Fault-tolerant quantum computation using large spin cat-codes

Abstract

We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous variable cat encoding. With this, we can correct the dominant error sources, namely processes that can be expressed as error operators that are linear or quadratic in the components of angular momentum. Such codes tailored to dominant error sources {can} exhibit superior thresholds and lower resource overheads when compared to those designed for unstructured noise models. To preserve the dominant errors during gate operations, we identify a suitable universal gate set. A key component is the CNOT gate that preserves the rank of spherical tensor operators. Categorizing the dominant errors as phase and amplitude errors, we demonstrate how phase errors, analogous to phase-flip errors for qubits, can be effectively corrected. Furthermore, we propose a measurement-free error correction scheme to address amplitude errors without relying on syndrome measurements. Through an in-depth analysis of logical CNOT gate errors, we establish that the fault-tolerant threshold for error correction in the spin-cat encoding surpasses that of standard qubit-based encodings. We consider a specific implementation based on neutral-atom quantum computing, with qudits encoded in the nuclear spin of ${}^{87}$Sr, and show how to generate the universal gate set, including the rank-preserving CNOT gate, using quantum control and the Rydberg blockade. These findings pave the way for encoding a qubit in a large spin with the potential to achieve fault tolerance, high threshold, and reduced resource overhead in quantum information processing.

Published in PRX Quantum

References in corpus (34)

• Simulated Quantum Computation of Molecular Energies
• Suppressing quantum errors by scaling a surface code logical qubit
• Logical quantum processor based on reconfigurable atom arrays
• Topological fault-tolerance in cluster state quantum computation
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• Quantum computing with neutral atoms
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• A universal qudit quantum processor with trapped ions
• Fidelity of quantum operations
• Demonstration of fault-tolerant universal quantum gate operations
• Quantum computing with alkaline earth atoms
• Quantum Information Scrambling in a Superconducting Qutrit Processor
• Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
• Fault-tolerant quantum computation against biased noise
• Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble
• Assembly and coherent control of a register of nuclear spin qubits
• Long-lived Bell states in an array of optical clock qubits
• Encoding a magic state with beyond break-even fidelity
• Robust Mølmer-Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing
• High threshold codes for neutral atom qubits with biased erasure errors
• Encoding a qubit in a spin
• Fermion-qudit quantum processors for simulating lattice gauge theories with matter
• The Fibonacci scheme for fault-tolerant quantum computation
• Measurement-free fault-tolerant quantum error correction in near-term devices
• Quantum Optimal Control of Nuclear Spin Qudecimals in ${}^{87}\text{Sr}$
• Stabilizing a Bosonic Qubit using Colored Dissipation
• Qudit entanglers using quantum optimal control
• Multispin Clifford codes for angular momentum errors in spin systems
• Neutral atom entanglement using adiabatic Rydberg dressing
• Fault-tolerant measurement-free quantum error correction with multi-qubit gates
• High-Fidelity, Low-Loss State Detection of Alkali-Metal Atoms in Optical Tweezer Traps
• Numerical Gate Synthesis for Quantum Heuristics on Bosonic Quantum Processors
• Measurement-free implementations of small-scale surface codes for quantum dot qubits
• Spin squeezed GKP codes for quantum error correction in atomic ensembles

Cited by in corpus (20)

• Schrödinger cat states of a nuclear spin qudit in silicon
• Empowering high-dimensional quantum computing by traversing the dual bosonic ladder
• Circuit-based leakage-to-erasure conversion in a neutral atom quantum processor
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit
• Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions
• Realization of a fast triple-magic all-optical qutrit in strontium-88
• Platonic dynamical decoupling sequences for interacting spin systems
• Synthetic high angular momentum spin dynamics in a microwave oscillator
• Designing quantum error correction codes for practical spin qudit
• Dark spin-cats as biased qubits
• Deterministic carving of quantum states with Grover's algorithm
• Dynamical decoupling of interacting spins through group factorization
• Unfolded distillation: very low-cost magic state preparation for biased-noise qubits
• Coherent Generation and Protection of Anticoherent Spin States
• Three-qubit encoding in ytterbium-171 atoms for simulating 1+1D QCD
• Generalized Parity Measurements and Efficient Large Multi-component Cat State Preparation with Quantum Signal Processing
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Observation of the electric Breit-Rabi Effect
• Non-Gaussianity from superselection rules