Related papers: Quantum algorithm for linear matrix equations
We provide necessary and sufficient conditions for the generalized $\star$-Sylvester matrix equation, $AXB + CX^\star D = E$, to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…
Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
The matrix logarithm is one of the important matrix functions. Recently, a quantum algorithm that computes the state $|f\rangle$ corresponding to matrix-vector product $f(A)b$ is proposed in [Takahira, et al. Quantum algorithm for matrix…
Superconducting quantum circuits are promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm…
Two quantum algorithms are presented, which tackle well--known problems in the context of numerical semigroups: the numerical semigroup membership problem (NSMP) and the Sylvester denumerant problem (SDP).
We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated…
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize…
Quantum computing is an emerging technology in which quantum mechanical properties are suitably utilized to perform certain compute-intensive operations faster than classical computers. Quantum algorithms are designed as a combination of…
We present new iterative algorithms for solving a square linear system $Ax=b$ in dimension $n$ by employing the {\it Triangle Algorithm} \cite{kal12}, a fully polynomial-time approximation scheme for testing if the convex hull of a finite…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
In this paper, we prove a conjecture which was presented in a recent paper [Linear Algebra Appl. 2016; 496: 549--593]. We derive some practical necessary and sufficient conditions for the existence of a solution to a system of coupled…
When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…