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arxiv: 2510.07195 · v2 · pith:NUP4QOQSnew · submitted 2025-10-08 · 🪐 quant-ph · cs.LG

Accelerating Inference for Multilayer Neural Networks with Quantum Computers

Arthur G. Rattew , Po-Wei Huang , Naixu Guo , Lirand\"e Pira , Patrick Rebentrost This is my paper

Pith reviewed 2026-05-21 20:54 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords quantum machine learningneural network inferenceresidual networksquantum algorithmsfault-tolerant quantum computingquantum random access memory
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The pith

With quantum access to inputs and weights, multilayer neural networks achieve polylogarithmic inference cost.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs explicit quantum circuits that implement full multilayer networks modeled on ResNet, including 2D convolutions, sigmoid activations, skip connections, and layer normalizations, all while preserving coherence. It measures inference cost in three access regimes: no special assumptions yield only quadratic speedup for shallow bilinear networks; efficient quantum access to weights alone produces quartic speedup; and efficient quantum access to both inputs and weights reduces the cost for an N-dimensional input, k residual blocks, and final pooling layer to O(polylog(N/ε)^k) operations at error ε. A sympathetic reader cares because this supplies a concrete route for future fault-tolerant quantum processors to accelerate deep-learning workloads without forcing architectural redesign.

Core claim

A network with an N-dimensional vectorized input, k residual block layers, and a final residual-linear-pooling layer can be implemented with an error of ε with O(polylog(N/ε)^k) inference cost when efficient quantum access to both the inputs and the network weights is available.

What carries the argument

Coherent quantum circuits for residual blocks that embed multi-filter 2D convolutions, sigmoid activations, skip connections, and layer normalizations, realized via quantum oracles for data and weight access.

Load-bearing premise

Efficient quantum oracles or quantum random access memory must exist that supply coherent, low-overhead access to the input data and all network weights.

What would settle it

A controlled simulation or small-scale quantum run that measures whether the total gate count for a fixed-depth ResNet-style network grows as polylog(N) rather than any polynomial in N when the input dimension N is increased while keeping error below a fixed ε.

Figures

Figures reproduced from arXiv: 2510.07195 by Arthur G. Rattew, Lirand\"e Pira, Naixu Guo, Patrick Rebentrost, Po-Wei Huang.

Figure 1
Figure 1. Figure 1: Architecture for Convolutional Neural Networks. This figure shows the architectures we consider with provable quantum complexity guarantees for inference under three regimes of quantum data access assumptions. (a) Depicts the architecture where both the inputs and network weights are provided in an efficient quantum data structure. (b) Only the network weights are provided in an efficient quantum data stru… view at source ↗
Figure 2
Figure 2. Figure 2: Generic Residual Architectural Block. This diagram illustrates the structure of a typical residual block used in deep neural networks. The input vector x is transformed through a sequence of operations: a learnable linear transformation W, a non-linear activation function f, and a residual (skip) connection that adds the original input to the transformed signal. The output is then passed through a normaliz… view at source ↗
Figure 3
Figure 3. Figure 3: Circuit for addition of VE encoded vectors. Given two unitary matrices, Uψ which is a (α, a, ϵ0)-VE for the n-qubit state |ψ⟩, and Uϕ which is a (β, b, ϵ1)-VE for the n-qubit state |ϕ⟩, define c := max(a, b). We define U˜ ψ by appropriately tensoring Uψ with Ic−a and we define U˜ ϕ by appropriately tensoring Uϕ with Ic−b, such that U˜ ψ and U˜ ϕ both act on n + c qubits. Then, the given circuit yields a VE… view at source ↗
Figure 4
Figure 4. Figure 4: Full-rank linear-pooling output block [PITH_FULL_IMAGE:figures/full_fig_p037_4.png] view at source ↗
read the original abstract

Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging this gap by presenting the first fully-coherent quantum implementation of a multilayer neural network with non-linear activation functions. Our constructions mirror widely used deep learning architectures based on ResNet, and consist of residual blocks with multi-filter 2D convolutions, sigmoid activations, skip-connections, and layer normalizations. We analyse the complexity of inference for networks under three quantum data access regimes. Without any assumptions, we establish a quadratic speedup over classical methods for shallow bilinear-style networks. With efficient quantum access to the weights, we obtain a quartic speedup over classical methods. With efficient quantum access to both the inputs and the network weights, we prove that a network with an $N$-dimensional vectorized input, $k$ residual block layers, and a final residual-linear-pooling layer can be implemented with an error of $\epsilon$ with $O(\text{polylog}(N/\epsilon)^k)$ inference cost.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents the first fully-coherent quantum implementation of multilayer neural networks modeled on ResNet architectures, consisting of residual blocks with multi-filter 2D convolutions, sigmoid activations, skip connections, and layer normalizations. It analyzes inference complexity under three quantum data-access regimes: no assumptions (quadratic speedup for shallow bilinear networks), efficient quantum access to weights only (quartic speedup), and efficient quantum access to both inputs and weights (O(polylog(N/ε)^k) cost for an N-dimensional input, k residual-block layers, and a final residual-linear-pooling layer with error ε).

Significance. If the constructions and complexity bounds hold, the work would constitute a concrete advance in quantum machine learning by showing how non-linear activations and residual connections can be realized coherently, with explicit scaling that improves from quadratic to polylogarithmic under progressively stronger access models. The regime-based analysis is useful for clarifying the oracle requirements needed for quantum advantage in deep-network inference.

major comments (2)
  1. [§5] §5 (polylog regime): the O(polylog(N/ε)^k) bound is derived under the assumption of efficient coherent quantum oracles/QRAM for both inputs and all network weights, yet the manuscript provides no explicit query-complexity analysis or circuit construction showing how these oracles are realized while preserving superposition and coherence through the k layers, convolutions, sigmoid activations, and layer norms. Any super-logarithmic overhead in oracle implementation would invalidate the claimed scaling.
  2. [§4 and §5] §4 (quartic regime) and §5: the transition from the no-assumption quadratic regime to the weight-access quartic and then to the joint-access polylog regimes is load-bearing for the central claim, but the paper does not quantify the concrete gate or query overhead of implementing the residual blocks and non-linear functions under each access model, nor does it include an error-propagation analysis across layers.
minor comments (2)
  1. [Abstract] The abstract states the three regimes and final bound but omits any reference to the specific sections or equations containing the derivations; adding such pointers would improve readability.
  2. [§2] Notation for the vectorized input dimension N and the number of layers k is introduced without an explicit table or diagram summarizing the network architecture parameters used in the complexity statements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for your thorough review and for recognizing the potential significance of our work on coherent quantum implementations of multilayer neural networks. We address each of the major comments in detail below and have made revisions to the manuscript to incorporate clarifications and additional analyses as suggested.

read point-by-point responses

  1. Referee: [§5] §5 (polylog regime): the O(polylog(N/ε)^k) bound is derived under the assumption of efficient coherent quantum oracles/QRAM for both inputs and all network weights, yet the manuscript provides no explicit query-complexity analysis or circuit construction showing how these oracles are realized while preserving superposition and coherence through the k layers, convolutions, sigmoid activations, and layer norms. Any super-logarithmic overhead in oracle implementation would invalidate the claimed scaling.

    Authors: We thank the referee for this observation. Our polylogarithmic bound is stated under the standard assumption of efficient coherent quantum oracles (QRAM-style) for inputs and weights, which by definition support O(polylog N) queries while preserving superposition. The network constructions (convolutions via quantum linear algebra techniques, sigmoid via coherent polynomial approximations, layer norms via quantum mean/variance estimation, and residual additions) are composed to interface directly with these oracles. To make the query complexity and coherence preservation explicit, we have added a dedicated subsection in §5 together with an appendix that tabulates the per-component oracle queries and shows that no super-logarithmic overhead is introduced beyond the factors already absorbed in the O(polylog(N/ε)^k) expression. revision: yes

  2. Referee: [§4 and §5] §4 (quartic regime) and §5: the transition from the no-assumption quadratic regime to the weight-access quartic and then to the joint-access polylog regimes is load-bearing for the central claim, but the paper does not quantify the concrete gate or query overhead of implementing the residual blocks and non-linear functions under each access model, nor does it include an error-propagation analysis across layers.

    Authors: We agree that explicit overhead quantification and error propagation strengthen the regime transitions. In the revised manuscript we have expanded §4 and §5 with (i) concrete gate-count estimates for each residual-block primitive (2-D convolution, sigmoid, layer norm, skip connection) under the three access models, and (ii) a new error-propagation subsection showing that choosing per-layer precision O(ε/k) keeps the total accumulated error ≤ ε while preserving the stated complexity scalings. These additions make the quartic-to-polylog transition fully rigorous. revision: yes

Circularity Check

0 steps flagged

No circularity; complexity bounds derived from standard quantum primitives under external access assumptions

full rationale

The paper derives quadratic, quartic, and polylog(N/ε)^k inference costs for ResNet-style networks by composing known quantum algorithms (block-encodings, quantum linear algebra for convolutions, and coherent implementations of sigmoid/layer-norm) under three explicitly stated regimes of quantum data access. The O(polylog(N/ε)^k) claim for k residual blocks follows directly from the assumed efficient oracles/QRAM without any reduction of a derived quantity to a fitted parameter, self-defined term, or unverified self-citation chain. All steps remain self-contained against external quantum query complexity benchmarks and do not invoke internal fits or renamings that would create circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard quantum computing assumptions about coherent operations and data access oracles rather than on new free parameters or invented entities.

axioms (2)
  • domain assumption Efficient quantum access to inputs and weights is possible via oracles or QRAM without destroying coherence
    Invoked to obtain the quartic and polylog speedups; stated in the abstract when describing the three regimes.
  • domain assumption Non-linear activations such as sigmoid can be implemented coherently on quantum states with controlled error
    Required for the multilayer construction to remain fully coherent.

pith-pipeline@v0.9.0 · 5745 in / 1550 out tokens · 36145 ms · 2026-05-21T20:54:41.666399+00:00 · methodology

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