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arXiv:2606.18835

Classical dissipative search of unstructured database

A. E. Allahverdyan, Y. Bisharyan

cond-mat.stat-mechcond-mat.dis-nnphysics.comp-phquant-phSubmitted Jun 17, 2026• Announced Jun 18, 2026• 0 citations
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Abstract

We propose a physical realization of the unstructured database search that works via classical, dissipative model of spherical spins. The database is implemented via spin-spin couplings, where the selected coupling refers to a larger ferromagnetic interaction between two selected spins. The low-temperature equilibrium of this model leads to magnetization strongly concentrated on the selected spins, which means that the search is complete. The search time refers to the relaxation time to equilibrium from a homogeneous initial state, and is described via Langevin equations. This time scales as ${\cal O}(M^a)$ with $a<1/2$, where $M$ is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.

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We propose a physical realization of the unstructured database search that works via classical, dissipative model of spherical spins. The database is implemented via spin-spin couplings, where the selected coupling refers to a larger ferromagnetic interaction between two selected spins. The low-temperature equilibrium of this model leads to magnetization strongly concentrated on the selected spins, which means that the search is complete. The search time refers to the relaxation time to equilibrium from a homogeneous initial state, and is described via Langevin equations. This time scales as O(Ma){\cal O}(M^a)O(Ma) with a<1/2a<1/2a<1/2, where MMM is the database volume. This is faster than Grover's search, showing how a dissipative, classical analog computer can overcome the quantum unitary computer.
The search of an unstructured database amounts to finding one element having a certain property out of NNN elements. The classical search with an oracle checking one element at a time requires on average N/2N/2N/2 steps. The Grover algorithm for the quantum search and its unitary Hamiltonian evolution analog accomplish the search asymptotically optimally in O(N)O(\sqrt{N})O(N​) time steps. We reformulate the search problem as a dissipative, incoherent Markov process acting on an NNN-level system weakly coupled to a thermal bath. Assuming that the energy levels of the system represent the database elements, we show that, with a proper choice of the spectrum and long-range but bounded transition rates between the energy levels, the system relaxes to the ground state, corresponding to the sought element, in time O(lnN)O(lnN)O(lnN).
In the classical model of a computer, the most fundamental building block, the bit, can only exist in one of two distinct states, a 0 or a 1. Computations are carried out by logic gates that act on these bits to produce other bits. Unless there is duplicate (parallel) hardware, only one problem instance (i.e. input data set) can be handled at a time. In this classical computing, increasing the number of bits increases the complexity of the problem and the time necessary to arrive at a solution. A quantum algorithm consists of a sequence of operations on a register, to transform it into a state which, when measured, yields the desired result with high probability. An n-bit quantum register can store an exponential amount of information. This paper aims at taking advantage of the superiority of quantum computing over classical computing to solve the problem of searching unstructured databases for a particular item or more than one item in good time. The general aim of this work is to establish the correctness and optimality of Grover’s quantum database search algorithm compared against classical database search methods in order to investigate the superiority or otherwise of quantum computing over classical computing. This is followed by a simulation of the algorithm using a classical computer, namely through functions that are present in MATLAB, referred to as “Quantum Computing Functions”. Povzetek: Clanek predstavlja implementacijo kvantnega iskanja v nestrukturiranih bazah.
Target item searching in large-scale, unstructured text databases is a major computational task for traditional systems and usually requires algorithms whose time complexity is on the order ofO(N)O(N)O(N). Quantum computing presents a strong competitor by using Grover's algorithm, where theoretically the search complexity comes down toO(N)O(\sqrt{N})O(N​), making faster retrieval possible. This research considers the design and assessment of Grover's algorithm as it is used to find a target word in a paragraph. The process entails encoding a group of unique words into a quantum register and implementing a circuit that incorporates a bespoke oracle and a diffusion operator to amplify the probability amplitude of the target state. Performance was evaluated in two situations: an ideal noise-free simulation with Qiskit's AerSimulator and a real-world run on IBM's quantum hardware. Simulation results demonstrated always-high accuracy in identifying the target word. But tests on real quantum machines indicated that the reliability of the algorithm decreases with an increase in qubits. Though circuits of up to five qubits had tolerable accuracy, larger configurations were plagued by noise, gate errors, and decoherence effects. These results highlight both the potential of quantum search algorithms for text processing and the limitations of NISQ today.
In my project I would have considered how the old search algorithms that are used when working with large unstructured data set end up taking linear time (O(N)) that in effect is the time that scales with the size of the data. These old ways get gradually sluggish, as everything gets bigger. Then I read about quantum computing, and especially Search Algorithm that was developed by Grover which is capable of quadratic speed-up with a complexity of O(sqrt(N)) of unstructured data. I created a hybrid system which fuses classical and quantum search applied on Flask as the web front end and Qiskit as the quantum one. This will enable me to compare the simple linear algorithm of searching through the list item-by-item with the quantum algorithm of Grover which uses superposition, a marking oracle to identify the desired item, and multiple amplitude amplification diffusion operators. The web page also accepts a student ID, and actually searches both simultaneously and allows me to tweak a depolarizing noise model so as to more closely mimic real quantum hardware. I measured such variables as the number of calls to the oracle, the number of qubits that I require, the quantum run time, and the number of measurements that I receive out of the quantum measurement. As the results indicate, the algorithm developed by Grover reduces the number of operations significantly compared to the classical one, and it must be emphasized that the algorithm remains quite effective even in the case of simulated noise. On the whole, it demonstrates that the classical and quantum components may be an efficient method to deal with the large search in the database.
In my project I would have considered how the old search algorithms that are used when working with large unstructured data set end up taking linear time (O(N)) that in effect is the time that scales with the size of the data. These old ways get gradually sluggish, as everything gets bigger. Then I read about quantum computing, and especially Search Algorithm that was developed by Grover which is capable of quadratic speed-up with a complexity of O(sqrt(N)) of unstructured data. I created a hybrid system which fuses classical and quantum search applied on Flask as the web front end and Qiskit as the quantum one. This will enable me to compare the simple linear algorithm of searching through the list item-by-item with the quantum algorithm of Grover which uses superposition, a marking oracle to identify the desired item, and multiple amplitude amplification diffusion operators. The web page also accepts a student ID, and actually searches both simultaneously and allows me to tweak a depolarizing noise model so as to more closely mimic real quantum hardware. I measured such variables as the number of calls to the oracle, the number of qubits that I require, the quantum run time, and the number of measurements that I receive out of the quantum measurement. As the results indicate, the algorithm developed by Grover reduces the number of operations significantly compared to the classical one, and it must be emphasized that the algorithm remains quite effective even in the case of simulated noise. On the whole, it demonstrates that the classical and quantum components may be an efficient method to deal with the large search in the database.