Nonstabilizerness (magic) is the quantum resource that, together with stabilizer operations, makes universal quantum computation possible. It appears in fault-tolerant codes and topological order. However, quantifying nonstabilizerness is difficult. The standard measure sums over exponentially many Pauli operators, and for quantum codes no quantitative theory has been available. We resolve this by a structural observation: the Clifford sector carries no magic and can be removed by a Clifford transformation, leaving an order-three object whose magic is an exactly evaluable fourth moment. Removing this inert background yields closed forms for several code families: a formula for all Dicke states, reducing a 100-qubit case from $4^{100}$ terms to a short binomial sum; a bound for cubic-phase codes (twisted quantum doubles and non-Abelian topological order), saturated only by the $D_4$ code; and a cyclic/zero criterion for group multiplication states. Together these results reduce the computation of nonstabilizerness for a broad class of codes to finite classical counting problems, and identify the maximally magical codes among them.
Fault-tolerant quantum computation requires non-Clifford gates, which stabilizer codes cannot supply transversally. Non-stabilizer codes are the natural place to look for them, yet no quantitative theory of the nonstabilizerness (or magic) carried by such a code has existed. We develop one for codeword-stabilized (CWS)...
Stabilizer operations describe a fragment of quantum theory that is known to be efficiently classically simulable, thanks to the Gottesman-Knill theorem. For this reason, nonstabilizer resources such as magic states are necessary for universal quantum computation. Interestingly, the operational and axiomatic approaches...
Leonardo Vaglini, Nasra Daher Ahmed, Ravi Kunjwal· 0 citations
Nonstabilizerness is a necessary resource for quantum systems to lie beyond the classically simulable regime. With the advent of stabilizer $\alpha$-R\'enyi entropies, nonstabilizerness has also become a many-body diagnostic, complementary to entanglement. While deciding whether an arbitrary quantum state has nonstabil...
Magic, or nonstabilizerness, is the resource that lifts Clifford circuits to universal quantum computation and has become a standard diagnostic of many-body states. For a state shared between two parties, however, a basic question has remained open: how much of the magic resides in the correlations between the parties...
The $n$-qubit Pauli group is an essential ingredient to most quantum applications, from computing and error correction to benchmarking and simulation. Despite comprising merely a discrete set of operators, it exhibits many quintessential features of quantum theory, including contextuality, which has been identified as...
We construct a two-parameter family of single-error-correcting seven-ququart codes with transversal $\tilde{A_7}$ symmetry, realizing the finite component of a two-qubit super-golden gate set. These $((7,4,3))_4$ codes encode two logical qubits and support non-Clifford operations by applying the same gate to each physi...
Ian Teixeira· 0 citations
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