Related papers: A Computer Code for Topological Quantum Spin Syste…
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes {\it any} classical code and explicitly constructs the corresponding QEC code. Our…
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
We review a recent theoretical proposal for a universal quantum computing platform based on tunable nonlinear electromechanical nano-oscillators, in which qubits are encoded in the anharmonic vibrational modes of mechanical resonators…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by…
Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of…
We present an architecture for the quantum simulation of many-body spin interactions based on ultracold polar molecules trapped in optical lattices. Our approach employs digital quantum simulation, i.e., the dynamics of the simulated system…
We present a scalable framework for accurately modeling many-body interactions in surface-code quantum processor units (QPUs). Combining a concise diagrammatic formalism with high-precision numerical methods, our approach efficiently…
We present an encoding technique that reduces the effects of noise on quantum spin systems whose operation is driven by Hamiltonian evolution. This technique is widely applicable, being most relevant to the scenarios where there are…
In numerical simulations of classical and quantum lattice systems, 2d corner transfer matrices (CTMs) and 3d corner tensors (CTs) are a useful tool to compute approximate contractions of infinite-size tensor networks. In this paper we show…
Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here,…
We show that a local Hamiltonian of spin-3/2 particles with only two-body nearest-neighbor Affleck-Kennedy-Lieb-Tasaki and exchange-type interactions has an unique ground state, which can be used to implement universal quantum computation…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close…
We propose a scheme for a ground-code measurement-based quantum computer, which enjoys two major advantages. First, every logical qubit is encoded in the gapped degenerate ground subspace of a spin-1 chain with nearest-neighbor two-body…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…
Interacting spins in quantum magnet can cooperate and exhibit exotic states like the quantum spin liquid. To explore the materialization of such intriguing states, the determination of effective spin Hamiltonian of the quantum magnet is…
We introduce a two-body quantum Hamiltonian model with spins-$\half$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non-perturbative effect.…
We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a…