Code Deformation and Lattice Surgery Are Gauge Fixing
arXiv:1810.10037 · doi:10.1088/1367-2630/ab0199
Abstract
The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate sets in subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations. We demonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel.
arXiv comment37 pages, 21 figures
References in corpus (18)
- Fault-tolerant quantum computation by anyons
- Surface codes: Towards practical large-scale quantum computation
- Topological quantum memory
- State preservation by repetitive error detection in a superconducting quantum circuit
- Fault-tolerant quantum computation with high threshold in two dimensions
- Surface code quantum computing by lattice surgery
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Topological Order with a Twist: Ising Anyons from an Abelian Model
- Quantum computing with nearest neighbor interactions and error rates over 1%
- Stabilizer Formalism for Operator Quantum Error Correction
- Detecting bit-flip errors in a logical qubit using stabilizer measurements
- Universal fault-tolerant quantum computation with only transversal gates and error correction
- Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
- Poking holes and cutting corners to achieve Clifford gates with the surface code
- Quantum Measurements and Gates by Code Deformation
- Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes
- Fault-tolerant interface between quantum memories and quantum processors
- Rewiring Stabilizer Codes
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- TISCC: A Surface Code Compiler and Resource Estimator for Trapped-Ion Processors
- XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
- Time-Efficient Logical Operations on Quantum Low-Density Parity Check Codes
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- Parallel Logical Measurements via Quantum Code Surgery
- iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
- Lattice Surgery for Dummies
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- Fault Tolerant Quantum Simulation via Symplectic Transvections