相关论文: A Generalized Deletion Machine
We describe a simple way of characterizing the average fidelity between a unitary (or anti-unitary) operator and a general operation on a single qubit, which only involves calculating the fidelities for a few pure input states, and discuss…
The quantum Fourier transform (QFT) plays an important role in many known quantum algorithms such as Shor's algorithm for prime factorisation. In this paper we show that the QFT algorithm can, on a restricted set of input states, be…
Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire…
Quantum classification and hypothesis testing are two tightly related subjects, the main difference being that the former is data driven: how to assign to quantum states $\rho(x)$ the corresponding class $c$ (or hypothesis) is learnt from…
Quantum computers are known to provide speedups over classical state-of-the-art machine learning methods in some specialized settings. For example, quantum kernel methods have been shown to provide an exponential speedup on a learning…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
This work delves into the complexities of machine unlearning in the face of distributional shifts, particularly focusing on the challenges posed by non-uniform feature and label removal. With the advent of regulations like the GDPR…
In this work, we investigate the role of functionals of generalized fidelity measures in deriving quantum speed limits (QSLs) within a geometric approach. We establish a general theoretical framework and show that, once a specific…
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…
We present Quantum Cloning Machines (QCM) that transform N identical qubits into $M>N$ identical copies and we prove that the fidelity (quality) of these copies is optimal. The connection between cloning and measurement is discussed in…
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum…
A quantum measurement involves energy exchanges between the system to be measured and the measuring apparatus. Some of them involve energy losses, for example because energy is dissipated into the environment or is spent in recording the…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
Various fidelity measures can be defined between two quantum processes especially when at least one of them is non-unitary. In this paper we consider two such measures of state averaged process fidelity, put forward an efficient procedure…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
A quantum mechanical generalization of superstatistics is presented here based on the positive operator valued measure transformation property of the system density matrix. This procedure reveals that the origin of the fluctuating factors…
The optimal N to M ($M>N$) quantum cloning machines for the d-level system are presented. The unitary cloning transformations achieve the bound of the fidelity.
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can…
Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of…