Related papers: Topological Quantum Gates in Homotopy Type Theory
Traditional error detection and correction codes focus on bit-level fidelity, which is insufficient for emerging technologies like eXtended Reality (XR) and holographic communications requiring high-data-rate, low-latency systems. Bit-level…
The development of a large scale quantum computer is a highly sought after goal of fundamental research and consequently a highly non-trivial problem. Scalability in quantum information processing is not just a problem of qubit…
We survey some recent work on topological quantum computation with gapped boundaries and boundary defects and list some open problems.
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and…
The design of time-independent local Hamiltonians that realise quantum algorithms is derived from the study of perfect state transfer. The novel features of this evolution are the perfect realisation of the computation, and the ability to…
We investigate entanglement naturally present in the 1D topologically ordered phase protected with the on-site symmetry group of an octahedron as a potential resource for teleportation-based quantum computation. We show that, as long as…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
We investigate topological order on fractal geometries embedded in $n$ dimensions. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a…
The homological product is a general-purpose recipe that forges new quantum codes from arbitrary classical or quantum input codes, often providing enhanced error-correcting properties. When the input codes are classical linear codes, it is…
Transversal gates are the ideal gates in a fault-tolerant scenario; relatively easy to implement, and minimally error propagating. Their availability will maximise fault tolerant thresholds, enabling universal quantum computation in a wider…
Transversal Pauli $Z$ rotations provide a natural route to fault-tolerant logical diagonal gates in quantum CSS codes, but their capability is inherently constrained. We develop a homological framework that organizes transversal diagonal…
A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein.…
Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…
Quantum holonomic gates hold built-in resilience to local noises and provide a promising approach for implementing fault-tolerant quantum computation. We propose to realize high-fidelity holonomic $(N+1)$-qubit controlled gates using…
The recent discovery of fully-homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumptions that solving certain computation problems…
As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification…
Existing and near-term quantum computers can only perform two-qubit gates between physically connected qubits. Research has been done on compilers to rewrite quantum programs to match hardware constraints. However, the quantum processor…
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum…
The efficient validation of quantum devices is critical for emerging technological applications. In a wide class of use-cases the precise engineering of a Hamiltonian is required both for the implementation of gate-based quantum information…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…