Bosonic quantum Fourier codes
arXiv:2505.16618 · doi:10.22331/q-2026-02-09-2000
Abstract
While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first level of redundancy and error correction that simplifies the overall fault-tolerant architecture. A challenge then is to ensure universal control over the encoded qubits. Here, we explore an approach where information is encoded in an irreducible representation of a finite subgroup of through an inverse quantum Fourier transform. We illustrate this idea by applying it to the real Pauli group in the bosonic setting. The resulting two-mode Fourier cat code displays good error correction properties and admits an experimentally-friendly universal gate set that we discuss in detail.
17 pages, 1 figure, 3 tables
References in corpus (32)
- Encoding a qubit in an oscillator
- Dynamically protected cat-qubits: a new paradigm for universal quantum computation
- Restrictions on Transversal Encoded Quantum Gate Sets
- The Kerr-Cat Qubit: Stabilization, Readout, and Gates
- Real-time quantum error correction beyond break-even
- New class of quantum error-correcting codes for a bosonic mode
- Encoding a qubit in a trapped-ion mechanical oscillator
- Quantum algorithms for algebraic problems
- Building a fault-tolerant quantum computer using concatenated cat codes
- Cavity State Manipulation Using Photon-Number Selective Phase Gates
- Repetition Cat Qubits for Fault-Tolerant Quantum Computation
- Quantum computing with rotation-symmetric bosonic codes
- Quantum Error Correction with the Toric-GKP Code
- Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
- Optimum Quantum Error Recovery using Semidefinite Programming
- Hardware-efficient quantum error correction via concatenated bosonic qubits
- Error-corrected gates on an encoded qubit
- Pair-cat codes: autonomous error-correction with low-order nonlinearity
- Quantum control of a cat-qubit with bit-flip times exceeding ten seconds
- Dual-rail encoding with superconducting cavities
- Encoding a qubit in a spin
- Quantum algorithm for Petz recovery channels and pretty good measurements
- High-fidelity parametric beamsplitting with a parity-protected converter
- Quantum capacity and codes for the bosonic loss-dephasing channel
- A Family of Quantum Codes with Exotic Transversal Gates
- Quantum spherical codes
- The Near-optimal Performance of Quantum Error Correction Codes
- The -qutrit, a two-mode bosonic qutrit
- Quantum Codes from Twisted Unitary -groups
- Quantum error-correcting codes with a covariant encoding
- Dissipative protection of a GKP qubit in a high-impedance superconducting circuit driven by a microwave frequency comb
- Letting the tiger out of its cage: bosonic coding without concatenation