Related papers: Stabilizer rank bounds for magic-state orbits
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…
Composite quantum states can be classified by how they behave under local unitary transformations. Each quantum state has a stabilizer subgroup and a corresponding Lie algebra, the structure of which is a local unitary invariant. In this…
We investigate the action of the first three levels of the Clifford hierarchy on sets of mutually unbiased bases comprising the Ivanovic MUB and the Alltop MUBs. Vectors in the Alltop MUBs exhibit additional symmetries when the dimension is…
We investigate how non-stabilizer resources enable the emergence of quantum state designs within the projected ensemble. Starting from initial states with finite magic and applying resource-free Clifford circuits to scramble them, we…
Characterizing quantum magic -- the resource enabling computational advantage beyond stabilizer circuits -- is subtle in qubit systems because established measures can give conflicting information about the same state. We introduce C(rho),…
The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and 'nearly diagonal' semi-Clifford gates are particularly important:…
The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists…
We investigate non-stabilizerness, also known as ``magic,'' to understand criticality and exceptional points in non-Hermitian quantum many-body systems. Our focus is on parity-time ($\mathcal{PT}$) symmetric spin chains, specifically the…
Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure non-stabilizer states which can be distilled from certain mixed non-stabilizer states via Clifford group operations alone.…
Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study party-local Clifford (PLC)…
We propose protocols to implement non-Clifford logical gates between stabilizer codes by entangling into a non-Abelian topological order as an intermediate step. Generalizing previous approaches, we provide a framework that generates a…
We introduce the notion of dismagicker: non-Clifford unitary gate designed to reduce the non-stabilizerness (also called magic) of quantum many-body states. Although both entanglement and non-stabilizerness are fundamental quantum…
Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
We propose using even and odd Sch\"odinger cat states formed from coherent states of U(3) of an ensemble of qutrits with a symmetrical V-configuration (a qubit-disguised qutrit) to encode a logical qubit. These carefully engineered logical…
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 a non-stabilizerness resource theory for operators, which is dual to that describing states. We identify that the stabilizer R\'enyi entropy analog in operator space is a good magic monotone satisfying the usual conditions while…
Magic is a property of a quantum state that characterizes its deviation from a stabilizer state, serving as a useful resource for achieving universal quantum computation e.g., within schemes that use Clifford operations. In this work, we…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same. Despite the fact this settles the LU-LC conjecture, a sufficient…
Magic states are a scarce resource for two-dimensional qubit stabilizer codes. Magic state cultivation was recently proposed to reduce the cost of magic state preparation by measuring the transversal Clifford operator of the color code.…