Related papers: Classification of topologically protected gates fo…
We introduce an intrinsic formulation of quantum error correction based on representation theory, in which error-protection structure is encoded directly in a unitary group representation, rather than being tied to a particular embedding…
Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block.…
We study measurement-induced symmetry-protected topological (SPT) order in a wide class of quantum random circuit models by combining calculations within the stabilizer formalism with tensor network simulations. We construct a family of…
While quantum low-density parity check (qLDPC) codes are a low-overhead means of quantum information storage, it is valuable for quantum codes to possess fault-tolerant features beyond this resource efficiency. In this work, we introduce…
Kliuchnikov, Maslov, and Mosca proved in 2012 that a $2\times 2$ unitary matrix $V$ can be exactly represented by a single-qubit Clifford+$T$ circuit if and only if the entries of $V$ belong to the ring $\mathbb{Z}[1/\sqrt{2},i]$. Later…
An algorithm which encodes the $L\times L$ 2D toric code logical state with a circuit of depth $2L+1$, using only local controlled-NOT($CX$) and Hadamard($H$) gates, is presented.
We introduce and demonstrate experimentally: (1) a framework called "gate set tomography" (GST) for self-consistently characterizing an entire set of quantum logic gates on a black-box quantum device; (2) an explicit closed-form protocol…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
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 address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…
In this work, we propose and study in depth a universal quantum computing architecture based on a quantum construction of transistors. Our teleportation-based quantum transistors, called ``telesistors'', are ground states of systems with…
The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are…
The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal $T$ gate play an important role in implementing a universal set of quantum operations. This paper…
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits.…
We introduce a novel type of quantum error correcting code, called the spinor code, based on spaces defined by total spin. The code is a nonstabilizer code, and is also a nonlinear quantum error correcting code, meaning that quantum…
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
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…