Related papers: Fast Stabiliser Simulation with Quadratic Form Exp…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
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…
Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply…
We propose an extension to the Pauli stabiliser formalism that includes fractional $2\pi/N$ rotations around the $Z$ axis for some integer $N$. The resulting generalised stabiliser formalism - denoted the XP stabiliser formalism - allows…
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…
The paper discusses work done to expand and extend the capabilities of the open-source QUCS circuit simulator through the implementation of a computationally efficient time-domain steady-state analysis module, supporting simulation of…
Quantum normalizer circuits were recently introduced as generalizations of Clifford circuits [arXiv:1201.4867]: a normalizer circuit over a finite Abelian group $G$ is composed of the quantum Fourier transform (QFT) over G, together with…
We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally [Lu et al., Phys. Rev. Lett. 119, 150502 (2017)]. That experiment utilized…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
We propose a heuristic method to obtain the approximate groundstate for a Hamiltonian in the qubit form, based on the stabilizer formalism. These states may serve as proper initial states for further refined computation. It would be…
We present a general protocol for stabilizer measurements and pumping in a system of N superconducting qubits. We assume always-on, equal dispersive couplings to a single mode of a high-Q microwave resonator in the ultra-strong dispersive…
According to the Gottesman-Knill theorem, a class of quantum circuits, namely the so-called stabilizer circuits, can be simulated efficiently on a classical computer. We introduce a new algorithm for this task, which is based on the…
Developing space- and time-efficient logical magic state preparation protocols will likely be an essential step towards building a large-scale fault-tolerant quantum computer. Motivated by this need, we introduce a scalable method for…
The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare…