Related papers: Improved Stabilizer Estimation via Bell Difference…
Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here…
In the realm of fault-tolerant quantum computing, stabilizer operations play a pivotal role, characterized by their remarkable efficiency in classical simulation. This efficiency sets them apart from non-stabilizer operations within the…
(Abridged abstract.) In this thesis we introduce new models of quantum computation to study the emergence of quantum speed-up in quantum computer algorithms. Our first contribution is a formalism of restricted quantum operations, named…
Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…
Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of $n$-qubit circuits rely on efficient procedures for…
Quantum superpositions of macroscopically distinct classical states, so-called Schr\"{o}dinger cat states, are a resource for quantum metrology, quantum communication, and quantum computation. In particular, the superpositions of two…
$k$-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of $k$-uniform states, at scale, faces major obstacles:…
Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without…
An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and…
We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…
We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group,…
Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge…
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…
Recent advances in quantum hardware are bringing fault-tolerant quantum computing (FTQC) closer to reality. In the early stage of FTQC, however, the numbers of available logical qubits and high-fidelity $T$ gates remain limited, making it…
Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a non-scalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
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…
We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation $T$ on all logical qubits. The new codes are used to construct protocols for distilling…