Related papers: Universal logical gates with constant overhead: in…
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…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of…
I discuss how to perform fault-tolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when next-to-nearest-neighbor…
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by…
Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
This paper proves the threshold result, which asserts that quantum computation can be made robust against errors and inaccuracies, when the error rate, $\eta$, is smaller than a constant threshold, $\eta_c$. The result holds for a very…
The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and…
Quantum error correction and fault-tolerance make it possible to perform quantum computations in the presence of imprecision and imperfections of realistic devices. An important question is to find the noise rate at which errors can be…
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to…
Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the…
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…
Reducing space and time overheads of fault-tolerant quantum computation (FTQC) has been receiving increasing attention as it is crucial for the development of quantum computers and also plays a fundamental role in understanding the…
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…
Based on the geometrical nature of quantum phases, non-adiabatic holonomic quantum control (NHQC) has become a standard technique for enhancing robustness in constructing quantum gates. However, the conventional approach of NHQC is…
Quantum computation in solid state quantum dots faces two significant challenges: Decoherence from interactions with the environment and the difficulty of generating local magnetic fields for the single qubit rotations. This paper presents…
We show that universal holonomic quantum computation (HQC) can be achieved fault-tolerantly by adiabatically deforming the gapped stabilizer Hamiltonian of the surface code, where quantum information is encoded in the degenerate ground…
Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: what circuits…
Hypergraph product codes are a class of quantum low density parity check (LDPC) codes discovered by Tillich and Z\'emor. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold.…