Designing quantum error correction codes for practical spin qudit

Abstract

The implementation of practical error correction protocols is essential for deployment of quantum information technologies. Ways of exploiting high-spin nuclei, which have multi-level quantum resources, have attracted interest in this context because they offer additional Hilbert space dimensions in a spatially compact and theoretically efficient structure. We present a quantitative analysis of the performance of a spin-qudit-based error-correctable quantum memory, with reference to the actual Hamiltonians of several potential candidate systems. First, the ideal code-word implemented on a spin-7/2 nucleus, which provides first order Pauli-$X$, $Y$ and $Z$ error correction, has intrinsic infidelity due to mixed eigenstates under realistic conditions. We confirm that expansion to a spin-9/2 system with tailored code-words can compensate this infidelity. Second, we claim that electric field fluctuations -- which are inevitable in real systems -- should also be considered as a noise source, and we illustrate an encoding/decoding scheme for a multi-spin-qudit-based error correction code that can simultaneously compensate for both electric and magnetic field perturbations. Such strategies are important as we move beyond the current noisy-intermediate quantum era, and fidelities above two or three nines becomes crucial for implementation of quantum technologies.

References in corpus (50)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Encoding a qubit in an oscillator
• Quantum Error Correction for Quantum Memories
• Sensing electric fields using single diamond spins
• Strong quantum computational advantage using a superconducting quantum processor
• Suppressing quantum errors by scaling a surface code logical qubit
• Logical quantum processor based on reconfigurable atom arrays
• A >99.9%-fidelity quantum-dot spin qubit with coherence limited by charge noise
• Computing with spin qubits at the surface code error threshold
• Fast universal quantum control above the fault-tolerance threshold in silicon
• Exponential suppression of bit or phase flip errors with repetitive error correction
• Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
• The XZZX Surface Code
• Decoherence in Crystals of Quantum Molecular Magnets
• Detection of a single fundamental charge with nanoscale resolution in ambient conditions using the NV${}^{-}$ center in diamond
• Silicon quantum processor with robust long-distance qubit couplings
• Robust encoding of a qubit in a molecule
• Decoherence of near-surface nitrogen-vacancy centers due to electric field noise
• Coherent electrical control of a single high-spin nucleus in silicon
• Tailoring surface codes for highly biased noise
• Competition between electric field and magnetic field noise in the decoherence of a single spin in diamond
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Electric field control of spins in molecular magnets
• Coherent Manipulation and Decoherence of S=10 Single-Molecule Magnets
• A perspective on scaling up quantum computation with molecular spins
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• Encoding an oscillator into many oscillators
• Donor spins in silicon for quantum technologies
• Quantum coherent spin-electric control in a molecular nanomagnet at clock transitions
• Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator
• Blackbody radiation shift assessment for a lutetium ion clock
• Deterministic single ion implantation of rare-earth ions for nanometer resolution colour center generation
• Coherent spin control by electrical manipulation of the magnetic anisotropy
• Encoding a qubit in a spin
• Minimal qudit code for a qubit in the phase-damping channel
• Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields
• Schrödinger cat states of a nuclear spin qudit in silicon
• Counteracting dephasing in Molecular Nanomagnets by optimized qudit encodings
• Tailored XZZX codes for biased noise
• Qudit entanglers using quantum optimal control
• Fault-tolerant quantum computation using large spin cat-codes
• Noisy Qudit vs Multiple Qubits : Conditions on Gate Efficiency for Enhancing Fidelity
• Multispin Clifford codes for angular momentum errors in spin systems
• Fault-tolerant qubit encoding using a spin-7/2 qudit
• Æ codes
• Errors in stimulated-Raman-induced logic gates in ${}^{133}$Ba${}^{+}$
• Magneto-optical trap of a Group III atom
• Spin squeezed GKP codes for quantum error correction in atomic ensembles
• Demonstrating experimentally the encoding and dynamics of an error-correctable logical qubit on a hyperfine-coupled nuclear spin qudit

Cited by in corpus (4)

• Qubit-qudit entanglement transfer in defect centers with high-spin nuclei
• Coherent Generation and Protection of Anticoherent Spin States
• Magnetoelectric effect in the mixed valence polyoxovanadate cage V${}_{12}$
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems