Year: 2025
Type: article
Abstract: Quantum error correction is necessary to perform large-scale quantum computation but requires extremely large overheads in both space and time. High-rate quantum low-density-parity-check (qLDPC) codes promise a route to reduce qubit numbers, but performing computation while maintaining low space cost has required serialization of operations and extra time costs. In this work, we design fast and parallelizable logical gates for qLDPC codes and demonstrate their utility for key algorithmic subroutines such as the quantum adder. Our gate gadgets utilize transversal logical s between a data qLDPC code and a suitably constructed ancilla code to perform parallel Pauli product measurements (PPMs) on the data logical qubits. For hypergraph product codes, we show that the ancilla can be constructed by simply modifying the base classical codes of the data code, achieving parallel PPMs on a subgrid of the logical qubits with a lower space-time cost than existing schemes for an important class of circuits. Generalizations to 3D and 4D homological product codes further feature fast PPMs in constant depth. While prior work on qLDPC codes has focused on individual logical gates, we initiate the study of fault-tolerant compilation with our expanded set of native qLDPC code operations, constructing algorithmic primitives for preparing k -qubit Greenberger-Horne-Zeilinger states and distilling or teleporting k magic states with O ( 1 ) space overhead in O ( 1 ) and O ( k log k ) logical cycles, respectively. We further generalize this to key algorithmic subroutines, demonstrating the efficient implementation of quantum adders using parallel operations. Our constructions are naturally compatible with reconfigurable architectures such as neutral atom arrays, paving the way to large-scale quantum computation with low space and time overheads.
Source: Physical Review X
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,200
Funders: National Science Foundation, David and Lucile Packard Foundation, U.S. Department of Energy, Hertz Foundation, Defense Advanced Research Projects Agency, Samsung, Intelligence Advanced Research Projects Activity, Multidisciplinary University Research Initiative, Center for Ultracold Atoms, Massachusetts Institute of Technology, Air Force Office of Scientific Research, Army Research Office, Lawrence Berkeley National Laboratory, NTT Research
Awards: G1404049065, QuSeC-TAQS: Nanoscale Covariance Magnetometry with Diamond Quantum Sensors, G1932254719, G2882288540, G3162985271, G3719423973, G42916606, QuIC - TaQS: Interconnects for a Superconducting-Atomic Hybrid Quantum Network, G4848018484, Graduate Research Fellowship Program (GRFP), Collaborative Research: FET: Medium: Efficient Compilation for Dynamically Reconfigurable Atom Arrays, G586693022, Physics and Applications of Quantum Nanophotonics Systems, G6167497367, Center for Ultracold Atoms, NSF Engineering Research Center for Quantum Networks (CQN), G7796153478, Collaborative Research: FET: Medium: Design and Implementation of Quantum Databases, G8672390710, QII-TAQS: Quantum Metrological Platform for Single-Molecule Bio-Sensing
OpenAlex ID: W4410596037