Quantum Random Access Memory (QRAM) holds the promise of enabling several large scale applications of quantum computers. However, designing fault tolerant QRAMs for large scale applications is still an open problem due to the poor error and resource scaling of current architectures. Existing protocols often overlook the need for error correcting QRAMs, which will be required for data-intensive, fault-tolerant applications. However, naively error correcting all qubits used to implement the QRAM is prohibitively resource intensive, quickly becoming infeasible for large applications. To fill this gap, we propose a novel QRAM architecture that leverages variable strength error correction. We strongly error-correct qubits that heavily influence query fidelity, and lightly correct less critical regions of the QRAM. This scheme produces queries with fidelity bounded by a constant for arbitrarily sized QRAMs without requiring improvements in physical hardware. Furthermore, the heterogeneous scheme requires 5x fewer resources (for depth 30 QRAM) and quadratically slower error scaling as compared to a uniformly error corrected Bucket Brigade QRAM. In this work, we present a rigorous analysis of the query fidelity scaling and perform resource analyses of two variations of the heterogeneous architecture using the surface code. We verify our results using numerical simulations and compare our results against several other existing QRAM techniques. Through our results, we quantitatively prove the optimal scaling of the heterogeneous architecture, paving a way for data-intensive and fault tolerant quantum applications.
Quantum Random Access Memory (QRAM) holds the promise of enabling several large scale applications of quantum computers. However, designing fault tolerant QRAMs for large scale applications is still an open problem due to the poor error and resource scaling of current architectures. Existing protocols often overlook the need for error correcting QRAMs, which will be required for data-intensive, fault-tolerant applications. However, naively error correcting all qubits used to implement the QRAM is prohibitively resource intensive, quickly becoming infeasible for large applications. To fill this gap, we propose a novel QRAM architecture that leverages variable strength error correction. We strongly error-correct qubits that heavily influence query fidelity, and lightly correct less critical regions of the QRAM. This scheme produces queries with fidelity bounded by a constant for arbitrarily sized QRAMs without requiring improvements in physical hardware. Furthermore, the heterogeneous scheme requires 5x fewer resources (for depth 30 QRAM) and quadratically slower error scaling as compared to a uniformly error corrected Bucket Brigade QRAM. In this work, we present a rigorous analysis of the query fidelity scaling and perform resource analyses of two variations of the heterogeneous architecture using the surface code. We verify our results using numerical simulations and compare our results against several other existing QRAM techniques. Through our results, we quantitatively prove the optimal scaling of the heterogeneous architecture, paving a way for data-intensive and fault tolerant quantum applications.
Quantum random access memory (QRAM)—memory which stores classical data but allows queries to be performed in superposition—is required for the implementation of numerous quantum algorithms. While naive implementations of QRAM are highly susceptible to decoherence and hence not scalable, it has been argued that the bucket-brigade QRAM architecture [Giovannetti et al., Phys. Rev. Lett. 100, 160501 (2008)] is highly resilient to noise, with the infidelity of a query scaling only logarithmically with the memory size. In prior analyses, however, this favorable scaling followed directly from the use of contrived noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage. In this work, we study the effects of decoherence on QRAM in full generality. Our main result is a proof that this favorable infidelity scaling holds for arbitrary error channels (including, e.g., depolarizing noise and coherent errors). Our proof identifies the origin of this noise resilience as the limited entanglement among the memory’s components, and it also reveals that significant architectural simplifications can be made while preserving the noise resilience. We verify these results numerically using a novel classical algorithm for the efficient simulation of noisy QRAM circuits. Our findings indicate that QRAM can be implemented with existing hardware in realistically noisy devices, and that high-fidelity queries are possible without quantum error correction. Furthermore, we also prove that the benefits of the bucket-brigade architecture persist when quantum error correction is used, in which case the scheme offers improved hardware efficiency and resilience to logical errors.
Quantum random access memory (QRAM)-memory which stores classical data but allows queries to be performed in superposition-is required for the implementation of numerous quantum algorithms.While naive implementations of QRAM are highly susceptible to decoherence and hence not scalable, it has been argued that the bucket-brigade QRAM architecture [Giovannetti et al., Phys. Rev. Lett. 100, 160501 (2008)] is highly resilient to noise, with the infidelity of a query scaling only logarithmically with the memory size.In prior analyses, however, this favorable scaling followed directly from the use of contrived noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage.In this work, we study the effects of decoherence on QRAM in full generality.Our main result is a proof that this favorable infidelity scaling holds for arbitrary error channels (including, e.g., depolarizing noise and coherent errors).Our proof identifies the origin of this noise resilience as the limited entanglement among the memory's components, and it also reveals that significant architectural simplifications can be made while preserving the noise resilience.We verify these results numerically using a novel classical algorithm for the efficient simulation of noisy QRAM circuits.Our findings indicate that QRAM can be implemented with existing hardware in realistically noisy devices, and that high-fidelity queries are possible without quantum error correction.Furthermore, we also prove that the benefits of the bucket-brigade architecture persist when quantum error correction is used, in which case the scheme offers improved hardware efficiency and resilience to logical errors.
Quantum random access memory (qRAM) is valuable for applying quantum computers to a broad range of problems and for successfully implementing large-scale quantum computation systems. Despite its importance, its adoption may be restricted by the fact that the decomposition of the qRAM function contains non-transversal gates, which cannot be executed transversally on any quantum error correction (QEC) code. To overcome these limitations, existing works employ techniques like magic state distillation. However, distillation is time-and qubit-intensive. This paper presents a fault-tolerant, resource-efficient implementation of qRAM based on pieceable fault tolerance. By breaking the logical CSWAP and Toffoli gate into simpler, easier-to-execute but non-transversal components, we first show that bucket-brigade qRAM can be implemented in polynomial depth without the need for ancillary magic states, further gate decomposition, or other gates. Afterward, we demonstrate the resource efficiency of this method of attaining fault tolerance in quantum operations. Based on resource estimation results, fault-tolerant bucket brigades using the pieceable technique perform better than fault-tolerant bucket brigades using magic state distillation with respect to the number of physical qubits, time, and cost.
Quantum Random Access Memory (QRAM) is a critical component for loading classical data into quantum computers. While constructing a practical QRAM presents several challenges, including the impracticality of an infinitely large QRAM size and a fully error-correction implementation, it is essential to consider a practical case where the QRAM has a limited size. In this work, we focus on the access of larger data sizes without keeping on increasing the size of the QRAM. Firstly, we address the challenge of word length, as real-world datasets typically have larger word lengths than the single-bit data that most previous studies have focused on. We propose a novel protocol for loading data with larger word lengths k without increasing the number of QRAM levels n. By exploiting the parallelism in the data query process, our protocol achieves a time complexity of O(n+k) and improves error scaling performance compared to existing approaches. Secondly, we provide a data-loading method for general-sized data access tasks when the number of data items exceeds 2n, which outperforms the existing hybrid QRAM+QROM architecture. Our method contributes to the development of time and error-optimized data access protocols for QRAM devices, reducing the qubit count and error requirements for QRAM implementation, and making it easier to construct practical QRAM devices with a limited number of physical qubits.
Quantum random-access memory (QRAM) enables coherent queries to classical data. However, the O(N) qubits required for a memory with N=2n addresses make QRAM appear vulnerable to noise. Though bucket-brigade routing provides intrinsic noise resilience to reduce the error in QRAM, improving the fidelity of QRAM queries is still an important and challenging problem. We introduce a low-overhead protection framework for bucket-brigade QRAM with two complementary components. First, we propose a one-fault-tolerant repeat-until-success logical controlled-SWAP gate using the [[4,2,2]] code under erasure noise channel. Interleaved erasure checks and local recovery correct every single erasure, so the leading logical failure probability is second order in the physical erasure error rates. Second, we exploit validity constraints of bucket-brigade routing to define local parity checks directly on the router states, without adding extra data qubits to create code redundancy. Under bit-flip noise, minimum-weight perfect matching with noiseless syndrome measurements corrects single interior faults, while open spatial boundaries retain a first-order contribution in the residual bit-flip rate. Monte Carlo simulations confirm quadratic suppression for the protected controlled-SWAP and improved depth scaling for decoded QRAM router-state snapshots. The two codes admit a concatenated realization in which the inner code supplies erasure protection and the outer code optionally corrects interior logical bit flips. Together, these results show how routing constraints and a protected non-Clifford routing gate can improve QRAM reliability under biased and erasure-dominant noise.
Quantum random access memory (QRAM) is a critical primitive for quantum algorithms that require data lookup in superposition, but its lack of fault tolerance poses a major obstacle to practical deployment. Error filtration (EF) has been proposed as a hardware-efficient alternative to error correction, capable of suppressing incoherent noise without encoding overhead. However, its performance in realistic QRAM systems with moderate fidelity has remained unclear, as existing analyses rely on asymptotic approximations and numerical simulations have been limited to small sizes. We address this gap using a new simulator for bucket-brigade (BB) QRAM that combines sparse state encoding with a noise-aware pruning algorithm. This framework provides full quantum state access and scales efficiently, enabling us to probe EF performance in size and noise regimes far beyond previous studies. Our simulations reveal suppression anomalies at high noise levels or large address sizes, where post-selection probability fundamentally constrains EF scaling. Incorporating this effect, we refine EF theory into near-deterministic criteria linking base infidelity to achievable suppression, thereby delineating the regime in which EF yields progressive improvement. Beyond refining EF, we quantitatively characterize the runtime and memory costs of our noisy BB QRAM simulator, achieving simulations of systems with 20 layers using less than 1 GB of memory. This efficiency is what enables us to probe parameter regimes beyond previous work and to establish the simulator as a practical, ``fine-print'' analysis tool for assessing QRAM as a quantum resource.