Related papers: Improved Gap Estimates for Simulating Quantum Circ…

We introduce a class of quantum adiabatic evolutions that we claim may be interpreted as the equivalents of the unitary gates of the quantum gate model. We argue that these gates form a universal set and may therefore be used as building…

Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyse a particular class of qauntum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on…

We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.

We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the…

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The…

The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases…

A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.

Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a…

Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We…

Quantum adiabatic evolution algorithm suggested by Farhi et al. was effective in solving instances of NP-complete problems. The algorithm is governed by the adiabatic theorem. Therefore, in order to reduce the running time, it is essential…

We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state.…

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 adiabatic evolutions find a broad range of applications in quantum physics and quantum technologies. The traditional form of the quantum adiabatic theorem limits the speed of adiabatic evolution by the minimum energy gaps of the…

A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a…

A major challenge facing adiabatic quantum computing is that algorithm design and error correction can be difficult for adiabatic quantum computing. Recent work has considered addressing his challenge by using coherently controlled…

Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state…

In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a…

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to…

In this paper,we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a non degenerate continuous spectrum. A new strategy is initiated by defining a kind of gap, "a virtual gap", for the…

Quantum adiabatic computation is a novel paradigm for the design of quantum algorithms, which is usually used to find the minimum of a classical function. In this paper, we show that if the initial hamiltonian of a quantum adiabatic…