Related papers: Hamiltonian quantum computer in one dimension
We propose a scheme for scalable and robust quantum computing on two-dimensional arrays of qubits with fixed longitudinal coupling. This opens the possibility for bypassing the device complexity associated with tunable couplers required in…
We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where…
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…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
The construction of the Hamiltonian matrix \textbf{H} is an essential, yet computationally expensive step in \textit{ab-initio} device simulations based on density-functional theory (DFT). In homogeneous structures, the fact that a unit…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a…
Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body…
In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open…
Holonomic quantum computation exploits a quantum state's non-trivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
Holonomic quantum computation is the idea to use non-Abelian geometric phases to implement universal quantum gates that are robust to fluctuations in control parameters. Here, we propose a compact design for a holonomic quantum computer…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. If based on current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when…
A family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family. If the encoding is efficient, universal…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources.…