Related papers: Exploring quantum weight enumerators from the $n$-…
We present a formalism based on tracking the flow of parity quantum information to implement algorithms on devices with limited connectivity without qubit overhead, SWAP operations or shuttling. Instead, we leverage the fact that entangling…
We introduce the concept of quantum weight as a fundamental property of insulating states of matter that is encoded in the ground-state static structure and measures quantum fluctuation in electrons' center of mass. We find a sum rule that…
Estimating delay tail probabilities in scheduling and load balancing systems is a critical but computationally prohibitive task due to the rarity of violation events. Quantum Amplitude Estimation (QAE) offers a generic quadratic reduction…
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…
Important quantum algorithm routines allow the implementation of specific quantum operations (a.k.a. gates) by combining basic quantum circuits with an iterative structure. In this structure, the number of repetitions of the basic circuit…
Fault-tolerant quantum computing relies on Quantum Error Correction, which encodes logical qubits into data and parity qubits. Error decoding is the process of translating the measured parity bits into types and locations of errors. To…
Readout errors are a significant source of noise for near term quantum computers. A variety of methods have been proposed to mitigate these errors using classical post processing. For a system with $n$ qubits, the entire readout error…
Driven by exploring the power of quantum computation with a limited number of qubits, we present a novel complete characterization for space-bounded quantum computation, which encompasses settings with one-sided error (unitary coRQL) and…
The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written…
To improve the performance of multi-qubit algorithms on quantum devices it is critical to have methods for characterizing non-local quantum errors such as crosstalk. To address this issue, we propose and test an extension to the analysis of…
Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the…
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 initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum…
Umbrella sampling efficiently yields equilibrium averages that depend on exploring rare states of a model by biasing simulations to windows of coordinate values and then combining the resulting data with physical weighting. Here, we…
Quantum entanglement is an essential resource for quantum technologies, and the controlled swap test provides a versatile tool for its detection and quantification. Here, we propose a SWAP-based entanglement witness that applies to…
We develop a novel method for measuring the similarity between complete weighted graphs, which are probed by means of discrete-time quantum walks. Directly probing complete graphs using discrete-time quantum walks is intractable due to the…
Quantum sensors are expected to be a prominent use-case of quantum technologies, but in practice, noise easily degrades their performance. Quantum sensors can for instance be afflicted with erasure errors. Here, we consider using quantum…
In quantum information theory, the accurate estimation of observables is pivotal for quantum information processing, playing a crucial role in compute and communication protocols. This work introduces a novel technique for estimating such…
While quantum computers provide exciting opportunities for information processing, they currently suffer from noise during computation that is not fully understood. Incomplete noise models have led to discrepancies between quantum program…