Related papers: Phase-sensitive representation of Majorana stabili…
Several designs of inter-qubit coupling are considered. It is shown that by a combination of Josephson and capacitive coupling one can realize qubit interactions of variable spin content. Qubit arrays are discussed as models of quantum spin…
Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be…
Perturbation theories provide valuable insights on quantum many-body systems. Systems of interacting particles, like electrons, are often treated perturbatively around exactly solvable Gaussian points. Systems of interacting qubits have…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
We provide a current perspective on the rapidly developing field of Majorana zero modes in solid state systems. We emphasize the theoretical prediction, experimental realization, and potential use of Majorana zero modes in future…
We investigate the generation of quantum states and unitary operations that are ``random'' in certain respects. We show how to use such states to estimate the average fidelity, an important measure in the study of implementations of quantum…
We propose a physical realization of a commuting Hamiltonian of interacting Majorana fermions realizing $Z_{2}$ topological order, using an array of Josephson-coupled topological superconductor islands. The required multi-body interaction…
Continuous-variable cluster states allow for fault-tolerant measurement-based quantum computing when used in tandem with the Gottesman-Kitaev-Preskill (GKP) encoding of a qubit into a bosonic mode. For quad-rail-lattice macronode cluster…
The Clifford group plays a central role in quantum information science. It is the building block for many error-correcting schemes and matches the first three moments of the Haar measure over the unitary group -a property that is essential…
Matchgates and Clifford circuits are two types of quantum circuits which can be efficiently simulated classically, though the underlying reasons are quite different. Matchgates are essentially the single particle basis transformations in…
We establish a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero time overhead. This is done by introducing a…
The realization and manipulation of Majorana zero modes is a key step in achieving topological quantum computation. In this paper, we demonstrate the existence of Majorana corner states in a superconductor-insulators-superconductor vertical…
Fermion-to-qubit mappings that preserve geometric locality are especially useful for simulating lattice fermion models (e.g., the Hubbard model) on a quantum computer. They avoid the overhead associated with geometric non-local parity terms…
With the discovery of Majorana quasiparticles in semiconductor-superconductor hybrid structures, topologically protected qubits have emerged as a promising contender for quantum information processing. While the construction of a universal…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid…
A quantum simulator is a device engineered to reproduce the properties of an ideal quantum model. It allows the study of quantum systems that cannot be efficiently simulated on classical computers. While a universal quantum computer is also…
Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on…
Fracton topological phases host fractionalized topological quasiparticles with restricted mobility, with promising applications to fault-tolerant quantum computation. While a variety of exactly solvable fracton models have been proposed,…