Related papers: Lower bound for the T count via unitary stabilizer…
A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
Magic states enable universal, fault-tolerant quantum computation within the stabilizer framework. Their non-stabilizerness supplies the resource needed to bypass the Eastin-Knill theorem while allowing fault-tolerant distillation. Although…
We investigate how noise impacts nonstabilizerness - a key resource for quantum advantage - in many-body qubit systems. While noise typically degrades quantum resources, we show that amplitude damping, a nonunital channel, can generate or…
Notions of nonstabilizerness, or "magic", quantify how non-classical quantum states are in a precise sense: states exhibiting low nonstabilizerness preclude quantum advantage. We introduce 'pseudomagic' ensembles of quantum states that,…
Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a…
Fault tolerant quantum computing relies on the ability to detect and correct errors, which in quantum error correction codes is typically achieved by projectively measuring multi-qubit parity operators and by conditioning operations on the…
The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error…
Quantum entanglement and quantum nonstabilizerness are fundamental resources that characterize distinct aspects of a quantum state: entanglement reflects non-local correlations, while nonstabilizerness quantifies the deviation from…
Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
We relate the the distinguishability of quantum states with their robustness of the entanglement, where the robustness of any resource quantifies how tolerant it is to noise. In particular, we identify upper and lower bounds on the…
Nonrelativistic bound states are studied using an effective field theory. Large logarithms in the effective theory can be summed using the velocity renormalization group. For QED, one can determine the structure of the leading and…
We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…
We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary…
Quantum discord quantifies quantum correlations beyond entanglement and assumes nonzero values, which are notoriously hard to compute, for almost all quantum states. Here we provide computable tight bounds for the quantum discord for…