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arXiv:2310.03130 · Optica Quantum

Machine learning for efficient generation of universal photonic quantum computing resources

Amanuel Anteneh, F. Brunel, Olivier Pfister

Published Jun 28, 2024• 4 citations
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Abstract

We present numerical results from simulations using deep reinforcement learning to control a measurement-based quantum processor—a time-multiplexed optical circuit sampled by photon-number-resolving detection—and find it generates squeezed cat states quasi-deterministically, with an average success rate of 98%, far outperforming all other proposals. Since squeezed cat states are deterministic precursors to the Gottesman–Kitaev–Preskill (GKP) bosonic error code, this is a key result for enabling fault tolerant photonic quantum computing. Informed by these simulations, we also discovered a one-step quantum circuit of constant parameters that can generate GKP states with high probability, though not deterministically.

DOI
10.1364/opticaq.523445

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We present numerical results from simulations using deep reinforcement learning to control a measurement-based quantum processor—a time-multiplexed optical circuit sampled by photon-number-resolving detection—and find it generates squeezed cat states quasi-deterministically, with an average success rate of 98%, far outperforming all other proposals. Since squeezed cat states are deterministic precursors to the Gottesman–Kitaev–Preskill (GKP) bosonic error code, this is a key result for enabling fault tolerant photonic quantum computing. Informed by these simulations, we also discovered a one-step quantum circuit of constant parameters that can generate GKP states with high probability, though not deterministically.
Gottesman-Kitaev-Preskill (GKP) qubits, known for their exceptional error-correction capabilities, are highly coveted in quantum computing. However, generating optical GKP qubits has been a significant challenge. Measurement-based methods, where a portion of entangled squeezed vacuum modes are measured with photon number resolving detectors heralding a desired state in the undetected modes, have emerged as leading candidates for optical GKP qubit generation due their minimal resource requirements. While the current measurement-based methods can produce high-quality GKP qubits, they suffer from low success probabilities limiting experimental realization. The heart of the problem lies in the duality of photon number resolving measurements, being both the source of nonlinearity needed to generate quality GKP qubits and the component driving down their probability of successful production. Our method, breeding approximate squeezed coherent state superpositions created by generalized photon subtraction, overcomes this problem by supplementing two photon number resolving measurements with a single high success probability homodyne measurement. This scheme achieves success probabilities $\ensuremath{\ge}{10}^{\ensuremath{-}5}$, two orders of magnitude higher than strictly photon number resolving measurement based methods, while still producing states with high fidelity, possessing error-correction capabilities equivalent to up to a 10 dB squeezed GKP qubit. This breakthrough significantly advances the practical use of the optical GKP qubit encoding.
Gottesman-Kitaev-Preskill (GKP) states are essential non-Gaussian resources for fault-tolerant photonic quantum computing, enabling logical qubit encoding with intrinsic robustness against errors. Several approaches to GKP state preparation have been explored, including measurement-based protocols in circuit QED and trapped-ion systems, cat-state breeding, and photon-subtraction schemes. However, these methods are either restricted to specific platforms or require deep non-Gaussian resource chains with exponentially low success probabilities. Gaussian Boson Sampling (GBS) offers a compelling all-photonic alternative by generating non-Gaussian states through measurement-induced nonlinearity, without the need for matter-based ancilla or active feedforward. Nevertheless, its practical implementation is limited by the exponential computational cost of evaluating matrix hafnians-#P-complete functions that govern photon-number probabilities. To address this challenge, we introduce a two-stage Histogram Gradient Boosting surrogate pipeline that predicts, without any hafnian computation, the optimal heralding pattern, circuit fidelity, and post-selection probability for candidate GBS circuits, while reserving exact quantum simulation exclusively for surrogate-selected candidates. Trained on circuit configurations across 3-5 optical modes, the surrogate achieves 90.0% GKP-detection accuracy on a held-out set, representing a 23.7 percentage-point improvement over the baseline, with a fidelity mean absolute error of 0.032 and a log-scale post-selection probability R2=0.837R^2 = 0.837R2=0.837, reducing the total simulation burden by approximately 90%.
The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.
Large-amplitude squeezed cat states and high-quality Gottesman-Kitaev-Preskill (GKP) states are essential for effective quantum error correction, yet their optical preparation has been hindered by challenges such as low success probabilities, small amplitudes, and insufficient squeezing. Addressing these limitations, our research introduces scalable optical schemes for the deterministic preparation of large-amplitude squeezed cat states from photon-number states. Fock states have the benefit of producing consistent cat states across all measurement outcomes and intrinsically provides a degree of squeezing. Notably, these squeezed cat states facilitate the deterministic generation of high-quality approximate GKP states via "breeding," showing that GKP error correction in optics is technically feasible in near-term experiments. Our schemes allow fault-tolerant quantum computation through the use of GKP error correction.