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Ammar Daskin

Publications and source records attributed to Ammar Daskin.

At least 19 recordsLinked to original sources
arXiv2026

Certifying Quantum Optimization and Circuit Cutting by Using Quantum-Classical Moment Duality

We establish a direct quantum--classical duality based on the degree-$2$ Sum-of-Squares (SoS) semidefinite programming cone: the matrix of two-qubit Pauli-$Z$ correlation functions obtained from \textbf{any} quantum state $\rho$ is automatically a feasible point of the classical Goemans--Williamson (GW) relaxation. This observation provides a universal safety net for variational quantum optimization algorithms: applying GW random hyperplane rounding to the quantum-driven moment matrix yields a certified expected cut value bounded below by $\alpha_{\text{GW}} \langle \mathcal{H} \rangle_\rho$, which holds for every state generated by variational algorithms such as the Quantum Alternating Operator Ansatz (QAOA) or the Variational Quantum Power Method (VQPM), regardless of convergence quality. We further show that the same moment matrix reveals the tensor-product structure of the underlying unitary circuit, enabling a polynomial-time, correlation-based circuit cutting procedure with rigorous error bounds. The framework is validated numerically on Max-Cut instances for variational algorithms and on random states for circuit cutting, demonstrating that two-point correlation data are sufficient to locate near-optimal bipartitions while theoretical error bounds hold in practice.

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arXiv2026

Lowering LCU Circuit Width through Maximum-Weight Birkhoff-von Neumann Decomposition

While classical Sinkhorn scaling applies to nonnegative matrices, we show that any complex square matrix whose element-wise absolute value has total support can be mapped to a phased doubly stochastic matrix, or alternatively embedded into a larger doubly stochastic matrix via matrix completion. Standard Birkhoff-von~Neumann and Pauli decompositions represent such matrices as linear combinations of $O(N^2)$ permutation or Pauli terms, leading to a large ancilla overhead in a quantum Linear Combination of Unitaries (LCU) implementation. We prove that a bottleneck variant of Birkhoff's algorithm reduces the number of permutations to $O(N\log(N/\varepsilon))$, where $\varepsilon$ is the $\ell_1$-norm approximation error of the reconstructed matrix, and demonstrate empirically that a largest-weight greedy variant requires only $\approx 2N$ terms for dense matrices (the exact average observed is $\approx 2.4N$). The quadratic reduction in term count directly shrinks the ancilla register from $2\log_2 N$ to $\log_2 N$ qubits, shortens the SELECT circuit, and is especially valuable in fixed-Hadamard LCU architectures, where---under the standard uniform-coefficient assumption---the success probability scales as $1/K$; our convex decomposition achieves $\alpha=1$ exactly and therefore avoids this penalty. The approach enables compact quantum implementations of dense operators appearing in optimal transport, non-Hermitian simulation, and other settings amenable to Sinkhorn preconditioning. Furthermore, because the decomposition is a convex combination, the LCU normalization constant for the scaled matrix $S$ is exactly $\alpha_S = 1$, and the uniform superposition is an eigenvector of $S$ with eigenvalue~1. This structure can be exploited to achieve high success probability without amplitude amplification in many practical scenarios, including quantum walks and Markov chain simulations.

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arXiv2026

Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions

The linear combination of unitaries (LCU) is a fundamental quantum algorithm primitive that embeds non-unitary operators via post-selection on an ancilla register. In standard LCU, only the $|0\dots0\rangle$ ancilla outcome is retained; the remaining "junk" outcomes are discarded. We study these discarded parts by introducing an alternative LCU circuit which simplifies the coefficient preparation unitary with Hadamard gates and a single rotation qubit. Every computational basis measurement of the ancilla projects the system onto a different linear combination of the target unitaries. Collecting these outcome states and reshaping them into a $2K\times N$ matrix reveals a factorization $\Phi = C X$, where $C$ encodes the coefficients and $X$ contains the action of each unitary on the input; this immediately shows $\operatorname{rank}(\Phi)\le K$. This structure enables two complementary applications: (i) classical low-rank matrix completion can reconstruct the full output (including the target) from a fraction of its entries, turning every shot into useful information; (ii) treating $C$ as a secret key hides the input state, leading to a candidate quantum trapdoor function and symmetric encryption. The scheme thus turns the "junk" ancilla outcomes into a structured resource, possibly opening paths for further applications.

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arXiv2026

Mitigating Frequency Learning Bias in Quantum Models via Multi-Stage Residual Learning

Quantum machine learning models based on parameterized circuits can be viewed as Fourier series approximators. However, they often struggle to learn functions with multiple frequency components, particularly high-frequency or non-dominant ones; a phenomenon we term the quantum Fourier parameterization bias. Inspired by recent advances in classical Fourier neural operators (FNOs), we adapt the multi-stage residual learning idea to the quantum domain, iteratively training additional quantum modules on the residuals of previous stages. We evaluate our method on a synthetic benchmark composed of spatially localized frequency components with diverse envelope shapes (Gaussian, Lorentzian, triangular). Systematic experiments show that the number of qubits, the encoding scheme, and residual learning are all crucial for resolving multiple frequencies; residual learning alone can improve test MSE significantly over a single-stage baseline trained for the same total number of epochs. Our work provides a practical framework for enhancing the spectral expressivity of quantum models and offers new insights into their frequency-learning behavior.

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arXiv2025

Quantum Voting Protocol for Centralized and Distributed Voting Based on Phase-Flip Counting

We introduce a quantum voting protocol that uses superposition and entanglement to enable secure, anonymous voting in both centralized and distributed settings. Votes are encoded via phase-flip operations on entangled candidate states, controlled by voter identity registers. Tallying is performed directly by measuring the candidate register, eliminating the need for iterative classical counting. The protocol is described for a centralized single-machine model and extended to a distributed quantum channel model with entanglement-based verification for enhanced security. Its efficiency relies on basic quantum gates (Hadamard and controlled-Z) and the ability to extract vote counts from quantum measurements. Practical validation is provided through analytical examples (4 voters with 2 candidates and 8 voters with 3 candidates) as well as numerical experiments that simulate ideal conditions, depolarizing noise, dishonest voter attacks, and sampling convergence. The results confirm exact probability preservation, robustness against errors, and statistical behavior consistent with theoretical bounds. The protocol ensures voter anonymity via superposition, formalized as the indistinguishability of tallying transcripts under vote permutations and reinforced by an identity-dephasing step that renders the identity register exactly maximally mixed, prevents double-voting through entanglement mechanisms, and offers favorable complexity for large-scale elections.

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arXiv2025

Dimension reduction with structure-aware quantum circuits for hybrid machine learning

Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying Schmidt decompositions via SVD to all subsystems. Given a vector expressed as a linear combination of tensor products, using only the $k$ principal terms yields a $k$-rank approximation of the vector. Therefore, writing a vector in this reduced form allows to retain most important parts of the vector while removing small noises from it, analogous to SVD-based denoising. In this paper, we show that quantum circuits designed based on a value $k$ (determined from the tensor network decomposition of the mean vector of the training sample) can approximate the reduced-form representations of entire datasets. We then employ this circuit ansatz with a classical neural network head to construct a hybrid machine learning model. Since the output of the quantum circuit for an $2^n$ dimensional vector is an $n$ dimensional probability vector, this provides an exponential compression of the input and potentially can reduce the number of learnable parameters for training large-scale models. We use datasets provided in the Python scikit-learn module for the experiments. The results confirm the quantum circuit is able to compress data successfully to provide effective $k$-rank approximations to the classical processing component.

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arXiv2025

Learnable quantum spectral filters for hybrid graph neural networks

In this paper, we describe a parameterized quantum circuit that can be considered as convolutional and pooling layers for graph neural networks. The circuit incorporates the parameterized quantum Fourier circuit where the qubit connections for the controlled gates derived from the Laplacian operator. Specifically, we show that the eigenspace of the Laplacian operator of a graph can be approximated by using QFT based circuit whose connections are determined from the adjacency matrix. For an $N\times N$ Laplacian, this approach yields an approximate polynomial-depth circuit requiring only $n=log(N)$ qubits. These types of circuits can eliminate the expensive classical computations for approximating the learnable functions of the Laplacian through Chebyshev polynomial or Taylor expansions. Using this circuit as a convolutional layer provides an $n-$ dimensional probability vector that can be considered as the filtered and compressed graph signal. Therefore, the circuit along with the measurement can be considered a very efficient convolution plus pooling layer that transforms an $N$-dimensional signal input into $n-$dimensional signal with an exponential compression. We then apply a classical neural network prediction head to the output of the circuit to construct a complete graph neural network. Since the circuit incorporates geometric structure through its graph connection-based approach, we present graph classification results for the benchmark datasets listed in TUDataset library. Using only [1-100] learnable parameters for the quantum circuit and minimal classical layers (1000-5000 parameters) in a generic setting, the obtained results are comparable to and in some cases better than many of the baseline results, particularly for the cases when geometric structure plays a significant role.

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arXiv2025

From Theory to Practice: Analyzing Variational Quantum Power Method for Quantum Optimization of QUBO Problems

The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a comprehensive theoretical and numerical analysis of VQPM by investigating its convergence, robustness, and qubit locking mechanisms. We present detailed strategies for applying VQPM to QUBO problems by leveraging these locking mechanisms, establishing systematic guidelines for their practical applications. Furthermore, we provide a comparative study against the Quantum Approximate Optimization Algorithm (QAOA). Our analysis evaluates classical optimization behaviors and evaluates performance using localized Hamming distance (bit difference of the combinatorial solution). Scaling simulations up to $n=18$ qubits demonstrate that the success probability in VQPM exhibits notable resilience. Finally, we evaluate VQPM under realistic quantum noise using the IBM Qiskit Aer framework. Our results indicate that VQPM serves as an effective quantum optimization algorithm for combinatorial problems, and this work can serve as an initial guideline for such applications.

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arXiv2025

Quantum RNNs and LSTMs Through Entangling and Disentangling Power of Unitary Transformations

In this paper, we present a framework for modeling quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks using the core ideas presented by Linden et al. (2009), where the entangling and disentangling power of unitary transformations is investigated. In particular, we interpret entangling and disentangling power as information retention and forgetting mechanisms in LSTMs. Thus, entanglement emerges as a key component of the optimization (training) process. We believe that, by leveraging prior knowledge of the entangling power of unitaries, the proposed quantum-classical framework can guide the design of better-parameterized quantum circuits for various real-world applications.

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arXiv2025

Quantum Simulations Based on Parameterized Circuit of an Antisymmetric Matrix

Given an antisymmetric matrix $A$ or the unitary matrix $U_A = e^A$-or an oracle whose answers can be used to infer information about $A$-in this paper we present a parameterized circuit framework that can be used to approximate a quantum circuit for $e^A$. We design the circuit based on a uniform antisymmetric matrix with $\{\pm 1\}$ elements, which has an eigenbasis that is a phase-shifted version of the quantum Fourier transform, and its eigenspectrum can be constructed by using rotation $Z$ gates. Therefore, we show that it can be used to directly estimate $e^A$ and its quantum circuit representation. Since the circuit is based on $O(n^2)$ quantum gates, which form the eigendecomposition of $e^A$ with separate building blocks, it can also be used to approximate the eigenvalues of $A$.

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arXiv2024

An alternative explicit circuit diagram for the quantum search algorithm by implementing a non-unitary gate

Since the final quantum state in the Grover search algorithm is the normalized marked quantum state from the Gram-Schmidt process, Abrams and Lloyd [1] has shown that we can generate this vector by using a non-unitary gate. Following their ideas, in this paper, we present multiple explicit unitary implementations by using the square root of the non-unitary matrix and by a unitary matrix that mimics the Gram-Schmidt process. We also discuss the implementation through a linear combination of unitary matrices or similar methods and how these approximations may change the complexity. The reading of the marked element from the given circuits with high probability still requires multiple repetitions similar to the original algorithm. However, it gives an alternative implementations which may be useful in certain platforms. In addition, in the appendix of the paper, we show that the circuits can be used to group set elements which can be integrated into different algorithmic schemes.

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arXiv2024

Error analysis of quantum operators written as a linear combination of permutations

In this paper, we consider matrices given as a linear combination of permutations and analyze the impact of bit and phase-flips on the perturbation of the eigenvalues. When the coefficients in the linear combination are positive, we observe that the eigenvalues of the resulting matrices exhibit resilience to quantum bit-flip errors. In addition, we analyze the bit-flips in combination with positive and negative coefficients and the phase-flips. Although matrices with mixed-sign coefficients show less resilience to the bit-flip and phase-flip errors, the numerical evidence shows that the perturbation of the eigenspectrum is very small when the rate of these errors is small. We also discuss the situation when this matrix is implemented through block encoding and there is a control register. Since any square matrix can be expressed as a linear combination of permutations multiplied by two scaling matrices from the left and right (via Sinkhorn's theorem), this paper gives a framework to study matrix computations in quantum algorithms related to numerical linear algebra. In addition, it can give ideas to design more error-resilient algorithms that may involve quantum registers with different error characteristics.

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arXiv2024

On the explainability of quantum neural networks based on variational quantum circuits

Ridge functions are used to describe and study the lower bound of the approximation done by the neural networks which can be written as a linear combination of activation functions. If the activation functions are also ridge functions, these networks are called explainable neural networks. In this brief paper, we first show that quantum neural networks which are based on variational quantum circuits can be written as a linear combination of ridge functions by following matrix notations. Consequently, we show that the interpretability and explainability of such quantum neural networks can be directly considered and studied as an approximation with the linear combination of ridge functions.

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arXiv2024

Federated learning with distributed fixed design quantum chips and quantum channels

The privacy in classical federated learning can be breached through the use of local gradient results combined with engineered queries to the clients. However, quantum communication channels are considered more secure because a measurement on the channel causes a loss of information, which can be detected by the sender. Therefore, the quantum version of federated learning can be used to provide better privacy. Additionally, sending an $N$-dimensional data vector through a quantum channel requires sending $\log N$ entangled qubits, which can potentially provide efficiency if the data vector is utilized as quantum states. In this paper, we propose a quantum federated learning model in which fixed design quantum chips are operated based on the quantum states sent by a centralized server. Based on the incoming superposition states, the clients compute and then send their local gradients as quantum states to the server, where they are aggregated to update parameters. Since the server does not send model parameters, but instead sends the operator as a quantum state, the clients are not required to share the model. This allows for the creation of asynchronous learning models. In addition, the model is fed into client-side chips directly as a quantum state; therefore, it does not require measurements on the incoming quantum state to obtain model parameters in order to compute gradients. This can provide efficiency over models where the parameter vector is sent via classical or quantum channels and local gradients are obtained through the obtained values these parameters.

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arXiv2024

A quantum compiler design method by using linear combinations of permutations

A matrix can be converted into a doubly stochastic matrix by using two diagonal matrices. And a doubly stochastic matrix can be written as a sum of permutation matrices. In this paper, we describe a method to write a given generic matrix in terms of quantum gates based on the block encoding. In particular, we first show how to convert a matrix into doubly stochastic matrices and by using Birkhoff's algorithm, we express that matrix in terms of a linear combination of permutations which can be mapped to quantum circuits. We then discuss a few optimization techniques that can be applied in a possibly future quantum compiler software based on the method described here.

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arXiv2024

A Simple Quantum Blockmodeling with Qubits and Permutations

Blockmodeling of a given problem represented by an $N\times N$ adjacency matrix can be found by swapping rows and columns of the matrix (i.e. multiplying matrix from left and right by a permutation matrix). Although classical matrix permutations can be efficiently done by swapping pointers for the permuted rows (or columns) of the matrix, by changing row-column order, a permutation changes the location of the matrix elements, which determines the membership of a group in the matrix based blockmodeling. Therefore, a brute force initial estimation of a fitness value for a candidate solution involving counting the memberships of the elements may require going through all the sum of the rows (or the columns). Similarly permutations can be also implemented efficiently on quantum computers, e.g. a NOT gate on a qubit. In this paper, using permutation matrices and qubit measurements, we show how to solve blockmodeling on quantum computers. In the model, the measurement outcomes of a small group of qubits are mapped to indicate the fitness value. However, if the number of qubits in the considered group is much less than $n=log(N)$, it is possible to find or update the fitness value based on the state tomography in $O(poly(log(N)))$. Therefore, when the number of iterations is less than $log(N)$ time and the size of the considered qubit group is small, we show that it may be possible to reach the solution very efficiently.

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arXiv2024

A unifying primary framework for quantum graph neural networks from quantum graph states

Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural network model can be understood and realized based on graph states. We show that they can be used either as a parameterized quantum circuits to represent neural networks or as an underlying structure to construct graph neural networks on quantum computers.

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