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arXiv:2011.07977 · IEEE Transactions on Computers

Circuit-Based Quantum Random Access Memory for Classical Data With Continuous Amplitudes

Tiago M. L. Veras, Ismael C. S. Araújo, Daniel K. Park, Adenilton José da Silva

Published Nov 13, 2020• 40 citations
arXivHTMLPDF

Abstract

Loading data in a quantum device is required in several quantum computing applications. Without an efficient loading procedure, the cost to initialize the algorithms can dominate the overall computational cost. A circuit-based quantum random access memory named FF-QRAM can load$M$$n$-bit patterns with computational cost$O(CMn)$to load continuous data where$C$depends on the data distribution. In this article, we propose a strategy to load continuous data without post-selection with computational cost$O(Mn$). The proposed method is based on the probabilistic quantum memory, a strategy to load binary data in quantum devices, and the FF-QRAM using standard quantum gates, and is suitable for noisy intermediate-scale quantum computers.

DOI
10.1109/tc.2020.3037932

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Loading data in a quantum device is required in several quantum computing applications. Without an efficient loading procedure, the cost to initialize the algorithms can dominate the overall computational cost. A circuit-based quantum random access memory named FF-QRAM can loadM$$n-bit patterns with computational costO(CMn)O(CMn)O(CMn)to load continuous data whereCCCdepends on the data distribution. In this article, we propose a strategy to load continuous data without post-selection with computational costO(MnO(MnO(Mn). The proposed method is based on the probabilistic quantum memory, a strategy to load binary data in quantum devices, and the FF-QRAM using standard quantum gates, and is suitable for noisy intermediate-scale quantum computers.
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.
In order to use a quantum device to assess a classical dataset D, we need to representthe set D in a quantum state. Applying a quantum algorithm, that is a quantum state preparation algorithm, to convert classical data into quantum data would be the common method. Loading classical data into a quantum device is required in many current applications. Efficiently preparing a quantum state to be used as the initial state of a quantum algorithm is an essential step in developing efficient quantum algorithms, since many algorithms need to reload the initial state several times during their execution. The cost to initialize a quantum state can compromise the algorithm efficiency if the process of quantum states preparation is not efficient. The topic of quantum states preparation in quantum computing has been the focus of much attention. In this scope, preparing sparse quantum states is a more specific problem that remains open since many quantum algorithms also require sparse initialization. This dissertation presents the results of an investigation on sparse quantum states preparation with the development of three algorithms, with highlight to the preparation of sparse quantum states, the main contributionof this dissertation. From a classical input dataset with M patterns formed by pairs composed of a complex number and a binary pattern with n bits, this algorithm can prepare a quantum state with n qubits and continuous amplitudes. The cost of its steps is O(nM), classical cost of o(MlogM+nM)and requires a lower CNOT number than the main quantum state preparation algorithms currently known. The preparation of a quantumstate with 2 non-zero amplitudes reveals the need of fewer CNOT gates in n>>1 relation to the main known state preparation algorithms, with even more favorable results with s higher and less 1S in the binary string.
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 kkk without increasing the number of QRAM levels nnn. By exploiting the parallelism in the data query process, our protocol achieves a time complexity of O(n+k)O(n+k)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 2n2^n2n, 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) 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) represents a crucial component in the realization of practical quantum computers, enabling fast and probabilistic data access for quantum algorithms. However, accurately simulating QRAM's operation presents a formidable challenge due to the inherent randomness and quantum mechanical nature of the system. This work investigates and proposes novel simulation techniques and optimization algorithms aimed at mitigating this computational complexity. We explore various approaches, including stochastic simulation methods, reduced-order modeling, and tailored optimization strategies, focusing on minimizing the number of quantum operations required for accurate QRAM simulation. The results demonstrate significant reductions in computational cost while maintaining a reasonable level of fidelity, paving the way for more efficient design and analysis of QRAM architectures. The core claim of this research is that the development of QRAM is fundamentally limited by the complexity of its simulation, and this work offers a direct path toward overcoming this bottleneck.
Quantum Random Access Memory (QRAM) plays a pivotal role in accelerating quantum algorithms, especially in quantum machine learning. However, its implementation on noisy intermediate-scale quantum (NISQ) computers faces major challenges due to high qubit requirements and large circuit depth. These factors amplify quantum noise, limiting QRAM performance and scalability. In this work, we introduce a gate-pruning strategy that mitigates noise while preserving QRAM functionality. Our approach reduces circuit depth by eliminating small-angle rotation gates which are particularly noise-sensitive on NISQ hardware. This pruning significantly improves QRAM resilience without compromising data-loading efficiency or superposition-based querying. We further show that the pruned QRAM supports a variational quantum classifier capable of parallel training with logarithmic qubit scaling. Experiments on benchmark datasets confirm that our approach enhances noise resilience and classification accuracy, underscoring its potential for practical quantum machine learning in the NISQ era.