On the robustness of bucket brigade quantum RAM

We study the robustness of the bucket brigade quantum random access memory model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100, 160501 (2008)]. Due to a result of Regev and Schiff [ICALP '08 pp. 773], we show that for a class of error models the error rate per gate in the bucket brigade quantum memory has to be of order $o(2^{-n/2})$ (where $N=2^n$ is the size of the memory) whenever the memory is used as an oracle for the quantum searching problem. We conjecture that this is the case for any realistic error model that will be encountered in practice, and that for algorithms with super-polynomially many oracle queries the error rate must be super-polynomially small, which further motivates the need for quantum error correction. By contrast, for algorithms such as matrix inversion [Phys. Rev. Lett. 103, 150502 (2009)] or quantum machine learning [Phys. Rev. Lett. 113, 130503 (2014)] that only require a polynomial number of queries, the error rate only needs to be polynomially small and quantum error correction may not be required. We introduce a circuit model for the quantum bucket brigade architecture and argue that quantum error correction for the circuit causes the quantum bucket brigade architecture to lose its primary advantage of a small number of "active" gates, since all components have to be actively error corrected.Comment: Replaced with the published version. 13 pages, 9 figure

Quantum Random Access Memory For Dummies

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.Comment: 12 pages, 10 figures, 4 tables, 65 citation

A Novel Efficient Quantum Random Access Memory

Owing to the significant progress in manufacturing desktop quantum computers, the quest to achieve efficient quantum random access memory (QRAM) became inevitable. In this paper, we propose a novel efficient random access memory for quantum computers. The proposed QRAM has a fixed structure and can be used efficiently to store both known and unknown classical/quantum data. The storage capacity of the proposed QRAM is more efficient than that of the classical RAMs and can be used to store both classical and quantum information. Furthermore, the proposed model can access an arbitrary location in O(1) compared with other state-of-the-art models

Fault tolerant resource estimation of quantum random-access memories

Quantum random-access look-up of a string of classical bits is a necessary ingredient in several important quantum algorithms. In some cases, the cost of such quantum random-access memory (qRAM) is the limiting factor in the implementation of the algorithm. In this paper we study the cost of fault-tolerantly implementing a qRAM. We construct generic families of circuits which function as a qRAM, and analyze their resource costs when embedded in a surface code.Comment: 17 pages, 12 figures. Code repository available in reference

Advances in quantum machine learning

Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms and experimental implementations in the discussion. The field's outlook is generally positive, showing significant promise. However, we believe there are appreciable hurdles to overcome before one can claim that it is a primary application of quantum computation.Comment: 38 pages, 17 Figure

Two-level Quantum Walkers on Directed Graphs II: An Application to qRAM

This is the second paper in a series of two. Using a multi-particle continuous-time quantum walk with two internal states, which has been formulated in the first paper (arXiv:2112.08119), we physically implement a quantum random access memory (qRAM). Data with address information are dual-rail encoded into quantum walkers. The walkers pass through perfect binary trees to access the designated memory cells and copy the data stored in the cells. A roundabout gate allocated at each node serves as a router to move the walker from the parent node to one of two child nodes, depending on the internal state of the walker. In this process, the address information is sequentially encoded into the internal states so that the walkers are adequately delivered to the target cells. The present qRAM, which processes $2^n$ $m$-qubit data, is implemented in a quantum circuit of depth $O(n\log(n+m))$ and requires $O(n+m)$ qubit resources. This is more efficient than the conventional bucket-brigade qRAM that requires $O(n^2+nm)$ steps and $O(2^{n}+m)$ qubit resources for processing. Moreover, since the walkers are not entangled with any device on the binary trees, the cost of maintaining coherence could be reduced. Notably, by simply passing quantum walkers through binary trees, data can be automatically extracted in a quantum superposition state. In other words, any time-dependent control is not required.Comment: 23 pages. This is the second paper in a series of two. The first paper is arXiv:2112.0811

Kvanttihajasaantimuisti

Tiivistelmä. Hajasaantimuisti (random access memory, RAM) on tärkeä osa klassisen tietokoneen toimintaa kaikkialla maailmassa. Hajasaantimuistia tullaan tarvitsemaan myös kvanttitietokoneissa, mutta jotta ennustettuja kvanttitietokoneiden mahdollistamia uskomattomia asioita voitaisi käytännössä tehdä, ei klassinen hajasaantimuisti ole riittävää. Klassisen hajasaantimuistin suora kvanttimekaaninen yleistys ei myöskään ole käytännöllinen, sillä muistiajon aikana O(2^n) laitteen reititinkomponenttia lomittuu maksimaalisesti, jossa n on muistin osoiterekisterin pituus, ja N = 2^n on muistipaikkojen määrä. Lomittuneiden komponenttien vähentämiseksi on ehdotettu niinkutsuttua bucket brigade arkkitehtuuria, joka laskee tätä määrää eksponentiaalisesti määrään O(n)

Quantum Data Center: Perspectives

A quantum version of data centers might be significant in the quantum era. In this paper, we introduce Quantum Data Center (QDC), a quantum version of existing classical data centers, with a specific emphasis on combining Quantum Random Access Memory (QRAM) and quantum networks. We argue that QDC will provide significant benefits to customers in terms of efficiency, security, and precision, and will be helpful for quantum computing, communication, and sensing. We investigate potential scientific and business opportunities along this novel research direction through hardware realization and possible specific applications. We show the possible impacts of QDCs in business and science, especially the machine learning and big data industries.Comment: 9 pages, many figures. This is a perspective papers introducing the ideas and impacts of quantum data centers in arXiv:2207.1433