Related papers: Qudit Noisy Stabilizer Formalism
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…
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…
We present novel algorithms to estimate outcomes for qubit quantum circuits. Notably, these methods can simulate a Clifford circuit in linear time without ever writing down stabilizer states explicitly. These algorithms outperform previous…
We consider protocols for estimating the parameter in a single-parameter unital qubit channel, assuming that the available initial states are highly mixed with very low purity. We compare two protocols, each invoking the channel once, via…
The stabiliser formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of N-qubit systems. That same formalism has important applications in the field of quantum error correcting codes, where…
Bell's Theorem started with two qubits, spins $1/2$. It is a no-go statement on classical (local causal) models of quantum correlations. Only after 25 years, it turned out that for three qubits the situation is even more mind boggling.…
Nonlocality is an essential concept that distinguishes quantum from classical models and has been extensively studied in systems of qubits. For higher-dimensional systems, certain results for their two-level counterpart, like Bell…
Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…
Quantum magic, quantified by nonstabilizerness, measures departures from stabilizer structure and underlies potential quantum speedups. We introduce an efficient classical framework for computing stabilizer R\'enyi entropies and stabilizer…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
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…
Bravyi and Gosset recently gave classical simulation algorithms for quantum circuits dominated by Clifford operations. These algorithms scale exponentially with the number of T-gate in the circuit, but polynomially in the number of qubits…
Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106…
Contextuality, a generalization of non-locality, has been proposed as the resource that provides the computational speed-up for quantum computation. For universal quantum computation using qudits, of odd-prime dimension, contextuality has…
We use a graphical representation of stabilizer states to describe, simply and efficiently, the effect of measurements of Pauli products on stabilizer states. This work complements our earlier work [Phys. Rev. A 77, 042307 (2008)], which…
The development of a framework for quantifying "non-stabiliserness" of quantum operations is motivated by the magic state model of fault-tolerant quantum computation, and by the need to estimate classical simulation cost for noisy…
We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of…
In this letter, we introduce a method to synthesize an $n$-qubit Clifford unitary $C$ from the stabilizer tableau of its inverse $C\dag$, using ancilla qubits and measurements. The procedure uses ancillary $|+\rangle$ states,…
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…
We discuss a method to adapt the codeword stabilized (CWS) quantum code framework to the problem of finding asymmetric quantum codes. We focus on the corresponding Pauli error models for amplitude damping noise and phase damping noise. In…