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
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.
Read full paperError 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.
Read full paperLearnable 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.
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