Related papers: Optimization of the HHL Algorithm
Linear system solvers are widely used in scientific computing, with the primary goal of solving linear system problems. Classical iterative algorithms typically rely on the conjugate gradient method. The rise of quantum computing has…
Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed,…
Variational quantum algorithms have been advocated as promising candidates to solve combinatorial optimization problems on near-term quantum computers. Their methodology involves transforming the optimization problem into a quadratic…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
We introduce a new quantum optimization algorithm for dense Linear Programming problems, which can be seen as the quantization of the Interior Point Predictor-Corrector algorithm \cite{Predictor-Corrector} using a Quantum Linear System…
We introduce two variations of the quantum phase estimation algorithm: quantum shifted phase estimation and quantum punctured phase estimation. The shifted method employs a bit-string left shift to discard the most significant bit and focus…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…
We present a fast algorithm for linear least squares problems governed by hierarchically block separable (HBS) matrices. Such matrices are generally dense but data-sparse and can describe many important operators including those derived…
In [\href{https://quantum-journal.org/papers/q-2022-12-07-872/}{Quantum 6, 872, 2022}], Linden and de Wolf proposed a lightweight protocol for verifying the average-case correct behavior of the quantum Fourier transform (QFT). They proved…
The goal of the load flow study is to ensure that electrical power is delivered efficiently and reliably to end-users while maintaining the stability and security of the power system. Newton-Raphson is a numerical method used widely for…
Fault-tolerant quantum computers promise the simulation of complex quantum systems beyond the reach of classical computation. In contrast, current noisy intermediate-scale quantum (NISQ) devices are constrained by hardware noise.…
Simulating dynamics of physical systems is a key application of quantum computing, with potential impact in fields such as condensed matter physics and quantum chemistry. However, current quantum algorithms for Hamiltonian simulation yield…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
Linear inverse problems arise in diverse engineering fields especially in signal and image reconstruction. The development of computational methods for linear inverse problems with sparsity is one of the recent trends in this field. The…
With the current increase in the data produced by the Large Hadron Collider (LHC) at CERN, it becomes important to process this data in a corresponding manner. To begin with, to efficiently select events that contain relevant information…
Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the…
Current quantum computers present significant noise, especially as circuit depth and qubit count increase. Prior work has demonstrated that erroneous outcomes exhibit some behavior in Hamming space, enabling improvements in the output…