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Quantum fidelity estimation is essential for benchmarking quantum states and processes on noisy quantum devices. While stabilizer operations form the foundation of fault-tolerant quantum computing, non-stabilizer resources further enable…
Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
Bell-state measurement (BSM) on entangled states shared between quantum repeaters is the fundamental operation used to route entanglement in quantum networks. Performing BSMs on Werner states shared between repeaters leads to exponential…
We develop a procedure for distilling magic states used in universal quantum computing that requires substantially fewer initial resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes that…
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…
Finding ways to quantify magic is an important problem in quantum information theory. Recently Leone, Oliviero and Hamma introduced a class of magic measures for qubits, the stabilizer entropies of order $\alpha$, to aid in studying…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
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…
Minimizing both experimental effort and consumption of valuable quantum resources in state estimation is vital in practical quantum information processing. Here, we explore characterizing states as an additional benefit of the entanglement…
Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
We introduce a mixed-state magic criterion, the Triangle Criterion, which plays a role for magic analogous to the Positive Partial Transposition (PPT) Criterion for entanglement: it combines strong detection capability, a clear geometric…
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits.…
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
Magic states are fundamental building blocks on the road to fault-tolerant quantum computing. CSS codes play a crucial role in the construction of magic distillation protocols. Previous work has cast quantum computing with magic states for…
Magic refers to the degree of "quantumness" in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a…
We show that using qutrits rather than qubits leads to a substantial reduction in the overhead cost associated with an approach to fault-tolerant quantum computing known as magic state distillation. We construct a family of $[[9m-k, k,…