Related papers: Quantum Adiabatic Evolution Algorithms with Differ…
This paper is devoted to a generalisation of the quantum adiabatic theorem to a nonlinear setting. We consider a Hamiltonian operator which depends on the time variable and on a finite number of parameters and acts on a separable Hilbert…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These…
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied "straight line" adiabatic evolution. In ways that…
We analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'.
We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. The…
In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic…
Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…
We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…
For slow--fast quantum systems, we compute first corrections to the quantum action and to the effective slow Hamiltonian.
Nonadiabatic geometric phases are only dependent on the evolution path of a quantum system but independent of the evolution details, and therefore quantum computation based on nonadiabatic geometric phases is robust against control errors.…
Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest.…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively…
We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate.…
The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation,…
Quantum adiabatic processes -that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian- are very useful to prepare and manipulate states, but take typically a long time. This is often problematic…
We present a general method for studying coupled qubits driven by adiabatically changing external parameters. Extended calculations are provided for a two-bit Hamiltonian whose eigenstates can be used as logical states for a quantum CNOT…