Partitioning qubits in hypergraph product codes to implement logical gates
arXiv:2204.10812 · doi:10.22331/q-2023-10-24-1153
Abstract
The promise of high-rate low-density parity check (LDPC) codes to substantially reduce the overhead of fault-tolerant quantum computation depends on constructing efficient, fault-tolerant implementations of logical gates on such codes. Transversal gates are the simplest type of fault-tolerant gate, but the potential of transversal gates on LDPC codes has hitherto been largely neglected. We investigate the transversal gates that can be implemented in hypergraph product codes, a class of LDPC codes. Our analysis is aided by the construction of a symplectic canonical basis for the logical operators of hypergraph product codes, a result that may be of independent interest. We show that in these codes transversal gates can implement Hadamard (up to logical SWAP gates) and control-Z on all logical qubits. Moreover, we show that sequences of transversal operations, interleaved with error correction, allow implementation of entangling gates between arbitrary pairs of logical qubits in the same code block. We thereby demonstrate that transversal gates can be used as the basis for universal quantum computing on LDPC codes, when supplemented with state injection.
References in corpus (36)
- Fault-tolerant quantum computation by anyons
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Good Quantum Error-Correcting Codes Exist
- Quantum Teleportation is a Universal Computational Primitive
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Multiple Particle Interference and Quantum Error Correction
- How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
- Restrictions on Transversal Encoded Quantum Gate Sets
- Magic state distillation with low overhead
- Methodology for quantum logic gate constructions
- Quantum Low-Density Parity-Check Codes
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- Degenerate Quantum LDPC Codes With Good Finite Length Performance
- Magic State Distillation: Not as Costly as You Think
- Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
- Classification of topologically protected gates for local stabilizer codes
- Unfolding the color code
- Balanced Product Quantum Codes
- Fault-tolerant quantum computation with few qubits
- Quantum "hyperbicycle" low-density parity check codes with finite rate
- Low-overhead fault-tolerant quantum computing using long-range connectivity
- Fault-tolerant logical gates in quantum error-correcting codes
- Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
- Fiber Bundle Codes: Breaking the Barrier for Quantum LDPC Codes
- Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
- Universal fault-tolerant gates on concatenated stabilizer codes
- Very low overhead fault-tolerant magic state preparation using redundant ancilla encoding and flag qubits
- Single-shot error correction of three-dimensional homological product codes
- The disjointness of stabilizer codes and limitations on fault-tolerant logical gates
- Transversal Clifford gates on folded surface codes
- Improved quantum hypergraph-product LDPC codes
- Fault-tolerant gates on hypergraph product codes
- Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
- Topological wormholes
- A four-dimensional toric code with non-Clifford transversal gates
- Fault-tolerant gates via homological product codes
Cited by in corpus (25)
- Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation
- Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
- Entangling four logical qubits beyond break-even in a nonlocal code
- High-rate quantum LDPC codes for long-range-connected neutral atom registers
- LDPC-cat codes for low-overhead quantum computing in 2D
- Many-hypercube codes: High-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing
- Long-range-enhanced surface codes
- Transversal Diagonal Logical Operators for Stabiliser Codes
- Distance-preserving stabilizer measurements in hypergraph product codes
- CSS code surgery as a universal construction
- Homological Quantum Rotor Codes: Logical Qubits from Torsion
- Weight Reduced Stabilizer Codes with Lower Overhead
- Code conversion with the quantum Golay code for a universal transversal gate set
- Adaptive Syndrome Extraction
- Letting the tiger out of its cage: bosonic coding without concatenation
- Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries
- Single-shot preparation of hypergraph product codes via dimension jump
- On the energy barrier of hypergraph product codes
- Non-local resources for error correction in quantum LDPC codes
- Parallel Logical Measurements via Quantum Code Surgery
- Targeted Clifford logical gates for hypergraph product codes
- Efficient simulation of logical magic state preparation protocols
- Hierarchical Quantum Error Correction with Hypergraph Product Code and Rotated Surface Code
- Color code with a logical control- gate using transversal rotations
- Transversal architecture for megaquop-scale quantum simulation with neutral atoms