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Mehdi Ramezani

Publications and source records attributed to Mehdi Ramezani.

10 recordsLinked to original sources

Parallel Data Processing in Quantum Machine Learning

We propose a Quantum Machine Learning (QML) framework that applies the core design principle of quantum algorithms-superposition, oracle, and interference-to accelerate training. Building on the structural analogy between feature extraction in foundational quantum algorithms and parameter optimization in QML, we reformulate the training process to leverage quantum parallelism: all training samples are encoded into a quantum superposition, processed through a parameterized quantum circuit, and classified via an interferometer module that implements quantum interference across the dataset. This architectural reformulation reduces the theoretical complexity of loss function evaluation from $O(N^{2})$ in conventional QML training to $O(N)$, where $N$ is the dataset size. Numerical simulations on multiple binary and multi-class classification datasets (with up to $N=128$ samples) demonstrate that our method achieves classification accuracies comparable to conventional circuits while reducing the number of quantum circuit executions per cost function evaluation from $N$ to 1. This represents a near $N$-fold reduction in quantum overhead per training iteration, reducing the required circuit executions without loss of accuracy. These results highlight the potential of quantum algorithmic design principles as a scalable pathway to efficient QML implementations.

quant-ph

Learning Hamiltonians for $O(1)$ Oracle-Query Quantum State Preparation

We propose a Hamiltonian-based quantum state preparation method implemented via a shallow parametrized quantum circuit. The approach learns the parameters of a diagonal Hamiltonian through a classical training phase, while the quantum circuit itself performs only fixed-depth Hamiltonian evolution and mixing operations. With oracle access to the learned Hamiltonian parameters, $N$ classical data values can be encoded into $n=\log_2{N}$ qubits using $O(1)$ quantum queries, shifting the overall computational cost to an $O(N\log{N})$ classical preprocessing stage. For structured datasets generated by an underlying function, oracle access can be avoided by expressing the Hamiltonian in the Walsh basis and retaining only a polynomial number of significant terms. In this regime, quantum state preparation is achieved in $\text{poly}(n)$ time using $\text{poly}(n)$ parameters, reaching infidelities on the order of $10^{-5}$. By restricting the Hamiltonian to one-local and two-local terms, the method naturally yields hardware-efficient circuits suitable for near-term quantum devices.

quant-ph

Novel Market Temperature Definition Through Fluctuation Theorem: A Statistical Physics Framework for Financial Crisis Prediction

This paper introduces a novel approach to financial crisis prediction by establishing a thermodynamic-like framework derived from the fluctuation theorem of statistical physics. We define market temperature through the probability ratio of positive to negative returns and demonstrate its effectiveness in identifying market states and predicting potential crises. Our empirical analysis spans nine major global indices from 2005 to 2025, revealing statistically significant differences in temperature dynamics between crisis and non-crisis periods. Most notably, we discover a counterintuitive relationship between market temperature stability and crisis occurrence: crises tend to emerge more frequently during periods of apparent temperature stability rather than instability. This finding suggests that unusually stable periods in market temperature might signal the accumulation of systemic risks, similar to the calm before a storm in physical systems.

cond-mat.stat-mech

Reducing the Number of Qubits from $n^2$ to $n\log_{2} (n)$ to Solve the Traveling Salesman Problem with Quantum Computers: A Proposal for Demonstrating Quantum Supremacy in the NISQ Era

In our pursuit of quantum supremacy during the NISQ era, this research introduces a novel approach rooted in the Quantum Approximate Optimization Algorithm (QAOA) framework to address the Traveling Salesman Problem (TSP). By strategically reducing the requisite qubit count from $n^2$ to $n\log_{2} (n)$, our QAOA-based algorithm not only contributes to the ongoing discourse on qubit efficiency but also demonstrates improved performance based on established metrics, underscoring its potential for achieving NISQ-era supremacy in solving real-world optimization challenges.

quant-ph

Quantum Multiplication Algorithm Based on the Convolution Theorem

The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their theoretical limit and offer little room for further enhancement. However, with the advent of quantum computers and the need for quantum algorithms that can perform multiplication on quantum hardware, a new paradigm emerges. In this paper, inspired by convolution theorem and quantum amplitude amplification paradigm we propose a quantum algorithms for integer multiplication with time complexity $O(\sqrt{n}\log^2 n)$ which outperforms the best-known classical algorithm, the Harvey algorithm with time complexity of $O(n \log n)$. Unlike the Harvey algorithm, our algorithm does not have the restriction of being applicable solely to extremely large numbers, making it a versatile choice for a wide range of integer multiplication tasks. The paper also reviews the history and development of classical multiplication algorithms and motivates us to explore how quantum resources can provide new perspectives and possibilities for this fundamental problem.

quant-ph

Continuous quantum clock with high precision and long recurrence time

Continuous clocks, i.e. the clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the framework of quantum estimation theory various models for continuous quantum clocks are proposed, where all tools of quantum estimation theory are employed to seek the characteristics of clocks with high precision and long recurrence time. Then, in a resource-based approach, the performance of the proposed models is compared. It is shown that quantum clocks based on $n$ two-qubits system not only can have better precision than quantum clocks based on $2n$ one-qubit system but also support long recurrence time. Finally, it is shown that while employing the number of $n$ entangled qubits improves the precision of clocks by a factor of $1/\sqrt n $, it inevitably worsens the recurrence time of the clock.

quant-ph

Optimal exploitation of the resource in remote state preparation

Transmission efficiency (TE) of remote state preparation (RSP) with a shared quantum state and one bit of classical communication is considered. Following [B. Daki et al., Nat. Phys. 8, 666 (2012)], the encoding and decoding strategies of the protocol are restricted to the physically relevant classes of projective measurements and unitary operators, respectively. It is shown that contrary to the previous arguments, the quadratic fidelity as well as the linear fidelity could be a valid figure of merit to quantify the TE of RSP. Then, the TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario which includes the maximization over the encoding parameters as well as a meaningful maximization over the decoding parameters. The results show that in this scenario, the TE scales with the sum of the two largest eigenvalues of the squared correlation matrix of the resource state that is zero only for product states. This approach successfully quantifies the performance of the protocol in terms of the resource state parameters and provides a means to compare the usefulness of any two resource states for RSP.

quant-ph

Impact of nonideal cycles on the efficiency of quantum heat engines

Given a quantum heat engine that operates in a cycle that reaches maximal efficiency for a time-dependent Hamiltonian H(t) of the working substance, with overall controllable driving H(t) = g(t) H, we study the deviation of the efficiency from the optimal value due to a generic time-independent perturbation in the Hamiltonian. We show that for a working substance consisting of two two-level systems, by suitably tuning the interaction, the deviation can be suppressed up to the third order in the perturbation parameter-and thus almost retaining the optimality of the engine.

quant-ph

A Thermodynamical derivation of the quantum potential and the temperature of the wave function

In this paper a thermodynamical derivation of the quantum potential is pro- posed. Within the framework of Bohmian mechanics we show how the quantum potential can be derived, by adding an additional informational degree of freedom to the ordinary degrees of freedom of a physical system. Such a derivation uses the First Law of thermodynamics for this additional degree of freedom and basic equilibrium thermodynamics methods. By doing that, one may associate a temper- ature to each wave function. Features and behavior of this temperature in different situations is studied.

quant-ph

Fluctuation relation for heat exchange in Markovian open quantum systems

A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability of that the system absorbs an amount of heat from its bath, at a given time interval, divided by the probability of the reverse process (releasing the same amount of heat to the bath) is given by an exponential factor which depends on the amount of heat and the difference between the temperatures of the system and the bath. We also argue that the probability of the violation of the second law of thermodynamics (here in the form of net heat transfer from a cold system to its hot bath) drops exponentially with both the amount of heat and the temperature differences.

quant-ph