Research
Main research interest and themes:
- Quantum compilers and circuit design
- Quantum algorithms
- Quantum optimization
- Quantum machine learning and data analysis
- Matrix computations
- Parallel and distributed computation
Tutorials
- A brief tutorial on grouping set elements on quantum computers
- it generates groups as quantum states in O(1) time
Latest Research Papers
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.
Quantum RNNs and LSTMs Through Entangling and Disentangling Power of Unitary Transformations
In this paper, we discuss how quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks, can be modeled using the core ideas presented by Linden et al., 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. Therefore, entanglement becomes 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 and help to design better-parameterized quantum circuits for various real-world applications.
From Theory to Practice: Analyzing VQPM 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. Based on the simulations for each strategy we have carried out, we give systematic guidelines for their practical applications. We also offer a simple numerical comparison with the quantum approximate optimization algorithm (QAOA) by running both algorithms on a set of trial problems. Our results indicate that VQPM can be employed as an effective quantum optimization algorithm on quantum computers for QUBO problems, and this work can serve as an initial guideline for such applications.
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.
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×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 (AIDS, Letter-high, Letter-med, Letter-low, MUTAG, ENZYMES, PROTEINS, COX2, BZR, DHFR, MSRC-9). 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.
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 2n 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.
Quantum Distortion Model for Running Variational Quantum Algorithms without Error Corrections
The classical distortion models similarly to temporal data analysis provide a way to predict the trends in the output of the algorithms and discard the anomalies in the output which may impact the accuracy of the method. In this paper, we introduce a quantum distortion modeling framework that enables variational quantum algorithms to operate effectively in the presence of errors without traditional error correction. Drawing inspirations from classical distortion-tolerant computing, we describe different distortions measures and formulation which can be used in variational quantum algorithms. In particular, we develop mathematical foundations for distortion metrics including energy progression, parameter stability, and state fidelity distortions, and demonstrate their applicability to variational quantum eigensolver, quantum approximate optimization algorithm, and quantum power method. We believe this paper will provide a milestone for distortion-aware quantum computing which can expand the practical applicability of the pre-fault-tolerant era devices to problems where approximate solutions provide sufficient value, representing a paradigm shift from exact error elimination to managed accuracy degradation. **Keywords: Variational Quantum Algorithms, Quantum Optimization, Quantum Distortion Model, Quantum Error Correction, Quantum Error Mitigation**
Quantum Voting Protocol for Centralized and Distributed Voting Based on Phase-Flip Counting
In this paper, we introduce a novel quantum voting protocol that leverages quantum superposition and entanglement to achieve secure, anonymous voting in both centralized and distributed settings. Our approach utilizes phase-flip encoding on entangled candidate states, where votes are recorded as controlled phase operations conditioned on voter identity registers. The protocol employs a simplified tallying mechanism based on candidate register measurements. We provide comprehensive mathematical formulations for a centralized single-machine model suitable for local voting systems, and a distributed quantum channel model enabling remote voting with enhanced security through entanglement verification. The efficiency of the protocol stems from its use of basic quantum gates (Hadamard and controlled-Z) and its ability to count votes through quantum measurements rather than iterative classical counting. We demonstrate the practicality of the protocol through examples with 4 voters (2 candidates) and 8 voters (3 candidates), showing exact probability preservation and correct vote tallying. The protocol ensures voter anonymity through quantum superposition, prevents double-voting through entanglement mechanisms, and can offer speedup potential for large-scale elections.