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arXiv:2610.02757

Design Automation for Gray-Code Quantum Read-Only Memory

Hao-Yu Lu, Yu-Ting Kao, Yeong-Jar Chang, Chao-Hung Wang, Darsen D. Lu

quant-phSubmitted Oct 2, 2026• Announced Oct 5, 2026• 0 citations
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Abstract

We propose a programmable quantum read-only memory based on Gray code encoding, termed GQROM, designed to efficiently load classical data into quantum circuits. This architecture mitigates critical bottlenecks in near-term quantum computing by reducing initialization overhead and gate-induced errors. By utilizing Gray code, in which consecutive addresses differ by only a single bit, GQROM minimizes state transition complexity. We demonstrate the architecture's flexibility in accessing targeted data through initial-state modification. The entire design, including a systematic EDA flow, was implemented and validated on the Qiskit platform, confirming its practical feasibility. These results underscore GQROM's potential as a scalable and hardware-friendly solution for efficient state preparation in quantum circuits.

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We propose a programmable quantum read-only memory based on Gray code encoding, termed GQROM, designed to efficiently load classical data into quantum circuits. This architecture mitigates critical bottlenecks in near-term quantum computing by reducing initialization overhead and gate-induced errors. By utilizing Gray code, in which consecutive addresses differ by only a single bit, GQROM minimizes state transition complexity. We demonstrate the architecture's flexibility in accessing targeted data through initial-state modification. The entire design, including a systematic EDA flow, was implemented and validated on the Qiskit platform, confirming its practical feasibility. These results underscore GQROM's potential as a scalable and hardware-friendly solution for efficient state preparation in quantum circuits.
We propose GQROM, a programmable quantum read-only memory based on Gray code, designed to efficiently load classical data into quantum circuits as initial states. We demonstrate that by utilizing Gray code, GQROM minimizes transition complexity and reduces the required gate count to about one-third of conventional implementations. The GQROM design was implemented and validated on the Qiskit platform over a wide range of qubit count, making it potentially a scalable and hardware-friendly solution for state preparation in quantum circuits.
Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum advantage. In quantum machine learning applications for example, a quantum memory can simplify the data loading process and potentially accelerate the learning task. Quantum memory can also store intermediate quantum state of qubits that can be reused for computation. However, the depth, gate count and compilation time of quantum memories such as, Quantum Read Only Memory (QROM) scale exponentially with the number of address lines making them impractical in state-of-the-art Noisy Intermediate-Scale Quantum (NISQ) computers beyond 4-bit addresses. In this paper, we propose techniques such as, pre-decoding logic and qubit reset to reduce the depth and gate count of QROM circuits to target wider address ranges such as, 8-bits. The proposed approach reduces the number of gates and depth count by at least 2X compared to the naive implementation at only 36% qubit overhead. A reduction in circuit depth and gate count as high as 75X and compilation time by 85X at the cost of a maximum of 2.28X qubit overhead is observed. Experimentally, the fidelity with the proposed pre-decoding circuit compared to existing optimization approach is also higher (as much as 73% compared to 40.8%) under reduced error rates.
Emerging quantum algorithms that process data require that classical input data be represented as a quantum state. These data-processing algorithms often follow the gate model of quantum computing-which requires qubits to be initialized to a basis state, typically| 0 〉-and thus often employ state generation circuits to transform the initialized basis state to a data-representation state. There are many ways to encode classical data in a qubit, and the oft-applied approach of basis encoding does not allow optimization to the extent that other variants do. In this work, we thus consider automatic synthesis of addressable, quantum read-only memory (QROM) circuits, which act as data-encoding state-generation circuits. We investi-gate three data encoding approaches, one of which we introduce to provide improved dynamic range and precision. We present experimental results that compare these encoding methods for QROM synthesis to better understand the implications of and applications for each.
Efficient encoding of classical data into quantum circuits is a critical challenge that directly impacts the scalability of quantum algorithms. In this work, we present an automated compilation framework for resource-aware quantum data loading tailored to a given input vector and target error tolerance. By explicitly exploiting the trade-off between exact and approximate state preparation, our approach systematically partitions the total error budget between precision and approximation errors, thereby minimizing quantum resource costs. The framework supports a comprehensive suite of state-of-the-art methods, including multiplexer-based loaders, quantum read-only memory (QROM) constructions, sparse encodings, matrix product states (MPS), Fourier series loaders (FSL), and Walsh transform-based diagonal operators. We demonstrate the effectiveness of our framework across several applications, where it consistently uncovers non-obvious, resource-efficient strategies enabled by controlled approximation. In particular, we analyze a computational fluid dynamics workflow where the automated selection of MPS state preparation and Walsh transform-based encoding, combined with a novel Walsh-based measurement technique, leads to resource reductions of over four orders of magnitude compared to previous approaches. We also introduce two independent advances developed through the framework: a more efficient circuit for d-diagonal matrices, and an optimized block encoding for kinetic energy operators. Our results underscore the indispensable role of automated, approximation-aware compilation in making large-scale quantum algorithms feasible on resource-constrained hardware.
The burgeoning field of machine learning (ML) is increasingly reliant on massive datasets for training complex models, particularly deep neural networks. However, the retrieval of data from conventional memory systems represents a significant bottleneck, limiting the scalability and efficiency of ML algorithms. This research proposes a Quantum Random Access Memory (QRAM) architecture designed to overcome this limitation by leveraging quantum mechanical principles. The core concept involves encoding data into qubits and utilizing quantum random access to achieve near-instantaneous data retrieval. This paper details a novel QRAM architecture, focusing on qubit arrangement, control mechanisms, and strategies for minimizing decoherence – a primary challenge in quantum computing. The theoretical framework explores the potential acceleration achievable through QRAM in deep neural network training, with the primary goal of dramatically reducing training times. We present a detailed mathematical model outlining the data encoding process, quantum access protocols, and the expected performance gains. The architecture incorporates error mitigation techniques and discusses the scalability of the design for increasingly complex datasets. The research highlights the transformative potential of QRAM in accelerating ML, addressing a fundamental constraint within the current landscape of computational learning.
The preparation of data in quantum states is a critical component in the design of quantum algorithms. The cost of this step can significantly limit the realization of quantum advantage in domains such as machine learning, finance, and chemistry. One of the main approaches to achieve efficient state preparation is through the use of Quantum Random Access Memory (QRAM), a theoretical device for coherent data access with several proposed hardware implementations. In this work, we present a framework that integrates the hardware model of the Bucket Brigade QRAM (BBQRAM) with the classical data structure of the Segment Tree to achieve efficient state preparation. We introduce a memory layout that embeds a segment tree within BBQRAM memory cells by preserving the segment tree's hierarchy and supporting data retrieval in logarithmic time via specialized access primitives. We demonstrate that our method encodes a matrix A∈RM×NA \in \mathbb{R}^{M \times N}A∈RM×N in a quantum register of Θ(log⁡2(MN))Θ(\log_2(MN))Θ(log2​(MN)) qubits in O(log⁡22(MN))\mathcal{O}(\log_2^2(MN))O(log22​(MN)) time, {requiring a constant number of working qubits (under fixed precision) and O(MN)\mathcal{O}(MN)O(MN) memory cells within the BBQRAM architecture.} We further illustrate the method through a numerical example. This framework provides theoretical support for quantum algorithms that assume negligible data loading overhead and establishes a foundation for designing classical-to-quantum encoding algorithms that are aware of the underlying hardware QRAM architecture.