量子计算的一致性与等效原理

有限能量下连续变量与离散变量基于门的量子计算机的等价性

Equivalence of continuous- and discrete-variable gate-based quantum computers with finite energy

本文建立了一个严格框架，将基于门的连续变量量子算法高效映射到离散变量量子处理器上，证明了在有限能量约束下两种计算范式等价。

Total and Partial Computation in Categorical Quantum Foundations

This paper uncovers the fundamental relationship between total and partial computation in the form of an equivalence of certain categories. This equivalence involves on the one hand effectuses, which are categories for total computation, introduced by Jacobs for the study of quantum/effect logic. On the other hand, it involves what we call FinPACs with effects; they are finitely partially additive categories equipped with effect algebra structures, serving as categories for partial computation. It turns out that the Kleisli category of the lift monad (-)+1 on an effectus is always a FinPAC wit…

经典Minicrypt等价性在量子计算经典通信模型中的崩溃

The Breakdown of Classical Minicrypt Equivalences in the Quantum-Computation Classical-Communication Model

本文通过预言机分离证明，在量子计算经典通信模型中，经典Minicrypt中签名与单向函数及比特承诺的等价关系崩溃，并开发了随机相位态分析技术。

Finite set of invariants to characterize local Clifford equivalence of stabilizer states

The classification of stabilizer states under local Clifford (LC) equivalence is of particular importance in quantum error-correction and measurement-based quantum computation. Two stabilizer states are called LC equivalent if there exists a local Clifford operation which maps the first state to the second. We present a finite set of invariants which completely characterizes the LC equivalence class of any stabilizer state. Our invariants have simple descriptions within the binary framework in which stabilizer states are usually described.

Equivalence of approximate Gottesman-Kitaev-Preskill codes

The Gottesman-Kitaev-Preskill (GKP) quantum error correcting code attracts much attention in continuous variable (CV) quantum computation and CV quantum communication due to the simplicity of error correcting routines and the high tolerance against Gaussian errors. Since the GKP code state should be regarded as a limit of physically meaningful approximate ones, various approximations have been developed until today, but explicit relations among them are still unclear. In this paper, we rigorously prove the equivalence of these approximate GKP codes with an explicit correspondence of the parame…

Equivalence classes and local asymptotic normality in system identification for quantum Markov chains

We consider the problems of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. On the identifiability question, we show that the knowledge of the output state completely fixes the dynamics up to a `coordinate transformation' consisting of a multiplication by a phase and a unitary conjugation of the Kraus operators. When the dynamics depends on an unknown parameter, we show that the latter can be estimated at the `standard' rate $n^{-1/2}$, and give an explicit expression of the (asymptotic) quantum…

Consistency of the Adiabatic Theorem

The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation is discussed.