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Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization…
Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of p steps; in each step a…
Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible,…
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 quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It…
In the search for quantum advantage in real--world problems, one promising avenue is to use a quantum algorithm to improve on the solution found using an efficient classical algorithm. The quantum approximate optimization algorithm (QAOA)…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary near intermediate-scale quantum (NISQ) era. The quantum approximate optimisation algorithm (QAOA)…
The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising variational quantum algorithm for addressing NP hard combinatorial optimization problems. However, a significant limitation lies in optimizing its classical…
We propose a hybrid quantum-classical algorithm for solving QUBO problems using an Imaginary Time Evolution-Mimicking Circuit (ITEMC). The circuit parameters are optimized to closely mimic imaginary time evolution, using only single- and…
The Quantum Approximate Optimization Algorithm (QAOA) is a powerful tool in solving various combinatorial problems such as Maximum Satisfiability and Maximum Cut. Hard computational problems, however, require deep circuits that place high…
Optimization is often cited as a promising application of quantum computers. However, the low degree of provable quantum speedups has led prior rigorous end-to-end resource analyses to conclude that a quantum computer is unlikely to surpass…
Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the…
Hybrid quantum-classical algorithms, such as variational quantum algorithms (VQA), are suitable for implementation on NISQ computers. In this Letter we expand an implicit step of VQAs: the classical pre-computation subroutine which can…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
The prospect of using quantum computers to solve combinatorial optimization problems via the quantum approximate optimization algorithm (QAOA) has attracted considerable interest in recent years. However, a key limitation associated with…
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…