The even-denominator fractional quantum Hall (FQH) states, understood as topological superconductors of composite fermions, are predicted to support elementary quasiparticles (QPs) or quasiholes (QHs) obeying non-Abelian braid statistics. Using the microscopic framework of parton theory, we investigate many experimentally observed paired composite-fermion states and find that their elementary QPs and QHs in general bind to form Abelian molecules, thus obscuring non-Abelian braid statistics. An exception is the $ν=1/2$ state in wide quantum wells, where our calculations show free QPs or QHs; we thus identify this state as an especially promising candidate for realizing and studying non-Abelian braid statistics. We also indicate how the study of such bound states can help reveal the topological structure of the state.The even-denominator fractional quantum Hall (FQH) states, understood as topological superconductors of composite fermions, are predicted to support elementary quasiparticles (QPs) or quasiholes (QHs) obeying non-Abelian braid statistics. Using the microscopic framework of parton theory, we investigate many experimentally observed paired composite-fermion states and find that their elementary QPs and QHs in general bind to form Abelian molecules, thus obscuring non-Abelian braid statistics. An exception is the $ν=1/2$ state in wide quantum wells, where our calculations show free QPs or QHs; we thus identify this state as an especially promising candidate for realizing and studying non-Abelian braid statistics. We also indicate how the study of such bound states can help reveal the topological structure of the state.

arXiv:2610.12645Oct 8, 20260 citations

The table maker's quantum search

Benjamin C. A. Morrison, Stefanos Kourtis

We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target precision of $n$ digits for all possible precision- $n$ floating-point inputs in a given interval. For elementary functions $f$ related to the exponential function, quantum search takes time $\tilde O(2^{n/2} \log (1/δ))$ to return, with probability $1-δ$ , the hardness to round $f$ over all $n$ -bit floating-point inputs in a given binade. For periodic elementary functions in large binades, standalone quantum search yields an asymptotic speedup over the best known classical algorithms and heuristics. We then estimate the resources required for a fault-tolerant implementation of the proposed algorithm for the $\sin$ and $\cos$ functions in double precision. We find that, although the algorithm can in principle compete with the fastest known practical method for computing the hardness to round over all binades in the format, it requires qubit coherence times that are unrealistically long for present technology.We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target precision of $n$ digits for all possible precision-$n$ floating-point inputs in a given interval. For elementary functions $f$ related to the exponential function, quantum search takes time $\tilde O(2^{n/2} \log (1/δ))$ to return, with probability $1-δ$, the hardness to round $f$ over all $n$-bit floating-point inputs in a given binade. For periodic elementary functions in large binades, standalone quantum search yields an asymptotic speedup over the best known classical algorithms and heuristics. We then estimate the resources required for a fault-tolerant implementation of the proposed algorithm for the $\sin$ and $\cos$ functions in double precision. We find that, although the algorithm can in principle compete with the fastest known practical method for computing the hardness to round over all binades in the format, it requires qubit coherence times that are unrealistically long for present technology.

quant-pharXiv:2601.13306Jan 21, 20260 citations

Introduction to Quantum Statistics

William Band, Gordon Frank Newell

American Journal of PhysicsOct 1, 195665 citations

Efficient simulation of quantum-based searching

Tamás Varga, László Bacsárdi

The efficient search in unsorted database is extremely important for our everydays' applications. This type of search is useful in communication networks as well, since routing can be considered as a search in the database of the routing table. From the viewpoint of quantum computing, the not quantum-based solutions are named as classical. The search could be very time-consuming and computationally task if we need to solve it using classical algorithms, particularly for large data sets. This process can be accelerated and be more efficient by the application of quantum search algorithms. To investigate the quantum search, we have developed a Java-based system to simulate different quantum algorithms which are based on elementary quantum gates. In our model, we took into account the computation errors of the elementary quantum gates. We analyzed how these errors affect the efficiency of quantum search.The efficient search in unsorted database is extremely important for our everydays' applications. This type of search is useful in communication networks as well, since routing can be considered as a search in the database of the routing table. From the viewpoint of quantum computing, the not quantum-based solutions are named as classical. The search could be very time-consuming and computationally task if we need to solve it using classical algorithms, particularly for large data sets. This process can be accelerated and be more efficient by the application of quantum search algorithms. To investigate the quantum search, we have developed a Java-based system to simulate different quantum algorithms which are based on elementary quantum gates. In our model, we took into account the computation errors of the elementary quantum gates. We analyzed how these errors affect the efficiency of quantum search.

International Conference on Software, Telecommunications and Computer Networks (SoftCOM)Sep 1, 20142 citations

Introduction to quantum statistics

Keith S. Stowe

Cambridge University Press eBooksMay 10, 20070 citations

ν=1/2

state in wide quantum wells, where our calculations show free QPs or QHs; we thus identify this state as an especially promising candidate for realizing and studying non-Abelian braid statistics. We also indicate how the study of such bound states can help reveal the topological structure of the state.

n

digits for all possible precision-

n

floating-point inputs in a given interval. For elementary functions

f

related to the exponential function, quantum search takes time

\tilde O(2^{n/2} \log (1/δ))

to return, with probability

1-δ

, the hardness to round

f

over all

n

-bit floating-point inputs in a given binade. For periodic elementary functions in large binades, standalone quantum search yields an asymptotic speedup over the best known classical algorithms and heuristics. We then estimate the resources required for a fault-tolerant implementation of the proposed algorithm for the

\sin

and

\cos

functions in double precision. We find that, although the algorithm can in principle compete with the fastest known practical method for computing the hardness to round over all binades in the format, it requires qubit coherence times that are unrealistically long for present technology.