相关论文: Hamiltonian Oracles
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…
The oracle identification problem (OIP) is, given a set $S$ of $M$ Boolean oracles out of $2^{N}$ ones, to determine which oracle in $S$ is the current black-box oracle. We can exploit the information that candidates of the current oracle…
Determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry [Nielsen et al, Science 311, 1133-1135 (2006)]. This paper investigates many…
In these notes we show that it is impossible to obtain a quantum speedup for a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous time oracle model has first been investigated in [1]. The authors consider a faulty…
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…
While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with…
One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
In the oracle identification problem we have oracle access to bits of an unknown string $x$ of length $n$, with the promise that it belongs to a known set $C\subseteq\{0,1\}^n$. The goal is to identify $x$ using as few queries to the oracle…
Given a loop or more generally 1-cycle $r$ of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks whether or not it is homologous to zero. We frame and tackle…
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…
We give a quantum algorithm for the binary NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a run time proportional to sqrt N. We also show a lower bound of sqrt N for the NAND tree…
A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems,…
We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second…
We study the query complexity of quantum learning problems in which the oracles form a group $G$ of unitary matrices. In the simplest case, one wishes to identify the oracle, and we find a description of the optimal success probability of a…
We investigate the implementation of an oracle for the Subset Sum problem for quantum search using Grover's algorithm. Our work concerns reducing the number of qubits, gates, and multi-controlled gates required by the oracle. We describe…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…