Multimode rotationally symmetric bosonic codes from group-theoretic construction

Abstract

We introduce a new family of multi-mode, rotationally symmetric bosonic codes inspired by the group-theoretic framework of [Phys. Rev. Lett. 133, 240603 (2024)]. Such a construction inverts the traditional paradigm of code design by identifying codes from the requirement that a group of chosen logical gates should be implemented by means of physically simple logical operations, such as linear optics. Leveraging previously unexplored degrees of freedom within this framework, our construction preserves rotational symmetry across multiple modes, enabling linear-optics implementation of the full Pauli group. These codes exhibit improved protection against dephasing noise, outperforming both single-mode analogues and earlier multi-mode constructions. Notably, they allow exact correction of correlated dephasing and support qudit encoding in arbitrary dimensions. We analytically construct and numerically benchmark two-mode binomial codes instances, and demonstrate that, unlike single-mode rotationally symmetric bosonic codes, these exhibit no trade-off between protection against dephasing and photon loss.

28 pages, 10 figures

References in corpus (32)

• Towards understanding two-level-systems in amorphous solids -- Insights from quantum circuits
• Real-time quantum error correction beyond break-even
• New class of quantum error-correcting codes for a bosonic mode
• Exponential suppression of bit-flips in a qubit encoded in an oscillator
• Ultrahigh Error Threshold for Surface Codes with Biased Noise
• Beating the break-even point with a discrete-variable-encoded logical qubit
• Fault-tolerant bosonic quantum error correction with the surface-GKP code
• Repetition Cat Qubits for Fault-Tolerant Quantum Computation
• High-threshold fault-tolerant quantum computation with analog quantum error correction
• Quantum computing with rotation-symmetric bosonic codes
• Decoherence in qubits due to low-frequency noise
• Decoherence from ensembles of two-level fluctuators
• Optimum Quantum Error Recovery using Semidefinite Programming
• Pair-cat codes: autonomous error-correction with low-order nonlinearity
• Low overhead fault-tolerant quantum error correction with the surface-GKP code
• Non-Markovianity of colored noisy channels
• Quantum error correction against photon loss using NOON states
• Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
• Decoherence of a qubit by non-Gaussian noise at an arbitrary working point
• Universal control of a bosonic mode via drive-activated native cubic interactions
• Encoding qubits in multimode grid states
• Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements
• LDPC-cat codes for low-overhead quantum computing in 2D
• The Near-optimal Performance of Quantum Error Correction Codes
• Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code
• Analog information decoding of bosonic quantum LDPC codes
• Quantum error-correcting codes with a covariant encoding
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Clifford operations and homological codes for rotors and oscillators
• Bosonic quantum Fourier codes