Related papers: Homological Quantum Rotor Codes: Logical Qubits fr…
Encoding logical quantum information in harmonic oscillator modes is a promising and hardware-efficient approach to the realization of a quantum computer. In this work, we propose to encode logical qubits in grid states of an ensemble of…
We utilize the symmetry groups of regular tessellations on two-dimensional surfaces of different constant curvatures, including spheres, Euclidean planes and hyperbolic planes, to encode a qubit or qudit into the physical degrees of freedom…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many…
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the…
Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC)…
Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…
A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert state space of rotational states of a rigid body. These codes, which protect against both drift in the body's…
Near term quantum devices have recently garnered significant interest as promising candidates for investigating difficult-to-probe regimes in many-body physics. To this end, various qubit encoding schemes targeting second quantized…
Spins and oscillators are foundational to much of physics and applied sciences. For quantum information, a spin 1/2 exemplifies the most basic unit, a qubit. High angular momentum spins (HAMSs) and harmonic oscillators provide multi-level…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…
Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be…
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…
Homological quantum error correction uses tools of algebraic topology and homological algebra to derive Calderbank-Shor-Steane quantum error correcting codes from cellulations of topological spaces. This work is an exploration of the…