One Qubit Can Beat One Bit: Quantum Advantage for Post-Training Quantization
Yuma Ichikawa, Moeto Mishima
quant-ph, cs.AI, cs.LG
Submitted: 2026-08-05
Comments: 40 pages, 6 figures
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: One-bit post-training quantization represents each weight using only its sign, requiring all deployment contexts to share the same binary weight matrix even when their activation statistics favor
Terminology
Abstract
One-bit post-training quantization represents each weight using only its sign, requiring all deployment contexts to share the same binary weight matrix even when their activation statistics favor different sign patterns. We study this shared-sign constraint and introduce Quantum Random Access Quantization (QRAQ). This framework encodes context-dependent signs in a quantum random-access code and retrieves them via context-matched Pauli measurements. Under an explicit fresh-copy logical readout model, QRAQ produces an unbiased, context-specific binary surrogate with a tractable shot-noise penalty. We prove a row-wise separation from shared-sign one-bit PTQ with signed per-row scales. When the optimal context-wise signs are incompatible, QRAQ achieves a strictly lower ideal reconstruction risk. We also derive finite-shot and calibrated-noise conditions under which this separation is retained. Fixed-readout quantum schemes are classically simulable, so the relevant resource in this model is measurement incompatibility rather than quantization alone. Finally, we characterize the role of scale granularity, provide finite-sample certificates, and evaluate the predicted ideal, finite-shot, noisy, and multi-context regimes in simulator experiments.
Sources
- Quantum Random Access Codes with Shared Randomness
- A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms
- The Llama 3 Herd of Models
- ARB-LLM: Alternating Refined Binarizations for Large Language Models
- Getting almost all the bits from a quantum random access code
- LoaQ: Layer-wise Output Approximation Quantization
- The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits
- LLaMA: Open and Efficient Foundation Language Models
- BitNet: Scaling 1-bit Transformers for Large Language Models
- Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization
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