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Approximate encoded permutations and piecewise quantum adders

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arxiv 1905.08488 v1 pith:I5RF2KPL submitted 2019-05-21 quant-ph

Craig Gidney This is my paper · ORCID
classification quant-ph
keywords approximateaddersadditioncircuitsencodedmodularcarryencodings
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We present a paradigm for constructing approximate quantum circuits from reversible classical circuits that operate on many possible encodings of an input and send almost all encodings of that input to an encoding of the correct output. We introduce oblivious carry runways, which use piecewise addition circuits to perform approximate encoded additions and reduce the asymptotic depth of addition to $O(\lg \lg n)$. We show that the coset representation of modular integers (Zalka 2006) is an approximate encoded modular addition, and that it can be used in combination with oblivious carry runways. We prove error bounds on these approximate representations, and use them to construct 2s-complement adders and modular adders with lower costs than in previous work at register sizes relevant in practice.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Classical-Quantum Adder with Constant Workspace and Linear Gates

    quant-ph 2025-07 accept novelty 8.0 of 10

    A classical-quantum adder achieves O(n) Toffoli gates with O(1) clean ancillae, closing a 20-year asymptotic gap.

  2. Towards Deploying Optimistic Quantum Fourier Transforms: An Architecture-Algorithm Co-Design Study

    quant-ph 2026-05 unverdicted novelty 6.0 of 10

    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 ...

  3. Quantum Arithmetic Circuits in Public-Key Cryptography

    quant-ph 2026-07 accept novelty 2.5 of 10

    A structured survey of optimized quantum adders, multipliers, modular exponentiation and point-addition circuits for public-key cryptanalysis, plus fault-tolerant resource estimation techniques.

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