Construction of Bias-preserving Operations for Pair-cat Code

Abstract

Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can achieve hardware-efficient fault-tolerant quantum computation with a more favorable error threshold. Distinct from two-level physical systems, multi-level systems (such as harmonic oscillators) can achieve a desirable set of bias-preserving quantum operations while using continuous engineered dissipation or Hamiltonian protection to stabilize to the encoding subspace. For example, cat codes stabilized with driven-dissipation or Kerr nonlinearity can possess a set of biased-preserving gates while continuously correcting bosonic dephasing error. However, cat codes are not compatible with continuous quantum error correction against excitation loss error, because it is challenging to continuously monitor the parity to correct photon loss errors. In this work, we generalize the bias-preserving operations to pair-cat codes, which can be regarded as a multimode generalization of cat codes, to be compatible with continuous quantum error correction against both bosonic loss and dephasing errors. Our results open the door towards hardware-efficient robust quantum information processing with both bias-preserving operations and continuous quantum error correction simultaneously correcting bosonic loss and dephasing errors.

arXiv comment16 pages, 3 figures

References in corpus (20)

• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• Confining the state of light to a quantum manifold by engineered two-photon loss
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Symmetries and conserved quantities in Lindblad master equations
• Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving
• Building a fault-tolerant quantum computer using concatenated cat codes
• Effective operator formalism for open quantum systems
• The XZZX Surface Code
• Exponential suppression of bit-flips in a qubit encoded in an oscillator
• Bosonic Quantum Codes for Amplitude Damping
• Fault-tolerant quantum computation against biased noise
• Bias-preserving gates with stabilized cat qubits
• Repetition Cat Qubits for Fault-Tolerant Quantum Computation
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Cat codes with optimal decoherence suppression for a lossy bosonic channel
• Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
• Pair-cat codes: autonomous error-correction with low-order nonlinearity
• 2-D Compass Codes
• Combined Dissipative and Hamiltonian Confinement of Cat Qubits
• Stabilizing a Bosonic Qubit using Colored Dissipation

Cited by in corpus (5)

• Letting the tiger out of its cage: bosonic coding without concatenation
• Dark spin-cats as biased qubits
• High-rate extended binomial codes for multiqubit encoding
• Mitigating Temporal Fragility in the XY Surface Code
• Environment-Assisted Generation of Non-Gaussian Wavepacket Quantum States