Pinnacle Architecture using QLDPC codes reduces physical qubits needed to factor RSA-2048 to under 100,000 at 10^{-3} error rate.
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Low-overhead fault-tolerant quantum computation by gauging logical operators
12 Pith papers cite this work, alongside 3 external citations. Polarity classification is still indexing.
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abstract
Quantum computation must be performed in a fault-tolerant manner to be realizable in practice. Recent progress has uncovered quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead. Existing schemes for fault-tolerant logical measurement do not always achieve low qubit overhead. Here we present a low-overhead method to implement fault-tolerant logical measurement in a quantum error-correcting code by treating the logical operator as a symmetry and gauging it. The gauging measurement procedure introduces a high degree of flexibility that can be leveraged to achieve a qubit overhead that is linear in the weight of the operator being measured up to a polylogarithmic factor. This flexibility also allows the procedure to be adapted to arbitrary quantum codes. Our results provide a new, more efficient, approach to performing fault-tolerant quantum computation, making it more tractable for near-term implementation.
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Z_N bivariate-bicycle codes have essential topological properties determined by their Z_p prime-factor counterparts, enabling generalization of algebraic-geometric methods to anyon fusion rules and resolution of quasifractonic behavior via symmetry-enriched topological order.
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
Tricycle codes generalize bicycle codes to three homological dimensions, enabling constant-depth CCZ circuits and single-shot magic state generation with circuit-level thresholds above 0.5% and low error rates at block lengths of 50-100 qubits.
A new code surgery protocol measures t logically disjoint Pauli products on any LDPC code using O(t ω (log t + log³ω)) ancillas in O(d) time while preserving LDPC property and fault distance.
Wire codes are a construction that converts any stabilizer code into a local weight-3 subsystem code on an arbitrary graph via low-density Tanner-graph embedding, with overhead governed by the embedding quality.
Gauging the spacetime code produces a lattice gauge theory inheriting circuit fault tolerance, with applications to foliated MBQC, classical memory in mixed topological states, and learnable Pauli noise degrees of freedom.
New structural conditions on affine permutation matrices yield ultra-high-rate quantum LDPC codes (rate >1/2) with near-teraquop logical error rates under circuit-level noise on reconfigurable atom arrays.
Gauging enables constant-depth logical XS dagger measurements for color-code magic state cultivation, achieving 10^{-12} logical error rates at 0.05% physical error for distance-7 codes while retaining over 1% of shots via post-selection.
A new scheme for fault-tolerant quantum computation on qLDPC codes achieves constant qubit overhead and time overhead O(d^{1+o(1)}) for good codes, faster than prior code surgery methods for a<2.
Two new heuristics reduce hardware-limited depth of commuting PPR groups by 10-20% on average (up to 50%) in QASMBench circuits compiled to PPRs.
GeneCS compiler reduces ancillary qubits and checks by over 85% on average for single- and cross-code logical operations on stabilizer codes while preserving error rates and scaling to over 10,000 qubits.
citing papers explorer
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The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes
Pinnacle Architecture using QLDPC codes reduces physical qubits needed to factor RSA-2048 to under 100,000 at 10^{-3} error rate.
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Symmetry-enriched topological order and quasifractonic behavior in $\mathbb{Z}_N$ stabilizer codes
Z_N bivariate-bicycle codes have essential topological properties determined by their Z_p prime-factor counterparts, enabling generalization of algebraic-geometric methods to anyon fusion rules and resolution of quasifractonic behavior via symmetry-enriched topological order.
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Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
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Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
Tricycle codes generalize bicycle codes to three homological dimensions, enabling constant-depth CCZ circuits and single-shot magic state generation with circuit-level thresholds above 0.5% and low error rates at block lengths of 50-100 qubits.
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Parallel Logical Measurements via Quantum Code Surgery
A new code surgery protocol measures t logically disjoint Pauli products on any LDPC code using O(t ω (log t + log³ω)) ancillas in O(d) time while preserving LDPC property and fault distance.
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Wire Codes
Wire codes are a construction that converts any stabilizer code into a local weight-3 subsystem code on an arbitrary graph via low-density Tanner-graph embedding, with overhead governed by the embedding quality.
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Gauging the Spacetime Code
Gauging the spacetime code produces a lattice gauge theory inheriting circuit fault tolerance, with applications to foliated MBQC, classical memory in mixed topological states, and learnable Pauli noise degrees of freedom.
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Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays
New structural conditions on affine permutation matrices yield ultra-high-rate quantum LDPC codes (rate >1/2) with near-teraquop logical error rates under circuit-level noise on reconfigurable atom arrays.
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Constant depth magic state cultivation with Clifford measurements by gauging
Gauging enables constant-depth logical XS dagger measurements for color-code magic state cultivation, achieving 10^{-12} logical error rates at 0.05% physical error for distance-7 codes while retaining over 1% of shots via post-selection.
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Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes
A new scheme for fault-tolerant quantum computation on qLDPC codes achieves constant qubit overhead and time overhead O(d^{1+o(1)}) for good codes, faster than prior code surgery methods for a<2.
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Optimizing Parallel Execution of Commuting Pauli Product Rotations
Two new heuristics reduce hardware-limited depth of commuting PPR groups by 10-20% on average (up to 50%) in QASMBench circuits compiled to PPRs.
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GeneCS: Synthesizing Resource-Efficient Code Surgery for Arbitrary Quantum Stabilizer Codes
GeneCS compiler reduces ancillary qubits and checks by over 85% on average for single- and cross-code logical operations on stabilizer codes while preserving error rates and scaling to over 10,000 qubits.