Quantum Measurements and Gates by Code Deformation

Abstract

The usual scenario in fault tolerant quantum computation involves certain amount of qubits encoded in each code block, transversal operations between them and destructive measurements of ancillary code blocks. We introduce a new approach in which a single code layer is used for the entire computation, in particular a surface code. Qubits can be created, manipulated and non-destructively measured by code deformations that amount to `cut and paste' operations in the surface. All the interactions between qubits remain purely local in a two-dimensional setting.

Revtex4, 6 figures

References in corpus (4)

• Topological Quantum Distillation
• Topological fault-tolerance in cluster state quantum computation
• Topological Computation without Braiding
• Homological Error Correction: Classical and Quantum Codes

Cited by in corpus (84)

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• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Magic state distillation with low overhead
• The XZZX Surface Code
• Fast Decoders for Topological Quantum Codes
• Quantum memories at finite temperature
• A Neural Decoder for Topological Codes
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Single-shot fault-tolerant quantum error correction
• Optimizing Quantum Error Correction Codes with Reinforcement Learning
• Unfolding the color code
• Digital simulation of non-Abelian anyons with 68 programmable superconducting qubits
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Topological Subsystem Codes
• Encoding a magic state with beyond break-even fidelity
• Fault-tolerant logical gates in quantum error-correcting codes
• The surface code with a twist
• A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost
• Fault tolerant architectures for superconducting qubits
• The ZX calculus is a language for surface code lattice surgery
• From Majorana Fermions to Topological Order
• Comparing neural network based decoders for the surface code
• Clifford Gates by Code Deformation
• Universal fault-tolerant gates on concatenated stabilizer codes
• Structure of 2D Topological Stabilizer Codes
• Floquet codes without parent subsystem codes
• Anyon condensation and the color code
• Logical blocks for fault-tolerant topological quantum computation
• 2-D color code quantum computation
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Code Deformation and Lattice Surgery Are Gauge Fixing
• Subsystem codes with spatially local generators
• Simulation of rare events in quantum error correction
• Efficient Decoding of Topological Color Codes
• Transversal Clifford gates on folded surface codes
• Universal fault-tolerant measurement-based quantum computation
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• Fault-Tolerant Quantum Gates with Defects in Topological Stabiliser Codes
• Fault-tolerant interface between quantum memories and quantum processors
• Fault-tolerant gates on hypergraph product codes
• Surface Code Error Correction on a Defective Lattice
• Fault-tolerant Quantum Error Correction on Near-term Quantum Processors using Flag and Bridge Qubits
• Demonstrating non-Abelian statistics of Majorana fermions using twist defects
• Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group
• Generalized Cluster States Based on Finite Groups
• Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
• Rewiring Stabilizer Codes
• Generalized Toric Codes Coupled to Thermal Baths
• Computing data for Levin-Wen with defects
• Adiabatic topological quantum computing
• Fault-tolerant Post-Selection for Low Overhead Magic State Preparation
• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case
• Fault-tolerant Holonomic Quantum Computation in Surface Codes
• Error rates and resource overheads of encoded three-qubit gates
• Domain walls in topological phases and the Brauer-Picard ring for $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$
• Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes
• Generalized Color Codes Supporting Non-Abelian Anyons
• 3-Fermion topological quantum computation
• Non-Abelian statistics with mixed-boundary punctures on the toric code
• Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences
• Universal resource-efficient topological measurement-based quantum computation via color-code-based cluster states
• Low-overhead quantum computing with the color code
• Realizing Lattice Surgery on Two Distance-Three Repetition Codes with Superconducting Qubits
• Computing Defects Associated to Bounded Domain Wall Structures: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ Case
• Hexagonal matching codes with 2-body measurements
• Constant Depth Code Deformations in the Parity Architecture
• State injection, lattice surgery and dense packing of the deformation-based surface code
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Introduction to Quantum Error Correction with Stabilizer Codes
• Low-density parity-check representation of fault-tolerant quantum circuits
• 1D Error Correcting Code for Majorana Qubits
• Color codes with twists: construction and universal gate set implementation
• Magic Boundaries of 3D Color Codes
• Layer-by-layer disentangling two-dimensional topological quantum codes
• Preparing topologically ordered states by Hamiltonian interpolation
• Universal fault tolerant quantum computation in 2D without getting tied in knots
• Dense packing of the surface code: code deformation procedures and hook-error-avoiding gate scheduling
• Color code with a logical control-$S$ gate using transversal $T$ rotations