Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation

Abstract

A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that shall be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC, and a physically-motivated error model that goes beyond standard simplifications in the QEC literature. Our large-scale numerical analysis shows that two-species trapped-ion crystals in high-optical aperture segmented traps, with the improvements hereby described, are a very promising candidate for fault-tolerant quantum computation.

References in corpus (78)

• Fault-tolerant quantum computation by anyons
• Quantum Computing
• Good Quantum Error-Correcting Codes Exist
• Dynamical Decoupling of Open Quantum Systems
• Topological quantum memory
• Dynamical suppression of decoherence in two-state quantum systems
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Error Correction for Quantum Memories
• 14-qubit entanglement: creation and coherence
• Multi-particle entanglement of hot trapped ions
• State preservation by repetitive error detection in a superconducting quantum circuit
• Fault-tolerant quantum computation with high threshold in two dimensions
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Entanglement and quantum computation with ions in thermal motion
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• Topological Quantum Distillation
• Keeping a Quantum Bit Alive by Optimized $\pi$-Pulse Sequences
• Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
• Surface code quantum computing by lattice surgery
• Fault-Tolerant Quantum Dynamical Decoupling
• Experimental Quantum Error Correction
• High-Fidelity Universal Gate Set for ${}^9$Be${}^{+}$ Ion Qubits
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Experimental Quantum Computations on a Topologically Encoded Qubit
• A quantum information processor with trapped ions
• Fault-Tolerant Error Correction with Efficient Quantum Codes
• High-fidelity readout of trapped-ion qubits
• Symmetrizing Evolutions
• Using Parity Kicks for Decoherence Control
• Single-qubit quantum memory exceeding $10$-minute coherence time
• Robust dynamical decoupling with bounded controls
• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Coherent Diabatic Ion Transport and Separation in a Multi-Zone Trap Array
• Controlling fast transport of cold trapped ions
• Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
• Repeated quantum error correction on a continuously encoded qubit by real-time feedback
• Arbitrarily accurate composite pulses
• Quantum error correction with only two extra qubits
• Implementation of the Five Qubit Error Correction Benchmark
• Layered architecture for quantum computing
• Optimal Dynamical Decoherence Control of a Qubit
• Dynamical decoupling sequence construction as a filter-design problem
• Arbitrarily Accurate Dynamical Control in Open Quantum Systems
• Fault-tolerant quantum error detection
• Multi-Element Logic Gates for Trapped-Ion Qubits
• Restoring Coherence Lost to a Slow Interacting Mesoscopic Bath
• Experimental noise filtering by quantum control
• Arbitrary quantum control of qubits in the presence of universal noise
• Effective fault-tolerant quantum computation with slow measurements
• EIT ground-state cooling of long ion strings
• Simulating open quantum systems: from many-body interactions to stabilizer pumping
• Preserving qubit coherence by dynamical decoupling
• A long-lived Zeeman trapped-ion qubit
• A General Transfer-Function Approach to Noise Filtering in Open-Loop Quantum Control
• Combining dynamical decoupling with fault-tolerant quantum computation
• Dynamical Quantum Error Correction of Unitary Operations with Bounded Controls
• Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes
• Realization of Universal Ion Trap Quantum Computation with Decoherence Free Qubits
• Observation of quantum interference between separated mechanical oscillator wavepackets
• Robustness of composite pulses to time-dependent control noise
• Phase-modulated decoupling and error suppression in qubit-oscillator systems
• Optimal control of entangling operations for trapped ion quantum computing
• High-order noise filtering in nontrivial quantum logic gates
• Arbitrary Waveform Generator for Quantum Information Processing with Trapped Ions
• Experimental realization of fast ion separation in segmented Paul traps
• Sustained state-independent quantum contextual correlations from a single ion
• Fast ion swapping for quantum information processing
• Empirical Determination of Bang-Bang Operations
• Controlling the transport of an ion: Classical and quantum mechanical solutions
• Concatenated composite pulses compensating simultaneous systematic errors
• A scalable, fast and multichannel arbitrary waveform generator
• Transformed Composite Sequences for Improved Qubit Addressing
• Quantum error correction failure distributions: comparison of coherent and stochastic error models
• Quantum fault tolerance in small experiments
• Comparison of ancilla preparation and measurement procedures for the Steane [[7,1,3]] code on a model ion trap quantum computer
• Iterative Phase Optimisation of Elementary Quantum Error Correcting Codes

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• Learning time-dependent noise to reduce logical errors: Real time error rate estimation in quantum error correction
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• Ion native variational ansatz for quantum approximate optimization
• Alibaba Cloud Quantum Development Platform: Surface Code Simulations with Crosstalk
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• An integrity measure to benchmark quantum error correcting memories
• Generating Target Graph Couplings for QAOA from Native Quantum Hardware Couplings
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• Simulation of the five-qubit quantum error correction code on superconducting qubits
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction
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• Precision measurement of the ionization energy of a single trapped ${}^{40}$Ca${}^{+}$ ion by Rydberg series excitation
• Digital-Analog Counterdiabatic Quantum Optimization with Trapped Ions
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• Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
• Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field
• Mitigating Quantum Gate Errors for Variational Eigensolvers Using Hardware-Inspired Zero-Noise Extrapolation
• Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
• A Universal Circuit Set Using the $S_3$ Quantum Double
• Quantum error correction in the NISQ regime for sequential quantum computing
• Localizing genuine multiparty entanglement in noisy stabilizer states
• Ultrafast coherent excitation of an Ytterbium ion with single laser pulses
• Impact of micromotion and field-axis misalignment on the excitation of Rydberg states of ions in a Paul trap
• Sub-Doppler cooling of a trapped ion in a phase-stable polarization gradient
• Boson sampling with ultracold atoms in a programmable optical lattice
• Sampling and the complexity of nature
• Individual addressing of ion qubits with counter-propagating optical frequency combs
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model
• Experimental measurement and a physical interpretation of quantum shadow enumerators
• Relaxation times do not capture logical qubit dynamics
• Ion-Trap Chip Architecture Optimized for Implementation of Quantum Error-Correcting Code
• Robust entanglement by continuous dynamical decoupling of the J-coupling interaction
• Characterization and cancellation of power-line-induced motional-mode frequency noise in a trapped-ion system
• Quantum dimension test using the uncertainty principle
• Convenient Real-Time Monitoring of the Contamination of Surface Ion Trap
• Closed-loop optimization of fast trapped-ion shuttling with sub-quanta excitation