Error suppression in adiabatic quantum computing with qubit ensembles

Abstract

Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size $N_{\mathrm{c}}$ where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than $N_{\mathrm{c}}$, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with $N$, as long as the decoherence rate is sufficiently low.

References in corpus (78)

• Quantum Computing in the NISQ era and beyond
• Quantum Annealing in the Transverse Ising Model
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Quantum metrology with nonclassical states of atomic ensembles
• Adiabatic Quantum Computing
• Quantum Error Correction for Quantum Memories
• Quantum interface between light and atomic ensembles
• Experimental long-lived entanglement of two macroscopic objects
• Quantum teleportation between light and matter
• Atom chip based generation of entanglement for quantum metrology
• Quantum annealing with more than one hundred qubits
• Solid-state electronic spin coherence time approaching one second
• Quantum Error Correction for Beginners
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Annealing and Analog Quantum Computation
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Quantum Search by Local Adiabatic Evolution
• Defining and detecting quantum speedup
• Separability of very noisy mixed states and implications for NMR quantum computing
• Robustness of adiabatic quantum computation
• Digitized adiabatic quantum computing with a superconducting circuit
• Bounds for the adiabatic approximation with applications to quantum computation
• Coherence of Nitrogen-Vacancy Electronic Spin Ensembles in Diamond
• Magnetic field imaging with NV ensembles
• Experimental signature of programmable quantum annealing
• Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in a Bose-Einstein condensate
• Spatially distributed multipartite entanglement enables Einstein-Podolsky-Rosen steering of atomic clouds
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Adiabatic Quantum Computation in Open Systems
• Quantum Optimization of Fully-Connected Spin Glasses
• Coherent manipulation of Bose-Einstein condensates with state-dependent microwave potentials on an atom chip
• Entanglement between two spatially separated atomic modes
• Error corrected quantum annealing with hundreds of qubits
• Quantum versus Classical Annealing of Ising Spin Glasses
• Spin self-rephasing and very long coherence times in a trapped atomic ensemble
• Experimental implementation of an adiabatic quantum optimization algorithm
• Experimental realization of a multiplexed quantum memory with 225 individually accessible memory cells
• How Powerful is Adiabatic Quantum Computation?
• Macroscopic quantum computation using Bose-Einstein condensates
• Error correcting codes for adiabatic quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Towards Fault Tolerant Adiabatic Quantum Computation
• Microwave potentials and optimal control for robust quantum gates on an atom chip
• Quantum teleportation between remote atomic-ensemble quantum memories
• Noise resistance of adiabatic quantum computation using random matrix theory
• Reexamining classical and quantum models for the D-Wave One processor
• Quantum Annealing Correction with Minor Embedding
• Adiabatic Quantum Computing for Random Satisfiability Problems
• Decoherence in a scalable adiabatic quantum computer
• Decoherence in adiabatic quantum computation
• Macroscopic quantum information processing using spin coherent states
• General error estimate for adiabatic quantum computing
• Entanglement generation in quantum networks of Bose-Einstein condensates
• Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model
• Experimental entanglement of 25 individually accessible atomic quantum interfaces
• Devil's crevasse and macroscopic entanglement in two-component Bose-Einstein condensates
• Nested Quantum Annealing Correction
• Adiabatic Quantum Computation and Deutsch's Algorithm
• Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics
• Local Realistic Model for the Dynamics of Bulk-Ensemble NMR Information Processing
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Performance of two different quantum annealing correction codes
• Mean Field Analysis of Quantum Annealing Correction
• A modified quantum adiabatic evolution for the Deutsch-Jozsa problem
• Effect of Local Minima on Adiabatic Quantum Optimization
• Quantum teleportation of spin coherent states: beyond continuous variables teleportation
• Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor
• Scalable effective temperature reduction for quantum annealers via nested quantum annealing correction
• Geometric phase gate for entangling two Bose-Einstein condensates
• Open systems dynamics: Simulating master equations in the computer
• Quantum and Classical in Adiabatic Computation
• Nested Quantum Annealing Correction at Finite Temperature: $p$-spin models
• An Anisotropic Landau-Lifschitz-Gilbert model of dissipation in qubits
• Decoherence induced deformation of the ground state in adiabatic quantum computation
• Quantum Atom Optics: Theory and Applications to Quantum Technology
• Entanglement as a resource in adiabatic quantum optimization
• Implementing the Deutsch-Jozsa algorithm with macroscopic ensembles

Cited by in corpus (8)

• Classical analog of qubit logic based on a magnon Bose-Einstein condensate
• Remote state preparation of two-component Bose-Einstein condensates
• Experimental observation of Josephson oscillations in a room-temperature Bose-Einstein magnon condensate
• Deep recurrent networks predicting the gap evolution in adiabatic quantum computing
• Quantum Atom Optics: Theory and Applications to Quantum Technology
• Measuring energy by measuring any other observable
• Using copies to improve precision in continuous-time quantum computing
• Adiabatic Dynamics of Entanglement