Universal resource-efficient topological measurement-based quantum computation via color-code-based cluster states
arXiv:2106.07530 · doi:10.1103/PhysRevResearch.4.013010
Abstract
Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the fault-tolerant implementation of the logical Hadamard, phase (), and () gates which are essential for building up arbitrary logical gates has not been achieved to date without using state distillation, while the controlled-NOT (CNOT) gate does not require it, to best of our knowledge. State distillation generally consumes many ancillary logical qubits, thus it is a severe obstacle against practical quantum computing. To solve this problem, we suggest an MBQC scheme via a family of cluster states called color-code-based cluster states (CCCSs) based on the two-dimensional color codes instead of the surface codes. We define logical qubits, construct elementary logical gates, and describe error correction schemes. We show that all the logical Clifford gates including the CNOT, Hadamard, and phase gates can be implemented fault-tolerantly without state distillation, although the fault-tolerant gate still requires it. We further prove that the minimal number of physical qubits per logical qubit in a CCCS is at most approximately 1.8 times smaller than the case of an RTCS. We lastly show that the error threshold of MBQC via CCCSs for logical- errors is 2.7-2.8%, which is comparable to the value for RTCSs, assuming a simple error model where physical qubits have -measurement or errors independently with the same probability.
arXiv comment23 pages, 22 figures
References in corpus (57)
- Fault-tolerant quantum computation by anyons
- Mixed State Entanglement and Quantum Error Correction
- Surface codes: Towards practical large-scale quantum computation
- Good Quantum Error-Correcting Codes Exist
- Topological quantum memory
- Measurement-based quantum computation with cluster states
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Error Correction for Quantum Memories
- Multiple Particle Interference and Quantum Error Correction
- State preservation by repetitive error detection in a superconducting quantum circuit
- Universal Quantum Computation with Continuous-Variable Cluster States
- Fault-tolerant quantum computation with high threshold in two dimensions
- Topological Quantum Distillation
- Topological fault-tolerance in cluster state quantum computation
- Optical quantum computation using cluster states
- Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
- Surface code quantum computing by lattice surgery
- Experimental Quantum Error Correction
- Information and Computation: Classical and Quantum Aspects
- Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
- High threshold universal quantum computation on the surface code
- Experimental Quantum Computations on a Topologically Encoded Qubit
- A fault-tolerant one-way quantum computer
- Repeated Quantum Error Detection in a Surface Code
- From three-photon GHZ states to ballistic universal quantum computation
- Experimental demonstration of topological error correction
- Magic State Distillation: Not as Costly as You Think
- Topological Computation without Braiding
- Fault tolerant quantum computation with very high threshold for loss errors
- Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
- Universal transversal gates with color codes - a simplified approach
- Multilevel distillation of magic states for quantum computing
- Resource costs for fault-tolerant linear optical quantum computing
- Foliated Quantum Codes
- Quantum Measurements and Gates by Code Deformation
- Architectural design for a topological cluster state quantum computer
- Decoding color codes by projection onto surface codes
- Triangular color codes on trivalent graphs with flag qubits
- Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
- Noise thresholds for optical cluster-state quantum computation
- Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
- A Photonic Implementation for the Topological Cluster State Quantum Computer
- Fully fault tolerant quantum computation with non-deterministic gates
- 2-D color code quantum computation
- The boundaries and twist defects of the color code and their applications to topological quantum computation
- Three-dimensional color code thresholds via statistical-mechanical mapping
- Fault-Tolerant Topological One-Way Quantum Computation with Probabilistic Two-Qubit Gates
- Resource-efficient and fault-tolerant topological quantum computation with hybrid entanglement of light
- Mapping of Lattice Surgery-based Quantum Circuits on Surface Code Architectures
- Topological code Autotune
- Universal fault-tolerant measurement-based quantum computation
- Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions
- Practical Topological Cluster State Quantum Computing Requires Loss Below 1%
- Coherent State Topological Cluster State Production
- Highly photon loss tolerant quantum computing using hybrid qubits
- Lattice Surgery on the Raussendorf Lattice
- Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes