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
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.
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