Related papers: Quantum linear system algorithm with optimal queri…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We describe an efficient quantum algorithm for solving the linear matrix equation AX+XB=C, where A, B, and C are given complex matrices and X is unknown. This is known as the Sylvester equation, a fundamental equation with applications in…
Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
The Quantum Approximate Optimisation Algorithm (QAOA) is a widely studied quantum-classical iterative heuristic for combinatorial optimisation. While QAOA targets problems in complexity class NP, the classical optimisation procedure…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H = H_A + H_B$ in infinite systems. The first algorithm is a generalization of the quantum…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
It is a useful fact in classical computer science that many search problems are reducible to decision problems; this has led to decision problems being regarded as the $\textit{de facto}$ computational task to study in complexity theory. In…
As a cornerstone for many quantum linear algebraic and quantum machine learning algorithms, controlled quantum state preparation (CQSP) aims to provide the transformation of $|i\rangle |0^n\rangle \to |i\rangle |\psi_i\rangle $ for all…
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
We propose a new method to extend the size of a quantum computation beyond the number of physical qubits available on a single device. This is accomplished by randomly inserting measure-and-prepare channels to express the output state of a…
Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Reliable preparation of entanglement between distant systems is an outstanding problem in quantum information science and quantum communication. In practice, this has to be accomplished via noisy channels (such as optical fibers) that…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
Quantum search/amplitude amplification algorithms are designed to be able to amplify the amplitude in the target state linearly with the number of operations. Since the probability is the square of the amplitude, this results in the success…