Related papers: Quantum Amplitude Amplification Operators
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently…
This article consists of a short introduction to the quantum approximation optimisation algorithm (QAOA). The mathematical structure of the QAOA, as well as its basic properties, are described. The implementation of the QAOA on MaxCut…
Consider a Boolean function $\chi: X \to \{0,1\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $\chi(x)=1$ and bad otherwise. Consider also a quantum algorithm $\mathcal A$ such that $A |0\rangle=…
This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…
Present-day, noisy, small or intermediate-scale quantum processors---although far from fault-tolerant---support the execution of heuristic quantum algorithms, which might enable a quantum advantage, for example, when applied to…
Quantum computers are increasing in size and quality, but are still very noisy. Error mitigation extends the size of the quantum circuits that noisy devices can meaningfully execute. However, state-of-the-art error mitigation methods are…
The quantum approximate optimization algorithm (QAOA) is a variational method for noisy, intermediate-scale quantum computers to solve combinatorial optimization problems. Quantifying performance bounds with respect to specific problem…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude…
The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate algorithm for demonstrating quantum advantage in optimization using near-term quantum computers. However, QAOA has high requirements on gate fidelity due to the…
Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked…
This paper concerns the Grover algorithm that permits to make amplification of quantum states previously tagged by an Oracle. Grover's algorithm allows searches in an unstructure database of n entries finding a marked element with a…
We propose and study Th-QAOA (pronounced Threshold QAOA), a variation of the Quantum Alternating Operator Ansatz (QAOA) that replaces the standard phase separator operator, which encodes the objective function, with a threshold function…
Quantum computing is an emerging field on the multidisciplinary interface between physics, engineering, and computer science with the potential to make a large impact on computational intelligence (CI). The aim of this paper is to introduce…
We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows…
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…
We use the mapping between two computation frameworks , Adiabatic Grover Search (AGS) and Adiabatic Quantum Computing (AQC), to translate the Grover search algorithm into the AQC regime. We then apply Trotterization on the…
The Quantum Approximate Optimization Algorithm (QAOA) has shown promise in solving combinatorial optimization problems by leveraging quantum computational power. We propose a simple approach, the Two-Step QAOA, which aims to improve the…
Solving hard optimization problems is one of the most promising application domains for quantum computers due to the ubiquity of such problems in industry and the availability of broadly applicable quantum speedups. However, the ability of…