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arXiv:2212.01271

Protecting the quantum interference of cat states by phase-space compression

Xiaozhou Pan, Jonathan Schwinger, Ni-Ni Huang, Pengtao Song, Weipin Chua, Fumiya Hanamura, Atharv Joshi, Fernando Valadares, Radim Filip, Yvonne Y. Gao

Published Dec 2, 2022• 4 citations
arXivHTMLPDF

Abstract

Cat states, with their unique phase-space interference properties, are ideal candidates for understanding fundamental principles of quantum mechanics and performing key quantum information processing tasks. However, they are highly susceptible to photon loss, which inevitably diminishes their quantum non-Gaussian features. Here, we protect these non-Gaussian features against photon loss by compressing the phase-space distribution of a cat state. We achieve this compression with a deterministic technique based on the echo conditional displacement operation in a circuit QED device. We present a versatile technique for creating robust non-Gaussian continuous-variable resource states in a highly linear bosonic mode and manipulating their phase-space distribution to achieve enhanced resilience against photon loss. Compressed cat states offer an attractive avenue for obtaining new insights into quantum foundations and quantum metrology, and for developing inherently more protected bosonic codewords for quantum error correction.

DOI
10.48550/arxiv.2212.01271

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Cat states, with their unique phase-space interference properties, are ideal candidates for understanding fundamental principles of quantum mechanics and performing key quantum information processing tasks. However, they are highly susceptible to photon loss, which inevitably diminishes their quantum non-Gaussian features. Here, we protect these non-Gaussian features against photon loss by compressing the phase-space distribution of a cat state. We achieve this compression with a deterministic technique based on the echo conditional displacement operation in a circuit QED device. We present a versatile technique for creating robust non-Gaussian continuous-variable resource states in a highly linear bosonic mode and manipulating their phase-space distribution to achieve enhanced resilience against photon loss. Compressed cat states offer an attractive avenue for obtaining new insights into quantum foundations and quantum metrology, and for developing inherently more protected bosonic codewords for quantum error correction.
We introduce a family of bosonic quantum error-correcting codes built as a rotation-symmetric superposition of squeezed vacuum states, which promise protection against both loss and dephasing noise channels. The robustness of these "squeezed-vacuum codes" arises from being arranged at evenly spaced angles in phase-space, and simultaneously in evenly spaced photon-number support n≡2k ⁣(mod2m)n \equiv {2k} \! \pmod {2m}n≡2k(mod2m). We present simple preparation circuits: a two-legged code using a Hadamard-conditional-squeezing-Hadamard sequence on an ancilla qubit, and for general "mmm-legged" codewords using sequences of conditional rotations. The performance of these codes is evaluated against loss and dephasing noises using the Knill-Laflamme violation function and benchmarked against cat codes. As the number mmm of squeezed-vacuum states in a code increases, the code exhibits improved loss tolerance at the cost of higher dephasing sensitivity. We outline implementations in circuit QED and trapped-ion platforms, where high-fidelity Gaussian operations and conditional controls are available or under active development. These results help establish squeezed-vacuum codes as practical, hardware-ready, members of the bosonic codes class.
Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.
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.
Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schr\"odinger cat codes---based on the superposition of two coherent states with opposite displacements---can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e., cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by particle loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both particle loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of state-of-the-art quantum hardware platforms, the squeezed cat code has a resilience to particle loss errors that significantly outperforms that of the conventional cat code.
In continuous-variable quantum computing, autonomous quantum error correction (QEC) can dissipatively steer a noisy quantum state into a target state or manifold, enabling robust quantum information processing without explicit syndrome measurements and feedback. Here, we propose a nullifier-based digital autonomous QEC enabled by conditional Gaussian operations. By designing jump operators for target nullifiers and compiling the resulting Lindbladian into a Trotterized sequence of elementary conditional Gaussian operations, we demonstrate two use cases: (i) deterministic preparation of non-Gaussian resource states for universal computation, including finitely squeezed cubic phase states and approximate trisqueezed states, and (ii) autonomous suppression of dephasing error for cat and squeezed cat states. We provide explicit gate decompositions for the required conditional Gaussian operations and numerically evaluate the performance under realistic imperfections, including photon loss in the bosonic mode and ancillary-qubit decoherence. Our results clarify the resource requirements and trade-offs, such as circuit depth, time-step choices, and the required set of conditional Gaussian operations, for scalable, gate-level implementations of autonomous state preparation and error suppression.