Related papers: Optimisation of Quantum Evolution Algorithms
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
A many-body Hamiltonian can be block-diagonalized by expressing it in terms of symmetry-adapted basis states. Finding the group orbit representatives of these basis states and their corresponding symmetries is currently a…
Quantum oracles play key roles in the studies of quantum computation and quantum information. But implementing quantum oracles efficiently with universal quantum gates is a hard work. Motivated by genetic programming, this paper proposes a…
We study the complexity of both time-optimal and time sub-optimal quantum Hamiltonian evolutions connecting arbitrary source and a target states on the Bloch sphere equipped with the Fubini-Study metric. This investigation is performed in a…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
We provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…
Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…
Many computationally hard problems can be encoded in quantum Hamiltonians. The solution to these problems is given by the ground states of these Hamiltonians. A state-of-the-art algorithm for finding the ground state of a Hamiltonian is the…
Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schr\"odinger's equation. In the former, the…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical…
This effort examines the intersection of the emerging field of quantum computing and the more established field of evolutionary computation. The goal is to understand what benefits quantum computing might offer to computational intelligence…
Combinatorial optimization problems that arise in science and industry typically have constraints. Yet the presence of constraints makes them challenging to tackle using both classical and quantum optimization algorithms. We propose a new…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…
Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly…
Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…