKP state with hexagonal lattice structure; and (3, 3, 5) and (4, 4, 4) show rectangular GKP states. States presented in a and b are reconstructed by state tomography using up to 2 × 10⁶ quadrature measurements for the (1, 1, 1) and (1, 3, 3) state, and roughly 5.9 × 10⁵, 3.6 × 10⁵ and 1.9 × 10⁶ quadrature measurements for the (3, 3, 5), (4, 4, 4) and (3, 3, 3) states, respectively. Each colour bar range shows the minimum and maximum of the corresponding Wigner function. The ħ = 1 convention is used.

Fig. 4. Symmetric effective squeezing versus device loss.

Symmetric effective squeezing for simulated output states of the four-mode GBS device as a function of the transmission of the heralding and heralded paths, η. Here we restrict to outcomes of the form (n, n, n) as they are among the highest quality output states. We see for transmissions in the range of 70–82% that the (3, 3, 3) outcome (dashed line) is best, as presented in this experiment. As transmission crosses 99.5%, the device is sufficient for making approximate GKP states compatible with fault tolerance.