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arXiv:2012.08401 · Journal of Applied Physics

Quantum computing without quantum computers: Database search and data processing using classical wave superposition

Mykhaylo Balynsky, Howard Chiang, David Gutierrez, A. V. Kozhevnikov, Yuri Filimonov, Alexander G. Khitun

Published Oct 28, 2021• 17 citations
arXivHTMLPDF

Abstract

Quantum computers are proven to be more efficient at solving a specific class of problems compared to traditional digital computers. Superposition of states and quantum entanglement are the two key ingredients that make quantum computing so powerful. However, not all quantum algorithms require quantum entanglement (e.g., search through an unsorted database). Is it possible to utilize classical wave superposition to speed up database searching as much as by using quantum computers? There were several attempts to mimic quantum computers using classical waves. It was concluded that the use of classical wave superposition comes with the cost of an exponential increase in resources. In this work, we consider the feasibility of building classical wave-based devices able to provide fundamental speedup over digital counterparts without the exponential overhead. We present experimental data on database searching through a magnetic database using spin wave superposition. The results demonstrate the same speedup as expected for quantum computers. Also, we present examples of numerical modeling demonstrating classical wave interference for period finding. This approach may not compete with quantum computers with efficiency but outperform classical digital computers. We argue that classical wave-based devices can perform some of the quantum algorithms with the same efficiency as quantum computers as long as quantum entanglement is not required.

DOI
10.1063/5.0068316

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Quantum computers are proven to be more efficient at solving a specific class of problems compared to traditional digital computers. Superposition of states and quantum entanglement are the two key ingredients that make quantum computing so powerful. However, not all quantum algorithms require quantum entanglement (e.g., search through an unsorted database). Is it possible to utilize classical wave superposition to speed up database searching as much as by using quantum computers? There were several attempts to mimic quantum computers using classical waves. It was concluded that the use of classical wave superposition comes with the cost of an exponential increase in resources. In this work, we consider the feasibility of building classical wave-based devices able to provide fundamental speedup over digital counterparts without the exponential overhead. We present experimental data on database searching through a magnetic database using spin wave superposition. The results demonstrate the same speedup as expected for quantum computers. Also, we present examples of numerical modeling demonstrating classical wave interference for period finding. This approach may not compete with quantum computers with efficiency but outperform classical digital computers. We argue that classical wave-based devices can perform some of the quantum algorithms with the same efficiency as quantum computers as long as quantum entanglement is not required.
Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speedups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speedup over classical methods, but that do not require entanglement. These methods rely instead on interference to provide a speedup. Search without entanglement comes at a cost: although they outperform analogous classical devices, the quantum devices that perform the search are not universal quantum computers and require exponentially greater overhead than a quantum computer that operates using entanglement. Quantum search without entanglement is compared to classical search using waves.
Sorting is a fundamental computational process that facilitates subsequent searching of a database. It can be thought of as factorization of the search process. The location of a desired item in a sorted database can be found by classical queries that inspect one letter of the label at a time. For an unsorted database, no such classical quick search algorithm is available. If the database permits quantum queries, however, then mere digitization is sufficient for efficient search. Sorting becomes redundant with the quantum superposition of states. A quantum algorithm is written down that locates the desired item in an unsorted database a factor of two faster than the best classical algorithm can in a sorted database. This algorithm has close resemblance to the assembly process in DNA replication.
Efficient classical database operations are crucial for modern data processing and data management tasks. At the same time, quantum computing algorithms may offer a substantial speed-up for certain computational use cases. Quantum systems allow access to superposition and entanglement, enabling quantum parallelism and the use of interference. We define a quantum database state [8, 9] as an indexed superposition state as given, e.g., by the state returned by a quantum random access memory call (see [3, 4]). The database state is assumed to be located in the central quantum processing unit of a quantum computer. We investigate the feasibility of transferring general classical database operations to the quantum domain, with indices in superposition.
Quantum computing is a young but intriguing field of science. It combines quantum mechanics with information theory and computer science to potentially solve certain formerly computationally expensive tasks more efficiently. Classical computers are based on bits that can take on the value zero or one. The values are distinguished by voltage differences in transistors. Quantum computers are instead based on quantum bits, or qubits, that are represented physically by something that exhibits quantum properties, like for example electrons. Qubits also take on the value zero or one, which could correspond to spin up and spin down of an electron. However, qubits can also be in a superposition state between the quantum states corresponding to the value zero and one. This property is what causes quantum computers to be able to outperform classical computers at certain tasks. One of these tasks is searching through an unstructured database. Whereas a classical computer in the worst case has to search through the whole database in order to find the sought element, i.e. the computation time is proportional to the size of the problem, it can be shown that a quantum computer can find the solution in a time proportional to the square root of the size of the problem. This report aims to illustrate the advantages of quantum computing by explicitly solving the classical Windows game Minesweeper, which can be reduced to a problem resembling the unstructured database search problem. It is shown that solving Minesweeper with a quantum algorithm gives a quadratic speedup compared to solving it with a classical algorithm. The report also covers introductory material to quantum mechanics, quantum gates, the particular quantum algorithm Grover's algorithm and complexity classes, which is necessary to grasp in order to understand how Minesweeper can be solved on a quantum computer.
Quantum computing introduces an efficient way for unfolding complex problems on computing systems. It uses concept of superposition and entanglement, & hence supports intrinsic parallelism for obtaining the speedup in context of time over classical computing. Quantum algorithms can be efficiently implemented over quantum computing system. Most popular quantum algorithms like Grover's and Shor's provide a great foundation to specifically design the algorithms. These algorithms work on improving the lower runtime bounds of classical algorithms. Grover's algorithm exhibits a quadratic polynomial speedup while searching an element among `N' elements unstructured database. The algorithmic strategy can be applied over various computer science related applications and some important are being considered in this article i.e. pattern matching, data mining and machine learning. This article explores quantum fundamentals; history based evolution followed by Grover's search algorithm in detail with cascading advantages, limitations & applications and also finally concludes with the significance of quantum computing & quantum algorithmic domains.
Grover’s database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using coupled simple harmonic oscillators, which can be exactly solved in both classical and quantum domains. Classical wave algorithms are far more stable against decoherence compared to their quantum counterparts. In addition to providing convenient demonstration models, they may have a role in practical situations, such as catalysis.