Related papers: The Power of Adiabatic Quantum Computation with No…

Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…

We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by…

We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…

We analyze the computational power and limitations of the recently proposed 'quantum adiabatic evolution algorithm'.

We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines…

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…

Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…

This is evident that the controllable quantum systems can be the reliable building blocks for Quantum computation. In reality we are witnessing the progress towards making the idea tractable enough, though optimistic but the threshold is…

Quantum adiabatic algorithm is of vital importance in quantum computation field. It offers us an alternative approach to manipulate the system instead of quantum gate model. Recently, an interesting work arXiv:1805.10549 indicated that we…

We outline an algorithm for the Quantum Counting problem using Adiabatic Quantum Computation (AQC). We show that using local adiabatic evolution, a process in which the adiabatic procedure is performed at a variable rate, the problem is…

Adiabatic quantum computation, based on the adiabatic theorem, is a promising alternative to conventional quantum computation. The validity of an adiabatic algorithm depends on the existence of a nonzero energy gap between the ground and…

Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single…

We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…

The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…

This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with…

We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the…

Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…

We discuss in this chapter the basics of adiabatic computation, as well as some physical implementations. After a short introduction of the quantum circuit model, we describe quantum adiabatic computation, quantum annealing, and the strong…

Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic…