Related papers: Stabilizer rank bounds for magic-state orbits
We characterize control of a qutrit implemented in the lowest three energy levels of a capacitively-shunted flux-biased superconducting circuit. Randomized benchmarking over the qutrit Clifford group yields an average fidelity of 98.89…
In most stabilizer-based quantum computing schemes, so-called magic states are a necessary resource for implementing non-transversal quantum gates. With the resource theory of magic, it is possible to analyze and quantify the generation of…
First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which…
Magic or non-stabilizerness is a resource for quantum computing that has been extensively studied in qudit networks. It describes the degree to which Clifford gates cannot generate a given state, capturing the advantage of quantum over…
We start by studying the subgroup structures underlying stabilizer circuits. Then we apply our results to provide two normal forms for stabilizer circuits. These forms are computed by induction using simple conjugation rules in the Clifford…
We consider four-dimensional qudits as qubit pairs and their qudit Pauli operators as qubit Clifford operators. This introduces a nesting, $C_1^2 \subset C_2^4 \subset C_3^2$, where $C_n^m$ is the $n$th level of the $m$-dimensional qudit…
Stabilizer states are fundamental families of quantum states with crucial applications such as error correction, quantum computation, and simulation of quantum circuits. In this paper, we study the problem of testing how close or far a…
In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of…
Stabilizer entropies (SEs) are measures of nonstabilizerness or `magic' that quantify the degree to which a state is described by stabilizers. SEs are especially interesting due to their connections to scrambling, localization and property…
Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum…
Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then…
It is well known that local gates have smaller error than non-local gates. For this reason it is natural to make two states equivalent if they differ by a local gate. Since two states that differ by a local gate have the same entanglement…
Nonstabilizerness, or magic, constitutes a fundamental resource for quantum computation and a crucial ingredient for quantum advantage. Recent progress has substantially advanced the characterization of magic in many-body quantum systems,…
Clifford codes can be understood as a generalization of stabilizer codes. To show the existence of a true Clifford code which is better than any stabilizer code is a well known open problem in the theory of Clifford codes. One of the main…
Magic state distillation (MSD) is a purification protocol that plays a central role in fault tolerant quantum computation. Repeated iteration of the steps of a MSD protocol, generates pure single non-stabilizer states, or magic states, from…
Stabilizer circuits arise in almost every area of quantum computation and communication, so there is interest in studying them from an information-theoretic perspective, i.e. as quantum channels. We consider several natural approaches to…
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…
Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here…
Stabilizer states admit compact classical descriptions, but many downstream tasks still require their full amplitude vectors. Since the output itself has size $2^n$, the main algorithmic question is whether one can materialize an $n$-qubit…
We examine the SLOCC classification of the (non-normalized) pure states of four qubits obtained by F. Verstraete et al. The rigorous proofs of their basic results are provided and necessary corrections implemented. We use Invariant Theory…