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Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL) - the fundamental precision bound set by quantum mechanics - is often…
Quantum machine learning (QML) is an emerging field that promises advantages such as faster training, improved reliability and superior feature extraction over classical counterparts. However, its implementation on quantum hardware is…
Universal fault-tolerant quantum computation requires overcoming the Eastin--Knill theorem on quantum error correction (QEC) codes that protect information from noise. This is often accomplished through strategies like magic state…
We present a generalization of the tilted Bell inequality for quantum [[n,k,d]] error-correcting codes and explicitly utilize the simplest perfect code, the [[5,1,3]] code, the Steane [[7,1,3]] code, and Shor's [[9,1,3]] code, to…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
The realistic coherent errors could induce very different behaviors compared with their stochastic counterparts in the quantum error correction (QEC) and fault tolerant quantum computation. Their impacts are believed to be very subtle, more…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
Collective coherent (CC) errors are inevitable, as every physical qubit undergoes free evolution under its kinetic Hamiltonian. These errors can be more damaging than stochastic Pauli errors because they affect all qubits coherently,…
In the ongoing race towards experimental implementations of quantum error correction (QEC), finding ways to automatically discover codes and encoding strategies tailored to the qubit hardware platform is emerging as a critical problem.…
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…
Exact quantum codes detecting a prescribed set of Pauli errors are approached through algebraic constructions--stabilizer, codeword-stabilized, permutation-invariant, topological, and related families. Geometrically, exact Pauli detection…
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system.…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
Encoding quantum information in a quantum error correction (QEC) code offers protection against decoherence and enhances the fidelity of qubits and gate operations. One of the fundamental challenges of QEC is to construct codes with…
Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
We investigate the most general notion of a private quantum code, which involves the encoding of qubits into quantum subsystems and subspaces. We contribute to the structure theory for private quantum codes by deriving testable conditions…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…