Quantum computation from dynamic automorphism codes

Abstract

We propose a new model of quantum computation comprised of low-weight measurement sequences that simultaneously encode logical information, enable error correction, and apply logical gates. These measurement sequences constitute a new class of quantum error-correcting codes generalizing Floquet codes, which we call dynamic automorphism (DA) codes. We construct an explicit example, the DA color code, which is assembled from short measurement sequences that can realize all 72 automorphisms of the 2D color code. On a stack of $N$ triangular patches, the DA color code encodes $N$ logical qubits and can implement the full logical Clifford group by a sequence of two- and, more rarely, three-qubit Pauli measurements. We also make the first step towards universal quantum computation with DA codes by introducing a 3D DA color code and showing that a non-Clifford logical gate can be realized by adaptive two-qubit measurements.

76+17 pages, 29+7 figures; v2: fixed the instances of small codes in sec. VII; minor edits; v3: final version accepted in Quantum

References in corpus (59)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Topological quantum memory
• Measurement-based quantum computation with cluster states
• Measurement-based quantum computation
• Resource-efficient linear optical quantum computation
• Topological Quantum Distillation
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• A fault-tolerant one-way quantum computer
• Magic state distillation with low overhead
• Quantum Low-Density Parity-Check Codes
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Higher Gauging and Non-invertible Condensation Defects
• Topological Computation without Braiding
• Anyon condensation and its applications
• Dynamically Generated Logical Qubits
• Unfolding the color code
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Universal topological phase of 2D stabilizer codes
• Decoding color codes by projection onto surface codes
• Triangular color codes on trivalent graphs with flag qubits
• Topological color code and symmetry-protected topological phases
• A Fault-Tolerant Honeycomb Memory
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• A fault-tolerant non-Clifford gate for the surface code in two dimensions
• Universal fault-tolerant gates on concatenated stabilizer codes
• Structure of 2D Topological Stabilizer Codes
• Floquet codes without parent subsystem codes
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• Coherence in logical quantum channels
• Pauli stabilizer models of twisted quantum doubles
• Logical blocks for fault-tolerant topological quantum computation
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Boundaries for the Honeycomb Code
• Performance of planar Floquet codes with Majorana-based qubits
• Efficient Decoding of Topological Color Codes
• Constructions and Noise Threshold of Topological Subsystem Codes
• High-threshold quantum computing by fusing one-dimensional cluster states
• Universal fault-tolerant measurement-based quantum computation
• Pauli topological subsystem codes from Abelian anyon theories
• Benchmarking the Planar Honeycomb Code
• Unifying flavors of fault tolerance with the ZX calculus
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Quantum computing by color-code lattice surgery
• Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders
• Engineering 3D Floquet codes by rewinding
• Floquetifying the Colour Code
• 2D quantum computation with 3D topological codes
• Numerical and analytical bounds on threshold error rates for hypergraph-product codes
• Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code
• Opportunities and Challenges in Fault-Tolerant Quantum Computation
• Topological error correcting processes from fixed-point path integrals
• Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models
• Spacetime codes of Clifford circuits
• Floquet codes with a twist
• Quantum 2-Body Hamiltonian for Topological Color Codes
• Measurement Quantum Cellular Automata and Anomalies in Floquet Codes

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• Competing automorphisms and disordered Floquet codes
• Anomalies of global symmetries on the lattice
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• Multiqubit Rydberg Gates for Quantum Error Correction
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