[Paper Review] Protecting the quantum interference of cat states by phase-space compression

Xiaozhou Pan, Jonathan Schwinger+8 more|arXiv (Cornell University)|Dec 2, 2022

Quantum Information and Cryptography4 citations

TL;DR

This paper proposes a deterministic method to protect the quantum interference of cat states against photon loss by compressing their phase-space distribution using a conditional displacement operation in circuit QED. The technique enhances resilience of non-Gaussian features by shifting high-frequency interference components closer to the origin, preserving quantum coherence; experimentally, compressed cat states achieved fidelities of 65(±5)% with fidelity improvements under decoherence-limited conditions.

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.

Motivation & Objective

• To address the vulnerability of cat states to photon loss, which degrades their non-Gaussian quantum interference features.
• To develop a deterministic, hardware-efficient method for enhancing the robustness of continuous-variable quantum states against decoherence.
• To demonstrate phase-space compression as a means to protect quantum interference by reshaping the characteristic function landscape.
• To validate the technique experimentally in a circuit QED platform using conditional displacement operations.
• To quantify the error budget and identify dominant decoherence channels limiting state fidelity.

Proposed method

• Phase-space compression is implemented via a deterministic echo conditional displacement operation using native single-cavity and transmon gates in a cQED architecture.
• The method manipulates the characteristic function of the cat state to reduce the spatial extent of interference features, making them less susceptible to low-pass filtering from photon loss.
• A sequence of three $\hat{U}\hat{V}$ operations is used to achieve compression levels of -3 to -7 dB with fidelity >0.99 in simulation.
• State preparation fidelity is assessed via overlap with ideal states under decoherence models, including cavity decay, dephasing, and readout errors.
• The protocol is adaptable to different hardware parameters, with post-selection reducing the impact of transmon T1 decay.
• Error analysis is performed using master equation simulations to isolate contributions from individual decoherence channels and readout infidelities.

Experimental results

Research questions

• RQ1 Can phase-space compression protect the non-Gaussian interference features of cat states from photon loss in a deterministic, scalable way?
• RQ2 How does compressing the phase-space distribution affect the resilience of quantum interference under realistic decoherence?
• RQ3 What is the achievable fidelity of compressed cat states in a cQED platform with realistic noise and gate imperfections?
• RQ4 Which decoherence channels dominate the error budget in the state preparation and measurement process?
• RQ5 Can the conditional displacement operation be implemented using only native gates in a standard cQED setup to enable practical implementation?

Key findings

• The phase-space compression technique effectively protects quantum interference features by shifting high-frequency components closer to the origin, reducing their susceptibility to photon loss-induced filtering.
• Simulations show that compression levels of -3 to -7 dB can be achieved with fidelity >0.99 using three $\hat{U}\hat{V}$ operations.
• Experimentally, compressed cat states achieved a fidelity of 65(±5)% under decoherence-limited conditions, consistent with error budget analysis.
• The dominant error sources are ancilla dephasing (4%) and decay (2%), along with readout errors (5% for |e⟩→|e⟩), which together limit overall fidelity.
• The measured vacuum state contrast of ≈88.4% validates the estimated 7% infidelity for the $\hat{U}$ gate and 3.2% for readout, providing a normalization baseline for state fidelity evaluation.
• Post-selection during measurement reduces the effective impact of transmon T1 decay, improving gate fidelity estimates to ~5% per operation in the state preparation chain.