Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits

Abstract

A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order the code distance, and thus braided, by a constant depth local unitary quantum circuit followed by a permutation of qubits. Our gates are protected in the sense that the length of error strings do not grow by more than a constant factor. When applied to the Fibonacci code, our results demonstrate that a universal logical gate set can be implemented on encoded qubits through a constant depth unitary quantum circuit, and without increasing the asymptotic scaling of the space overhead. These results also apply directly to braiding of topological defects in surface codes. Our results reformulate the notion of braiding in general as an effectively instantaneous process, rather than as an adiabatic, slow process.

arXiv comment5 pages, 4 figures; updated the discussions on fault tolerance and time overhead for decoding; added appendices

References in corpus (35)

• Fault-tolerant quantum computation by anyons
• Surface codes: Towards practical large-scale quantum computation
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• String-net condensation: A physical mechanism for topological phases
• Coupling Superconducting Qubits via a Cavity Bus
• Quantum Error Correction for Quantum Memories
• Entanglement renormalization
• Roads towards fault-tolerant universal quantum computation
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Experimental Comparison of Two Quantum Computing Architectures
• Restrictions on Transversal Encoded Quantum Gate Sets
• Deterministic Quantum State Transfer and Generation of Remote Entanglement using Microwave Photons
• Blueprint for a microwave trapped-ion quantum computer
• Complete methods set for scalable ion trap quantum information processing
• Deterministic teleportation of a quantum gate between two logical qubits
• Coherent Diabatic Ion Transport and Separation in a Multi-Zone Trap Array
• On-demand quantum state transfer and entanglement between remote microwave cavity memories
• Universal fault-tolerant quantum computation with only transversal gates and error correction
• Braid Topologies for Quantum Computation
• Deterministic remote entanglement of superconducting circuits through microwave two-photon transitions
• Classification of topologically protected gates for local stabilizer codes
• Random access quantum information processors
• Quantum computation with Turaev-Viro codes
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Exact entanglement renormalization for string-net models
• Two-dimensional cavity grid for scalable quantum computation with superconducting circuits
• Reliable transport through a microfabricated X-junction surface-electrode ion trap
• A Photonic Implementation for the Topological Cluster State Quantum Computer
• Protected gates for topological quantum field theories
• The disjointness of stabilizer codes and limitations on fault-tolerant logical gates
• Quantum Circuits for Measuring Levin-Wen Operators
• Fault-Tolerant Quantum Error Correction for non-Abelian Anyons
• Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological Order
• Topological Quantum Computation with Gapped Boundaries
• Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code

Cited by in corpus (9)

• Topological Order, Quantum Codes and Quantum Computation on Fractal Geometries
• Enhancing Detection of Topological Order by Local Error Correction
• Instantaneous braids and Dehn twists in topologically ordered states
• Quantum error correction with fractal topological codes
• 3-Fermion topological quantum computation
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Measurement-based infused circuits for variational quantum eigensolvers
• Non-Abelian Self-Correcting Quantum Memory and Transversal Non-Clifford Gate beyond the $n^{1/3}$ Distance Barrier
• Spin chains, defects, and quantum wires for the quantum-double edge