Related papers: Poly-locality in quantum computing
Locality is a central notion in modern physics, but different disciplines understand it in different ways. Quantum field theory focuses on relativistic locality, based on spacetime regions, while quantum information theory focuses circuit…
Shor's algorithm for factoring in polynomial time on a quantum computer\cite{Shor} gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled…
For a bipartite local quantum correlation, superlocality refers to the requirement for a larger dimension of the random variable in the classical simulation protocol than that of the quantum states that generate the correlations. In this…
We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local)…
The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would…
Subsystems of entangled quantum systems are not traditionally described in a local way. This paper begins to address the issue by constructing an explicit local hidden variable theory for quantum subsystems. The interpretation is based on a…
Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…
To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. Existing decoding systems fail to satisfy both of these…
We give an exposition of the hidden subgroup problem for dihedral groups from the point of view of the standard hidden subgroup quantum algorithm for finite groups. In particular, we recall the obstructions for strong Fourier sampling to…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's…
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n…
Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shor's algorithm in a…
Adapting a definition of Aaronson and Ambainis [Theory Comput. 1 (2005), 47--79], we call a quantum dynamics on a digraph "saturated Z-local" if the nonzero transition amplitudes specifying the unitary evolution are in exact correspondence…
Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic…
We show that in principle, $N$-partite unitary transformations can be perfectly discriminated under local measurement and classical communication (LOCC) despite of their nonlocal properties. Based on this result, some related topics,…
Polymer quantization is a non-standard representation of the quantum mechanics that inspired by loop quantum gravity. To study the associated statistical mechanics, one needs to find microstates' energies which are eigenvalues of the…
Wavelet transforms are widely used in various fields of science and engineering as a mathematical tool with features that reveal information ignored by the Fourier transform. Unlike the Fourier transform, which is unique, a wavelet…
Nonlocality is arguably one of the most fundamental and counterintuitive aspects of quantum theory. Nonlocal correlations could, however, be even more nonlocal than quantum theory allows, while still complying with basic physical principles…
We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally…