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Cambridge University Press eBooks

Loading classical data

Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, Fernando G. S. L. Brandão

Published Apr 24, 2025• 0 citations
Publisher

Abstract

This chapter covers quantum algorithmic primitives for loading classical data into a quantum algorithm. These primitives are important in many quantum algorithms, and they are especially essential for algorithms for big-data problems in the area of machine learning. We cover quantum random access memory (QRAM), an operation that allows a quantum algorithm to query a classical database in superposition. We carefully detail caveats and nuances that appear for realizing fast large-scale QRAM and what this means for algorithms that rely upon QRAM. We also cover primitives for preparing arbitrary quantum states given a list of the amplitudes stored in a classical database, and for performing a block-encoding of a matrix, given a list of its entries stored in a classical database.

DOI
10.1017/9781009639651.020

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This chapter covers quantum algorithmic primitives for loading classical data into a quantum algorithm. These primitives are important in many quantum algorithms, and they are especially essential for algorithms for big-data problems in the area of machine learning. We cover quantum random access memory (QRAM), an operation that allows a quantum algorithm to query a classical database in superposition. We carefully detail caveats and nuances that appear for realizing fast large-scale QRAM and what this means for algorithms that rely upon QRAM. We also cover primitives for preparing arbitrary quantum states given a list of the amplitudes stored in a classical database, and for performing a block-encoding of a matrix, given a list of its entries stored in a classical database.
Using quantum algorithms to carry out ML tasks is what is known as Quantum Machine Learning (QML) and the methods developed within this field have the potential to outperform their classical counterparts in solving certain learning problems. The development of the field is partly dependent on that of a functional quantum random access memory (QRAM), called for by some of the algorithms devised. Such a device would store data in a superposition and could then be queried when algorithms require it, similarly to its classical counterpart, allowing for efficient data access. Taking an axiomatic approach to QRAM, this thesis provides the main considerations, assumptions and results regarding QRAM and yields a QRAM handbook and comprehensive introduction to the literature pertaining to it.
A prerequisite for many quantum information processing tasks to truly surpass classical approaches is an efficient procedure to encode classical data in quantum superposition states. In this work, we present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way. For registering or updating classical data consisting of M entries, each represented by n bits, the method requires O(n) qubits and O(Mn) steps. With post-selection at an additional cost, our method can also store continuous data as probability amplitudes. As an example, we present a procedure to convert classical training data for a quantum supervised learning algorithm to a quantum state. Further improvements can be achieved by reducing the number of state preparation queries with the introduction of quantum forking.
Quantum random access memory (QRAM) is an essential ingredient for many quantum algorithms, such as quantum machine learning models. The quantum resources (qubit counts and circuit depths) required to load classical data into a circuit severely prohibit many reasonably sophisticated demonstrations in the near term. To this end, we propose a method to construct a compact QRAM circuit, leveraging classical preprocessing to design as shallow a circuit with as few auxiliary qubits as possible. The underlying idea is to map data-encoded quantum states into an orthogonal set of quantum states (characterized by a family of parametrized circuits); then one can straightforwardly entangle the data qubits with the address qubits using cnot gates to realize a data-loading QRAM circuit. The nonunitary transformation to convert the orthogonalized quantum states back to the original data-encoded quantum states can be easily achieved with the help of a small set of auxiliary qubits and postselections. Numerical simulations on handwritten digits and Iris data sets are performed to assess the effectiveness of the proposed method, and we also highlight how noise influences quantum circuit performance across diverse configurations using random data sets. The proposed method for constructing a QRAM circuit can potentially facilitate the development and testing of many quantum machine learning methods in the near term.
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.
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Quantum memory is proposed as an analogue to classical computer memory, like the random-access memory (RAM). RAM is a form of computer memory that can be read and changed in any order, typically used to store working data. In quantum machine learning domain, the usage of quantum random access memory (qRAM) is proposed to avoid input destruction problem. The method of qRAM is related to the entanglement of the index qubits that are in the superposition with the patterns. The method of qRAM is related to the entanglement of the index qubits that are in the superposition with the patterns. As in the method of the entanglement of the index qubits, the qubits of qRAM are entangled during the reading operation and have to be un-computed after computation.