Local Fault-tolerant Quantum Computation

Abstract

We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due to encoding. We carry out a detailed semi-numerical threshold analysis for concatenated coding using the 7-qubit CSS code in the local and `nonlocal' setting. First, we find that the threshold in the local model for the [[7,1,3]] code has a 1/r dependence, which is in correspondence with our analytical estimate. Second, the threshold, beyond the 1/r dependence, does not depend too strongly on the noise levels for transporting qubits. Beyond these results, we find that it is important to look at more than one level of concatenation in order to estimate the threshold and that it may be beneficial in certain places, like in the transportation of qubits, to do error correction only infrequently.

REVTeX, 44 pages, 19 figures, to appear in Physical Review A

References in corpus (12)

• Mixed State Entanglement and Quantum Error Correction
• Quantum Computing with Very Noisy Devices
• Quantum repeaters based on entanglement purification
• Overhead and noise threshold of fault-tolerant quantum error correction
• Resilient Quantum Computation: Error Models and Thresholds
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Efficient fault-tolerant quantum computing
• Fault-Tolerant Quantum Computation with Local Gates
• Space, time, parallelism and noise requirements for reliable quantum computing
• Fault-Tolerant Postselected Quantum Computation: Threshold Analysis
• Threshold Estimate for Fault Tolerant Quantum Computation
• Improved ancilla preparation scheme increases fault-tolerant threshold

Cited by in corpus (54)

• Quantum Computing
• Quantum Computing with Very Noisy Devices
• Spin qubits in graphene quantum dots
• Quantum Optics with Surface Plasmons
• Distributed Quantum Computation Based-on Small Quantum Registers
• Strong coupling of single emitters to surface plasmons
• Low-distance Surface Codes under Realistic Quantum Noise
• Spin transport and quasi 2D architectures for donor-based quantum computing
• Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
• Spin dynamics in InAs-nanowire quantum-dots coupled to a transmission line
• Quantum dots and spin qubits in graphene
• Bounding quantum gate error rate based on reported average fidelity
• Quantum computers based on electron spins controlled by ultra-fast, off-resonant, single optical pulses
• Scaling the neutral atom Rydberg gate quantum computer by collective encoding in Holmium atoms
• Fault tolerant architectures for superconducting qubits
• Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays
• Efficient multiqubit entanglement via a spin-bus
• Noise thresholds for optical cluster-state quantum computation
• Neural network decoder for topological color codes with circuit level noise
• Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
• Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication
• Scalable quantum information processing with atomic ensembles and flying photons
• Quantum Computation under Micromotion in a Planar Ion Crystal
• Using hybrid topological-spin qubit systems for two-qubit-spin gates
• Long-Distance Entanglement of Spin Qubits via Quantum Hall Edge States
• Error-detection-based quantum fault tolerance against discrete Pauli noise
• An $\Theta (\sqrt{n})$-depth Quantum Adder on a 2D NTC Quantum Computer Architecture
• What is a quantum computer, and how do we build one?
• Electron Spin Relaxation in Graphene Nanoribbon Quantum Dots
• Spintronics with graphene quantum dots
• Long-distance quantum communication over noisy networks without long-time quantum memory
• Information Complexity of Quantum Gates
• High Fidelity Quantum Gates for Trapped Ions under Micromotion
• On the Effect of Quantum Interaction Distance on Quantum Addition Circuits
• Hierarchical memories: Simulating quantum LDPC codes with local gates
• Towards Large-Scale Quantum Computation
• On the Use of Shor States for the [7,1,3] Quantum Error Correcting Code
• Non-Fault Tolerant T-Gates for the [7,1,3] Quantum Error Correction Code
• Mediated gates between spin qubits
• An introduction to one-way quantum computing in distributed architectures
• Quantum Error Correction Implementation after Multiple Gates
• Quantum Error Correction During 50 Gates
• Scalable Quantum Networks based on Few-Qubit Registers
• Quantum information processing in a spin-bus system of coupled chains
• Quantum error correction benchmarks for continuous weak parity measurements
• Coherent transfer of singlet-triplet qubit states in an architecture of triple quantum dots
• Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors
• Difficulties in the Implementation of Quantum Computers
• Postselection threshold against biased noise
• Error Channels and the Threshold for Fault-tolerant Quantum Computation
• A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing
• Multiplexed bi-layered realization of fault-tolerant quantum computation over optically networked trapped-ion modules
• Work-sharing of qubits in topological error corrections
• Performance and Error Analysis of Knill's Postselection Scheme in a Two-Dimensional Architecture