Related papers: The Clifford hierarchy for one qubit or qudit
We use our Clifford algebra technique, that is nilpotents and projectors which are binomials of the Clifford algebra objects $\gamma^a$ with the property $\{\gamma^a,\gamma^b\}_+ = 2 \eta^{ab}$, for representing quantum gates and quantum…
We explore the implementation of pseudo-random single-qubit rotations and multi-qubit pseudo-random circuits constructed only from Clifford gates and the T-gate, a phase rotation of pi/4. Such a gate set would be appropriate for…
We provide and experimentally demonstrate an accreditation protocol that upper-bounds the variation distance between noisy and noiseless probability distributions of the outputs of arbitrary quantum computations. We accredit the outputs of…
Assuming the polynomial hierarchy is infinite, we prove a sufficient condition for determining if uniform and polynomial size quantum circuits over a non-universal gate set are not efficiently classically simulable in the weak…
We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance…
Clifford Circuit Initializaton improves on initial guess of parameters on Parametric Quantum Circuits (PQCs) by leveraging efficient simulation of circuits made out of gates from the Clifford Group. The parameter space is pre-optimized by…
Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set…
IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement…
We investigate quantum circuits built from arbitrary single-qubit operations combined with programmable all-to-all multiqubit entangling gates that are native to, among other systems, trapped-ion quantum computing platforms. We report a…
We implement a complete randomized benchmarking protocol on a system of two superconducting qubits. The protocol consists of randomizing over gates in the Clifford group, which experimentally are generated via an improved two-qubit…
We study the resources required to achieve universal quantum computing via the gate sets that provide the fundamental instructions from which quantum algorithms are built. While single-gate universal sets are known, they rely on precisely…
We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each…
We present a universal quantum computing architecture which combines the measurement-driven aspect of MBQC with the circuit model's algorithm dependent generation of qubit entanglement. Our architecture, which we call QGATE, is tailored for…
The Clifford group is a fundamental structure in quantum information with a wide variety of applications. We discuss the tensor representations of the $q$-qubit Clifford group, which is defined as the normalizer of the $q$-qubit Pauli group…
Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of $n$-qubit circuits rely on efficient procedures for…
A quantum computer has the potential to effciently solve problems that are intractable for classical computers. Constructing a large-scale quantum processor, however, is challenging due to errors and noise inherent in real-world quantum…
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…
Quantum teleportation is a powerful protocol with applications in several schemes of quantum communication, quantum cryptography and quantum computing. The present work shows the required conditions for a two-qubit quantum gate to be…
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…
The representation theory of the Clifford group is playing an increasingly prominent role in quantum information theory, including in such diverse use cases as the construction of protocols for quantum system certification, quantum…