REVIEW 10 cited by
Fast and Parallelizable Logical Computation with Homological Product Codes
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Fast and Parallelizable Logical Computation with Homological Product Codes
read the original 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 CNOTs 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 GHZ states and distilling/teleporting $k$ magic states with $O(1)$ space overhead in $O(1)$ and $O(\sqrt{k} \log k)$ 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.
Forward citations
Cited by 10 Pith papers
-
In-Situ Simultaneous Magic State Injection on Arbitrary CSS qLDPC Codes
A new in-situ scheme prepares logical magic states inside arbitrary CSS qLDPC codes using only syndrome-extraction ancillas, with simulations on the [[144,12,12]] BB code and [[225,9,4]] hypergraph-product code showin...
-
Logical Spectroscopy: Lifted-Product Codes with Addressable Bases
Logical spectroscopy decomposes Abelian lifted-product codes into Frobenius packets, builds a complete addressable conjugate logical basis by finite-field algebra plus idempotent lifts, and supplies design diagnostics...
-
Fault-tolerant quantum computation with a neutral atom processor
A 256-atom neutral ytterbium processor demonstrates fault-tolerant entanglement of 24 logical qubits and runs Bernstein-Vazirani on 28 logical qubits with better-than-physical error rates using erasure conversion.
-
Towards Deploying Optimistic Quantum Fourier Transforms: An Architecture-Algorithm Co-Design Study
A hot-zone architecture for OQFT on reconfigurable neutral-atom hardware yields tunable latency via 2-4 zones, converging to roughly 500 extra logical ancillae and 128-qubit peak parallelism for half-time performance ...
-
CAbLECAR: efficiently scheduling QLDPC codes on a tileable spin qubit chip with shuttling
CAbLECAR provides a robotics-inspired shuttle scheduler that enables QLDPC codes on tileable spin-qubit hardware, yielding up to 86% faster schedules and orders-of-magnitude gains in encoding efficiency and logical er...
-
Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits
Shor's algorithm for cryptographically relevant problems becomes feasible on neutral-atom systems with as few as 10,000 reconfigurable physical qubits via high-rate quantum error correction.
-
Multivariate Multicycle Codes for Complete Single-Shot Decoding
Koszul complexes built from four polynomial generators over cyclic group rings yield CSS codes with both X and Z metachecks, giving small, high-confinement, single-shot-decodable quantum codes.
-
Native Non-Clifford Gates in Quantum LDPC Codes: Conditions, Synthesis, and Scaling Limits
The main theorem claiming constant-depth logical CCZ gates exist from many 'magic-friendly triples' has mutually inconsistent hypotheses, and its key local-implementation step is unproved.
-
Mind the gaps: The fraught road to quantum advantage
The authors identify four transitions needed to reach fault-tolerant application-scale quantum computing from current NISQ devices.
-
Mind the gaps: The fraught road to quantum advantage
The paper identifies four key hurdles in the transition from NISQ to FASQ quantum computers and argues that targeting them will accelerate progress toward useful quantum advantage.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.