Related papers: (Sub)Exponential Quantum Speedup for Optimization
In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
The quantum adiabatic theorem ensures that a slowly changing system, initially prepared in its ground state, will evolve to its final ground state with arbitrary precision. As a first result this thesis extends the original theorem to…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in [E. Farhi, et al., arXiv:quant-ph/0208135]. The algorithm is applied to a random binary optimization problem (a version…
We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Quantum computing promises significant improvements of computation capabilities in various fields such as machine learning and complex optimization problems. Recent technological advancements suggest that the adiabatic quantum computing…
Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
This thesis investigates quantum algorithms for eigenstate preparation, with a focus on solving eigenvalue problems such as the Schrodinger equation by utilizing near-term quantum computing devices. These problems are ubiquitous in several…
We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
Existing quantum discrete adiabatic approaches are hindered by circuit depth that increases linearly with the number of evolution steps, a significant challenge for current quantum hardware with limited coherence times. To address this, we…
For slow--fast quantum systems, we compute first corrections to the quantum action and to the effective slow Hamiltonian.
We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that for problems that have exponentially large number of…
We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to…
The challenge in building high-fidelity quantum gates lies in overcoming control errors and decoherence effects caused by the coupling between the quantum system and the external environment. Nonadiabatic holonomic quantum computation uses…
Adiabatic state preparation provides an analytical solution for generating the ground state of a target Hamiltonian, starting from an easily prepared ground state of the initial Hamiltonian. While effective for time-dependent Hamiltonians…