Related papers: Subsystem stabilizer codes cannot have a universal…
Qudits, generalizations of qubits to multi-level quantum systems, offer enhanced computational efficiency by encoding more information per lattice cell, avoiding costly swap operations and providing even exponential speedup in some cases.…
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…
Qudits can be described by a state vector in a $q$-dimensional Hilbert space, enabling a more extensive encoding and manipulation of information compared to qubits. This implies that conducting fault-tolerant quantum computations using…
In this paper, we prove how to extend a subset of quantum stabilizer codes into a qudit hybrid code storing $\log_2 p$ classical bits over a qudit space with dimension $p$, with $p$ prime. Our proof also gives an explicit procedure for…
The realisation of a universal quantum computer at scale promises to deliver a paradigm shift in information processing, providing the capability to solve problems that are intractable with conventional computers. A key limiting factor of…
We provide a simplified, yet rigorous presentation of the ideas from Bomb\'{i}n's paper "Gauge Color Codes" [arXiv:1311.0879v3]. Our presentation is self-contained, and assumes only basic concepts from quantum error correction. We provide…
Recently, Bravyi and K\"onig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a…
Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum…
We show an equivalence relation between fault-tolerant circuits for a stabilizer code and fault-tolerant adiabatic processes for holonomic quantum computation (HQC), in the case where quantum information is encoded in the degenerated ground…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
Continuous-variable (CV) systems have shown remarkable potential for quantum computation, particularly excelling in scalability and error correction through bosonic encoding. Within this framework, the foundational notion of computational…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
Assuming an array that consists of two parallel lines of qubits and that permits only nearest neighbor interactions, we construct physical and logical circuitry to enable universal fault tolerant quantum computation under the [[7,1,3]]…
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…
Recently an algorithm has been constructed that shows the binary icosahedral group $\2I$ together with a $T$-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code…
We present a fault-tolerant semi-global control strategy for universal quantum computers. We show that N-dimensional array of qubits where only (N-1)-dimensional addressing resolution is available is compatible with fault-tolerant universal…
A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only…
We show that universal quantum computation can be concretely made fault-tolerant without mid-circuit measurements. To this end, we introduce a measurement-free deformation protocol of the Bacon-Shor code to realize a logical $\mathit{CCZ}$…
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…