Transversality and lattice surgery: exploring realistic routes towards coupled logical qubits with trapped-ion quantum processors

Abstract

Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This mid-term challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing the capability of current trapped-ion architectures in facing one of the most demanding parts of this quest: the implementation of an entangling CNOT gate between encoded logical qubits. We present a detailed comparative study of two alternative strategies for trapped-ion topological color codes, either a transversal or a lattice-surgery approach, characterized by a detailed microscopic modeling of both current technological capabilities and experimental sources of noise afflicting the different operations. Our careful fault-tolerant design, together with a low-resource optimization, allows us to determine via exhaustive numerical simulations the experimental regimes where each of the approaches becomes favorable. We hope that our study thereby contributes to guiding the future development of trapped-ion quantum computers.

References in corpus (28)

• Quantum Computing
• Quantum computing with trapped ions
• Randomized Benchmarking of Quantum Gates
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Towards fault-tolerant quantum computing with trapped ions
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Modular Entanglement of Atomic Qubits using both Photons and Phonons
• Low-distance Surface Codes under Realistic Quantum Noise
• Complete methods set for scalable ion trap quantum information processing
• Fast quantum logic gates with trapped-ion qubits
• Ultrafast Gates for Single Atomic Qubits
• Effective fault-tolerant quantum computation with slow measurements
• Ion trap quantum gates with amplitude-modulated laser beams
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
• Optimal control of entangling operations for trapped ion quantum computing
• Design, Fabrication, and Experimental Demonstration of Junction Surface Ion Traps
• Demonstration of two-atom entanglement with ultrafast optical pulses
• Simulating the performance of a distance-3 surface code in a linear ion trap
• Experimental realization of fast ion separation in segmented Paul traps
• Heating and ion transport in a Y-junction surface-electrode trap
• Approximation of real error channels by Clifford channels and Pauli measurements
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes
• Comparison of a quantum error correction threshold for exact and approximate errors
• Quantum computing by color-code lattice surgery
• Lattice Surgery Translation for Quantum Computation

Cited by in corpus (27)

• Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
• Entangling logical qubits with lattice surgery
• Flag fault-tolerant error correction for any stabilizer code
• Neural network decoder for topological color codes with circuit level noise
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• The Impact of Hardware Specifications on Reaching Quantum Advantage in the Fault Tolerant Regime
• Fault-tolerant protection of near-term trapped-ion topological qubits under realistic noise sources
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device
• Muzzle the Shuttle: Efficient Compilation for Multi-Trap Trapped-Ion Quantum Computers
• Demonstration of Shor encoding on a trapped-ion quantum computer
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits
• Achieving fault tolerance on capped color codes with few ancillas
• Fault-tolerant quantum error correction using error weight parities
• Ising model formulation for highly accurate topological color codes decoding
• Improving threshold for fault-tolerant color code quantum computing by flagged weight optimization
• Dynamical subset sampling of quantum error correcting protocols
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction
• Low-Depth Flag-Style Syndrome Extraction for Small Quantum Error-Correction Codes
• Taming Thiemann's Hamiltonian constraint in canonical loop quantum gravity: reversibility, eigenstates and graph-change analysis
• TILT: Achieving Higher Fidelity on a Trapped-Ion Linear-Tape Quantum Computing Architecture
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Feasibility of Logical Bell State Generation in Memory Assisted Quantum Networks
• Robust Syndrome Extraction via BCH Encoding
• Architecting Scalable Trapped Ion Quantum Computers using Surface Codes
• Relativistic meson spectra on ion-trap quantum simulators
• Comparison of spin-qubit architectures for quantum error-correcting codes