Low overhead quantum computation using lattice surgery

Abstract

When calculating the overhead of a quantum algorithm made fault-tolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7\times 10^5$ physical qubits capable of executing gates with error $p\sim 10^{-3}$. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery.

arXiv comment15 pages, 26 figures, download source for algorithm overhead calculation spreadsheet and SketchUp 3D model of two-level state distillation. V2: Source actually contains spreadsheet and no unnecessary files. Spreadsheet and model in anc/ directory in source. V3: minor bug fixed in spreadsheet, runtimes now slightly longer. V4: minor bug fixed in logical Hadamard

Cited by in corpus (25)

• Quantum computational chemistry
• Building a fault-tolerant quantum computer using concatenated cat codes
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Magic State Distillation: Not as Costly as You Think
• Focus beyond quadratic speedups for error-corrected quantum advantage
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Universal quantum computing with twist-free and temporally encoded lattice surgery
• The ZX calculus is a language for surface code lattice surgery
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer
• A scalable and fast artificial neural network syndrome decoder for surface codes
• Towards Quantum Advantage in Financial Market Risk using Quantum Gradient Algorithms
• Techniques for combining fast local decoders with global decoders under circuit-level noise
• Pseudo-2D superconducting quantum computing circuit for the surface code: the proposal and preliminary tests
• Inplace Access to the Surface Code Y Basis
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Realistic Cost to Execute Practical Quantum Circuits using Direct Clifford+T Lattice Surgery Compilation
• Decoding Merged Color-Surface Codes and Finding Fault-Tolerant Clifford Circuits Using Solvers for Satisfiability Modulo Theories
• Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays
• Synchronization for Fault-Tolerant Quantum Computers
• Measurement sequences for magic state distillation
• Quantum resource estimates for computing binary elliptic curve discrete logarithms
• Distributed-HISQ: A Distributed Quantum Control Architecture
• Averting multi-qubit burst errors in surface code magic state factories
• Managing Classical Processing Requirements for Quantum Error Correction