Parametrization of Quantum States and Channels

Parametrization and optimization of Gaussian non-Markovian unravelings for open quantum dynamics

We derive a family of Gaussian non-Markovian stochastic Schrödinger equations for the dynamics of open quantum systems. The different unravelings correspond to different choices of squeezed coherent states, reflecting different measurement schemes on the environment. Consequently, we are able to give a single shot measurement interpretation for the stochastic states and microscopic expressions for the noise correlations of the Gaussian process. By construction, the reduced dynamics of the open system does not depend on the squeezing parameters. They determine the non-hermitian Gaussian correla…

Contractions, Matrix Paramatrizations, and Quantum Information

In this note, we discuss dilation-theoretic matrix parametrizations of contractions and positive matrices. These parametrizations are then applied to some problems in quantum information theory. First we establish some properties of positive maps, or entanglement witnesses. Two further applications, concerning concrete dilations of completely positive maps, in particular quantum operations, are given.

Action Variable Quantization, Energy Quantization, and Time Parametrization

The additional information within a Hamilton-Jacobi representation of quantum mechanics is extra, in general, to the Schrödinger representation. This additional information specifies the microstate of $ψ$ that is incorporated into the quantum reduced action, $W$. Non-physical solutions of the quantum stationary Hamilton-Jacobi equation for energies that are not Hamiltonian eigenvalues are examined to establish Lipschitz continuity of the quantum reduced action and conjugate momentum. Milne quantization renders the eigenvalue $J$. Eigenvalues $J$ and $E$ mutually imply each other. Jacobi's theo…

量子代价函数集中性对参数化表达能力的依赖

The quantum cost function concentration dependency on the parametrization expressivity

本文解析证明量子变分电路参数化表达能力越强，代价函数越集中于依赖可观测量和量子比特数的值，并首次建立表达能力与代价函数集中性的显式联系。

最优一次性纠缠共享

Optimal one-shot entanglement sharing

该研究针对一次性量子信道纠缠共享场景，提出了求解最大保真度及最优输入的方法，证明了保真度的可乘性，还给出了带量子比特环境的量子比特信道的严格噪声参数化方案。

On Quantum Channel Estimation with Minimal Resources

We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically admissible solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.

有色噪声下门集断层扫描的微观参数化

Microscopic parametrizations for gate set tomography under coloured noise

本研究提出了一种在驱动相位时间相关噪声下量子门的微观参数化方法，利用滤波函数形式体系包含有限相关时间和非马尔可夫演化，从而减少了所需资源并实现了更高效的GST版本。

Selfcomplementary quantum channels

Selfcomplementary quantum channels are characterized by such an interaction between the principal quantum system and the environment that leads to the same output states of both interacting systems. These maps can describe approximate quantum copy machines, as perfect copying of an unknown quantum state is not possible due to the celebrated no-cloning theorem. We provide here a parametrization of a large class of selfcomplementary channels and analyze their properties. Selfcomplementary channels preserve some residual coherences and residual entanglement. Investigating some measures of non-Mar…

Quantum fluids in the Kaehler parametrization

In this paper we address the problem of the quantization of the perfect relativistic fluids formulated in terms of the Kähler parametrization. This fluid model describes a large set of interesting systems such as the power law energy density fluids, Chaplygin gas, etc. In order to maintain the generality of the model, we apply the BRST method in the reduced phase space in which the fluid degrees of freedom are just the fluid potentials and the fluid current is classically resolved in terms of them. We determine the physical states in this setting, the time evolution and the path integral formu…

Suboptimal quantum-error-correcting procedure based on semidefinite programming

In this paper, we consider a simplified error-correcting problem: for a fixed encoding process, to find a cascade connected quantum channel such that the worst fidelity between the input and the output becomes maximum. With the use of the one-to-one parametrization of quantum channels, a procedure finding a suboptimal error-correcting channel based on a semidefinite programming is proposed. The effectiveness of our method is verified by an example of the bit-flip channel decoding.

Anti-crossings and spectral gap during quantum adiabatic evolution

We aim to give more insights on adiabatic evolution concerning the occurrence of anti-crossings and their link to the spectral minimum gap $Δ_{min}$. We study in detail adiabatic quantum computation applied to a specific combinatorial problem called weighted max $k$-clique. A clear intuition of the parametrization introduced by V. Choi is given which explains why the characterization isn't general enough. We show that the instantaneous vectors involved in the anti-crossing vary brutally through it making the instantaneous ground-state hard to follow during the evolution. This result leads to a…

Positive-definite parametrization of mixed quantum states with deep neural networks

We introduce the Gram-Hadamard Density Operator (GHDO), a new deep neural-network architecture that can encode positive semi-definite density operators of exponential rank with polynomial resources. We then show how to embed an autoregressive structure in the GHDO to allow direct sampling of the probability distribution. These properties are especially important when representing and variationally optimizing the mixed quantum state of a system interacting with an environment. Finally, we benchmark this architecture by simulating the steady state of the dissipative transverse-field Ising model.…

Optimal quantum phase estimation in an atomic gyroscope based on Bose-Hubbard model

We investigate the optimal quantum state for an atomic gyroscope based on a three-site Bose-Hubbard model. In previous studies, various states such as the uncorrelated state, the BAT state and the NOON state are employed as the probe states to estimate the phase uncertainty. In this article, we present a Hermitian operator $\mathcal{H}$ and an equivalent unitary parametrization transformation to calculate the quantum Fisher information for any initial states. Exploiting this equivalent unitary parametrization transformation, we can seek the optimal state which gives the maximal quantum Fisher …

量子态的参数化与量子态鉴别问题

Parametrization of quantum states and the quantum state discrimination problem

本研究针对量子态鉴别问题，提出基于问题参数的满秩密度矩阵新参数化方式，定义对应经典对角密度矩阵，以二者保真度作为可鉴别性度量，该度量计算简便，可用于估计量子态集合的可鉴别程度。

Parameter estimation of quantum processes using convex optimization

A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of optimization variables, and formulate a semidefinite programming problem with a least squares objective function. Possible convex relations between the optimization variables are also taken into account to improve the estimation. Simulation case studies show, that the proposed method can significantly increase the accuracy of the parameter estimation, if th…

Structure and Parametrization of Generic Stochastic Maps of Density Matrices

The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence diagonalizable. The positivity of the density matrix does not make the associated supermatrix positive though. If the map itself is positive, it is called completely positive and they have a simple parame…

神经量子态的连续时间参数化用于量子动力学

Continuous-time parametrization of neural quantum states for quantum dynamics

本文提出了一种连续时间参数化的神经量子态方法，用于更高效地模拟量子动力学，通过线性组合时间基函数实现可微参数化，从而减少变分参数并提升模拟精度。

经典与量子复动力学

Classical and quantum complex dynamics

本研究通过相空间复参数化推广经典力学，构建支持非保守系统的复哈密顿形式体系，并提出可纳入非稳态物理过程的通用量子化方案。

Parametrization of spin-1 classical states

We give an explicit parametrization of the set of mixed quantum states and of the set of mixed classical states for a spin--1. Classical states are defined as states with a positive Glauber-Sudarshan P-function. They are at the same time the separable symmetric states of two qubits. We explore the geometry of this set, and show that its boundary consists of a two-parameter family of ellipsoids. The boundary does not contain any facets, but includes straight-lines corresponding to mixtures of pure classical states.

Jarlskog's Parametrization of Unitary Matrices and Qudit Theory

In the paper (math-ph/0504049) Jarlskog gave an interesting simple parametrization to unitary matrices, which was essentially the canonical coordinate of the second kind in the Lie group theory (math-ph/0505047). In this paper we apply the method to a quantum computation based on multi-level system (qudit theory). Namely, by considering that the parametrization gives a complete set of modules in qudit theory, we construct the generalized Pauli matrices which play a central role in the theory and also make a comment on the exchange gate of two-qudit systems. Moreover we give an explicit constru…

Robustness of quantum key distribution with discrete and continuous variables to channel noise

We study the robustness of quantum key distribution protocols using discrete or continuous variables to the channel noise. We introduce the model of such noise based on coupling of the signal to a thermal reservoir, typical for continuous-variable quantum key distribution, to the discrete-variable case. Then we perform a comparison of the bounds on the tolerable channel noise between these two kinds of protocols using the same noise parametrization, in the case of implementation which is perfect otherwise. Obtained results show that continuous-variable protocols can exhibit similar robustness …

过程矩阵的框架视角：从坐标参数化到时空表示

Frame perspectives for process matrices: from coordinate parametrization to spacetime representation

本文研究了过程矩阵框架中框架视角的实现与转换，指出纯过程的因果参考框架和时间非局域子系统形式化可视为单一中性高阶对象的坐标参数化。通过选择操作性分层将过程赋予额外框架数据，现有否定结果得到明确界定，并通过量子开关构建了转换视角的单位元映射。

Proper time derivatives in quantum mechanics

Several quantum proper time derivatives are obtained from the Beck one in the usual framework of relativistic quantum mechanics (spin 1/2 case). The ``scalar Hamiltonians'' of these derivatives should be thought of as the conjugate variables of the proper time. Then, the Hamiltonians would play the role of mass operators, suggesting the formulation of an adequate extended indefinite mass framework. We propose and briefly develop the framework corresponding to the Feynman parametrization of the Dirac equation. In such a case we derive the other parametrizations known in the literature, linking …

Almost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics

We propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.

A variational lower bound on the ground state of a many-body system and the squaring parametrization of density matrices

A variational upper bound on the ground state energy $E_{\rm gs}$ of a quantum system, $E_{\rm gs} \leqslant \langle Ψ|H| Ψ\rangle$, is well-known (here $H$ is the Hamiltonian of the system and $Ψ$ is an arbitrary wave function). Much less known are variational {\it lower} bounds on the ground state. We consider one such bound which is valid for a many-body translation-invariant lattice system. Such a lattice can be divided into clusters which are identical up to translations. The Hamiltonian of such a system can be written as $H=\sum_{i=1}^M H_i$, where a term $H_i$ is supported on the $i$'th…

A complete POVM description of multi-channel quantum electro-optic sampling with monochromatic field modes

We propose a multi-channel version of quantum electro-optic sampling involving monochromatic field modes. It allows for multiple simultaneous measurements of arbitrarily many $\hat{X}$ and $\hat{Y}$ field-quadrature for a single quantum-state copy, while independently tuning the interaction strengths at each channel. In contrast to standard electro-optic sampling, the sampled mid-infrared (MIR) mode undergoes a nonlinear interaction with multiple near-infrared (NIR) pump beams. We present a complete positive operator-valued measure (POVM) description for quantum states in the MIR mode. The pro…

非厄米散射中倏逝隧穿与传输延迟的复时间参数化

Complex-Time Parametrization of Evanescent Tunneling and Transmission Delay in non-Hermitian Scattering

本文提出复时间参数化方法解决量子隧穿中虚动量的反常问题，证明隧穿受光速限制，且在微波散射实验中得到类比验证。

Random Sampling of Quantum States: A Survey of Methods

The numerical generation of random quantum states (RQS) is an important procedure for investigations in quantum information science. Here we review some methods that may be used for performing that task. We start by presenting a simple procedure for generating random state vectors, for which the main tool is the random sampling of unbiased discrete probability distributions (DPD). Afterwards the creation of random density matrices is addressed. In this context we first present the standard method, which consists in using the spectral decomposition of a quantum state for getting RQS from random…

通过位点能量参数化实现自旋链中的准完美态传输

Quasi-Perfect State Transfer in Spin Chains via Parametrization of On-Site Energies

本文通过参数化位点能量并利用遗传算法，实现了自旋链中的准完美态传输，为高保真量子信息传输提供了替代方案。

Complex Time Evolution of Open Quantum Systems

We combine, in a single set-up,the complex time parametrization in path integration, and the closed time formalism of non-equilibrium field theories to produce a compact representation of the time evolution of the reduced density matrix. In this framework we introduce a cluster-type expansion that facilitates perturbative and non-perturbative calculations in the realm of open quantum systems. The technical details of some very simple examples are discussed.

限制在芯片架构上可保持量子神经网络精度

Restricting to the chip architecture maintains the quantum neural network accuracy

本文研究量子芯片架构对变分量子算法的影响，证明当参数化趋近2-design时代价函数收敛至平均值，从而提出直接利用芯片固有架构定义参数化，以减少swap门、降低电路深度和错误。

Quantum Codes from Neural Networks

We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we initiate the study of neural network states in quantum information-processing tasks. We demonstra…

Pade approximation of the S-matrix as a way of locating quantum resonances and bound states

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc.) provided that there is a way of obtaining the S-matrix (or scattering phase-shifts) at real collision en…

Exploiting symmetry in variational quantum machine learning

Variational quantum machine learning is an extensively studied application of near-term quantum computers. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes an inductive bias relevant to the learning task. However, precious little is known about guiding principles for the construction of suitable parametrizations. In this work, we holistically explore when and how symmetries of the learning problem can be exploited to construct quantum learning models with outcomes invariant under the symmetry of the learning ta…

神经化费米子张量网络用于量子多体系统

Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems

本文提出了一种神经化费米子张量网络状态（NN-fTNS），通过局部张量的配置依赖神经网络变换引入非线性，从而提升表达能力，实验表明其在地面态能量上相比纯fTNS有数量级提升，并实现了线性标度的构造。