相关论文: The 2D AKLT state on the honeycomb lattice is a un…

We build a framework allowing for a systematic investigation of the issue: "Which quantum states are universal resources for one-way quantum computation?" We start by re-examining what is exactly meant by "universality" in quantum…

Universal quantum computation using photonic systems requires gates whose Hamiltonians are of order greater than quadratic in the quadrature operators. We first review previous proposals to implement such gates, where specific non-Gaussian…

What is the simplest Hamiltonian which can implement quantum computation without requiring any control operations during the computation process? In a previous paper we have constructed a 10-local finite-range interaction among qubits on a…

We construct a family of time-independent nearest-neighbor Hamiltonians coupling eight-state systems on a 1D ring that enables universal quantum computation. Hamiltonians in this family can achieve universality either by driving a…

Numerical simulation of lattice gauge theories is an indispensable tool in high energy physics, and their quantum simulation is expected to become a major application of quantum computers in the future. In this work, for an Abelian lattice…

We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states |0>, |1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1] describes how…

We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbour two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one-,…

The $S=1$ Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the $S=3/2$ AKLT model on the hexagonal lattice is also in a gapped phase…

From Feynman diagrams to tensor networks, diagrammatic representations of computations in quantum mechanics have catalysed progress in physics. These diagrams represent the underlying mathematical operations and aid physical interpretation,…

The AKLT Hamiltonian is a particular instance of a general class of model Hamiltonians defined in lattices with coordination $z$ where each site hosts a spins $S=z/2$, interacting both with linear and non-linear exchange couplings. In two…

We consider a two-dimensional spin system that exhibits abelian anyonic excitations. Manipulations of these excitations enable the construction of a quantum computational model. While the one-qubit gates are performed dynamically the model…

Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations…

We consider the problem of minimizing resources required for universal quantum computation using only projective measurements. The resources we focus on are observables, which describe projective measurements, and ancillary qubits. We show…

An emerging insight is that ground states of symmetry-protected topological orders (SPTO's) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the…

The digital quantum simulation of lattice gauge theories is expected to become a major application of quantum computers. Measurement-based quantum computation is a widely studied competitor of the standard circuit-based approach. We…

We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt--rank width, a measure recently introduced to assess universality of resource states,…

A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…

Unravelling the source of quantum computing power has been a major goal in the field of quantum information science. In recent years, the quantum resource theory (QRT) has been established to characterize various quantum resources, yet…

We show that universal quantum computation can be achieved in the standard pure-state circuit model while, at any time, the entanglement entropy of all bipartitions is small---even tending to zero with growing system size. The result is…

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…