Fault-Tolerant Computing with Single Qudit Encoding

Abstract

We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth. Notably, this outperforms qubit codes using thousands of units. We also outline the required properties for a generic physical system to Fault-Tolerantly implement these embedded codes.

References in corpus (40)

• Surface codes: Towards practical large-scale quantum computation
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Error Correction for Quantum Memories
• Quantum Computing with Very Noisy Devices
• Quantum Error Correction for Beginners
• Roads towards fault-tolerant universal quantum computation
• High threshold universal quantum computation on the surface code
• Experimental Quantum Computations on a Topologically Encoded Qubit
• A universal qudit quantum processor with trapped ions
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Semiconductor Qubits In Practice
• Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Implementation of the Five Qubit Error Correction Benchmark
• Towards practical classical processing for the surface code
• Bosonic quantum error correction codes in superconducting quantum circuits
• Bias-preserving gates with stabilized cat qubits
• Beating the break-even point with a discrete-variable-encoded logical qubit
• Enhanced fault-tolerant quantum computing in $d$-level systems
• Analysis of dephasing mechanisms in a standing wave dipole trap
• Fault-tolerant detection of a quantum error
• Fault-tolerant thresholds for quantum error correction with the surface code
• Fault-tolerant quantum computation with few qubits
• Three addressable spin qubits in a molecular single-ion magnet
• Coherent manipulation of a molecular Ln-based nuclear qudit coupled to an electron qubit
• Error-transparent operations on a logical qubit protected by quantum error correction
• A perspective on scaling up quantum computation with molecular spins
• Error-corrected gates on an encoded qubit
• Donor spins in silicon for quantum technologies
• An Introduction to Quantum Error Correction
• Enhanced molecular spin-photon coupling at superconducting nanoconstrictions
• Minimal qudit code for a qubit in the phase-damping channel
• Performance of planar Floquet codes with Majorana-based qubits
• Thresholds for universal concatenated quantum codes
• The Grover algorithm with large nuclear spins in semiconductors
• Blueprint of a Molecular Spin Quantum Processor
• Quantum Stabilizer Codes Embedding Qubits Into Qudits
• Counteracting dephasing in Molecular Nanomagnets by optimized qudit encodings
• Fault-tolerant qubit encoding using a spin-7/2 qudit
• Comparison of memory thresholds for planar qudit geometries

Cited by in corpus (5)

• Proof-of-concept Quantum Simulator based on Molecular Spin Qudits
• Dephasing-tolerant quantum sensing for transverse magnetic fields with spin qudits
• Comparison of Two Optimization Methods for a Rydberg Quantum Gate
• Quantum Information Processing with Molecular Nanomagnets: an introduction
• Mitigating decoherence in molecular spin qudits