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arXiv:0807.4994 · Physical Review A

Architectures for a quantum random access memory

Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone

Published Nov 5, 2008• 305 citations
arXivHTMLPDF

Abstract

A random access memory, or RAM, is a device that, when interrogated, returns the content of a memory location in a memory array. A quantum RAM, or qRAM, allows one to access superpositions of memory sites, which may contain either quantum or classical information. RAMs and qRAMs with $n$-bit addresses can access ${2}^{n}$ memory sites. Any design for a RAM or qRAM then requires $O({2}^{n})$ two-bit logic gates. At first sight this requirement might seem to make large scale quantum versions of such devices impractical, due to the difficulty of constructing and operating coherent devices with large numbers of quantum logic gates. Here we analyze two different RAM architectures (the conventional fanout and the ``bucket brigade'') and propose some proof-of-principle implementations, which show that, in principle, only $O(n)$ two-qubit physical interactions need take place during each qRAM call. That is, although a qRAM needs $O({2}^{n})$ quantum logic gates, only $O(n)$ need to be activated during a memory call. The resulting decrease in resources could give rise to the construction of large qRAMs that could operate without the need for extensive quantum error correction.

DOI
10.1103/physreva.78.052310

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A random access memory, or RAM, is a device that, when interrogated, returns the content of a memory location in a memory array. A quantum RAM, or qRAM, allows one to access superpositions of memory sites, which may contain either quantum or classical information. RAMs and qRAMs with nnn-bit addresses can access 2n{2}^{n}2n memory sites. Any design for a RAM or qRAM then requires O(2n)O({2}^{n})O(2n) two-bit logic gates. At first sight this requirement might seem to make large scale quantum versions of such devices impractical, due to the difficulty of constructing and operating coherent devices with large numbers of quantum logic gates. Here we analyze two different RAM architectures (the conventional fanout and the ``bucket brigade'') and propose some proof-of-principle implementations, which show that, in principle, only O(n)O(n)O(n) two-qubit physical interactions need take place during each qRAM call. That is, although a qRAM needs O(2n)O({2}^{n})O(2n) quantum logic gates, only O(n)O(n)O(n) need to be activated during a memory call. The resulting decrease in resources could give rise to the construction of large qRAMs that could operate without the need for extensive quantum error correction.
A random access memory (RAM) uses n bits to randomly address N=2(n) distinct memory cells. A quantum random access memory (QRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.
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 a critical component for achieving quantum advantage in algorithms ranging from database search to quantum machine learning. In a recently introduced model [arXiv:2508.02855], we proposed a resource-efficient qRAM architecture based on discrete-time quantum walkers. This article serves as a comprehensive technical follow-up, providing the full mathematical derivations, detailed protocol specifications, and in-depth resource analysis. Moreover, we extend the original proposal with novel techniques for the purpose of making the qRAM implementation more realistic. Our model resolves the primary drawbacks of leading qRAM proposals: it avoids the exponential number of active nodes O(2n)\mathcal{O}(2^n)O(2n) required by the "Bucket Brigade" architecture by employing a number of quantum walkers that scales linearly with the address and message sizes, nnn and mmm, respectively. Simultaneously, it overcomes the spatial bottlenecks of previous quantum-walker schemes by eliminating the need for multiple parallel trees. We propose two algorithmic paradigms: the long- and the short-range approaches, which differ by the length of interaction of the main routing gates employed in the qRAM. We formalize the routing, message-copy, and walker retrieval phases for both variants and we show how, while the long-range scheme employs controlled gates having a multitude of target systems, the short-range approach decomposes these interactions into sequences of 2- and 3-body local gates, which improves the architecture's feasibility for near-term experimental implementation. Finally, our comprehensive resource analysis confirms that the short-range approach achieves the optimal O(n+m)\mathcal{O}(n+m)O(n+m) circuit depth. Within these two paradigms, we explore the potential of different types of quantum walkers, namely bosons, dual-rail qubits and four-level qudits.
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.
Abstract A novel concept of quantum random access memory (qRAM) employing a quantum walk is provided. Our qRAM relies on a bucket brigade scheme to access the memory cells. Introducing a bucket with chirality left and right as a quantum walker, and considering its quantum motion on a full binary tree, we can efficiently deliver the bucket to the designated memory cells, and fill the bucket with the desired information in the form of quantum superposition states. Our procedure has several advantages. First, we do not need to place any quantum devices at the nodes of the binary tree, and hence in our qRAM architecture, the cost to maintain the coherence can be significantly reduced. Second, our scheme is fully parallelized. Consequently, only O(n) steps are required to access and retrieve O(2 n ) data in the form of quantum superposition states. Finally, the simplicity of our procedure may allow the design of qRAM with simpler structures.
Quantum Random Access Memory (QRAM) has the potential to revolutionize the area of quantum computing. QRAM uses quantum computing principles to store and modify quantum or classical data efficiently, greatly accelerating a wide range of computer processes. Despite its importance, there is a lack of comprehensive surveys that cover the entire spectrum of QRAM architectures. We fill this gap by providing a comprehensive review of QRAM, emphasizing its significance and viability in existing noisy quantum computers. By drawing comparisons with conventional RAM for ease of understanding, this survey clarifies the fundamental ideas and actions of QRAM. QRAM provides an exponential time advantage compared to its classical counterpart by reading and writing all data at once, which is achieved owing to storage of data in a superposition of states. Overall, we compare six different QRAM technologies in terms of their structure and workings, circuit width and depth, unique qualities, practical implementation, and drawbacks. In general, with the exception of trainable machine learning-based QRAMs, we observe that QRAM has exponential depth/width requirements in terms of the number of qubits/qudits and that most QRAM implementations are practical for superconducting and trapped-ion qubit systems.