Quantum Error Correction of Qudits Beyond Break-even

Abstract

Hilbert space dimension is a key resource for quantum information processing. A large Hilbert space is not only an essential requirement for quantum error correction, but it can also be advantageous for realizing gates and algorithms more efficiently. There has thus been considerable experimental effort in recent years to develop quantum computing platforms using qudits (d-dimensional quantum systems with d>2) as the fundamental unit of quantum information. Just as with qubits, quantum error correction of these qudits will be necessary in the long run, but to date error correction of logical qudits has not been demonstrated experimentally. Here we report the experimental realization of an error-corrected logical qutrit (d=3) and ququart (d=4) by employing the Gottesman-Kitaev-Preskill (GKP) bosonic code. Using a reinforcement learning agent, we optimize the GKP qutrit (ququart) as a ternary (quaternary) quantum memory and achieve beyond break-even error correction with a gain of 1.82 +/- 0.03 (1.87 +/- 0.03). This work represents a new way of leveraging the large Hilbert space of a harmonic oscillator for hardware-efficient quantum error correction.

References in corpus (44)

• Negativity of the Wigner function as an indicator of nonclassicality
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Quantum error correction below the surface code threshold
• New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds
• Qudits and high-dimensional quantum computing
• Real-time quantum error correction beyond break-even
• Encoding a qubit in a trapped-ion mechanical oscillator
• Implementation of a Toffoli Gate with Superconducting Circuits
• A universal qudit quantum processor with trapped ions
• A quantum memory with near-millisecond coherence in circuit QED
• Efficient Toffoli Gates Using Qudits
• Beating the break-even point with a discrete-variable-encoded logical qubit
• Enhanced fault-tolerant quantum computing in $d$-level systems
• Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
• Fault-tolerant detection of a quantum error
• Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator
• Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Towards Scalable Bosonic Quantum Error Correction
• Quantum Error Correction with the Gottesman-Kitaev-Preskill Code
• Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble
• Model-Free Quantum Control with Reinforcement Learning
• Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures
• Excitation and coherent control of spin qudit modes with sub-MHz spectral resolution
• Asymptotic Improvements to Quantum Circuits via Qutrits
• Maximizing the Hilbert space for a finite number of distinguishable quantum states
• Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States
• Direct characteristic-function tomography of quantum states of the trapped-ion motional oscillator
• Encoding a qubit in a spin
• Climbing Mount Scalable: Physical-Resource Requirements for a Scalable Quantum Computer
• Scalable algorithm simplification using quantum AND logic
• Sustained state-independent quantum contextual correlations from a single ion
• Quantum Error Correction of Qudits Beyond Break-even
• Simulating 2D lattice gauge theories on a qudit quantum computer
• Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields
• Quantum Stabilizer Codes Embedding Qubits Into Qudits
• Systematic study of High $E_J/E_C$ transmon qudits up to $d=12$
• Empowering high-dimensional quantum computing by traversing the dual bosonic ladder
• Quantum error correction with higher Gottesman-Kitaev-Preskill codes: minimal measurements and linear optics
• Hyperfine spectroscopy and fast, all-optical arbitrary state initialization and readout of a single, ten-level ${}^{73}$Ge vacancy nuclear spin qudit in diamond
• Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings
• Passive environment-assisted quantum communication with GKP states
• Synthetic high angular momentum spin dynamics in a microwave oscillator
• Universal Quantum Gate Set for Gottesman-Kitaev-Preskill Logical Qubits

Cited by in corpus (29)

• Quantum Error Correction of Qudits Beyond Break-even
• Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits
• Agents for self-driving laboratories applied to quantum computing
• Characterization of drive-induced unwanted state transitions in superconducting circuits
• Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction
• Balanced cross-Kerr coupling for superconducting qubit readout
• Demonstration of Discrete-Time Quantum Walks and Observation of Topological Edge States in a Superconducting Qutrit Chain
• Qudit low-density parity-check codes
• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures
• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
• Continuous-variable designs and design-based shadow tomography from random lattices
• Simple ways of preparing qudit Dicke states
• Achievable rates for concatenated square Gottesman-Kitaev-Preskill codes
• Single-Qudit Quantum Neural Networks for Multiclass Classification
• High-Fidelity Controlled-Phase Gate for Binomial Codes via Geometric Phase Engineering
• Gate-Based Microwave Quantum Repeater Via Grid-State Encoding
• Estimating the performance boundary of Gottesman-Kitaev-Preskill codes and number-phase codes
• Single-shot conditional displacement gate between a trapped atom and traveling light
• Transversal AND in Quantum Codes
• Quantum Error Correction with Superpositions of Squeezed Fock States
• Enlarging the GKP stabilizer group for enhanced noise protection
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
• Passive quantum error correction of photon loss at breakeven
• Automated discovery and optimization of autonomous quantum error correction codes for a general open quantum system
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing