参数化量子电路作为连续多变量分布的通用生成模型
Alice Barthe1,2,3, Michele Grossi1, Sofia Vallecorsa1
1Quantum Technology Initiative, CERN, Geneva, Switzerland.
概括
这项研究为产生连续概率分布的量子机器学习模型奠定了理论基础. 我们证明了电路的普遍性,并得出了资源界限,揭示了量子比特和测量之间的权衡,以获得量子优势.
科学领域:
- 量子计算是一种量子计算.
- 量子机器学习就是量子机器学习
背景情况:
- 参数化量子电路对于量子机器学习任务至关重要.
- 量子电路产生的机器产生离散分布,限制其应用到连续变量.
- 现有的模型将经典的随机性上传到连续分布的量子电路中,但它们的表达性尚未得到充分探索.
研究的目的:
- 为了正式化和建立量子电路模型的理论基础,产生连续的多变量分布.
- 为此任务证明变量量子电路架构的普遍性.
- 为了获得实现普遍性的资源界限,并探索实际应用.
主要方法:
- 证明特定变量量子电路架构的普遍性.
- 使用与Holevo相关的工具来得出密切的资源限制.
- 分析量子比特数量与所需测量之间的权衡.
主要成果:
- 证明了几个变量电路架构的普遍性,用于生成连续的多变量分布.
- 为了实现通用性,推导出了严格的资源限制,突出了量子比特数量和测量要求之间的权衡.
- 通过宽松的普遍性概念和实际用例,确定了量子优势的潜在领域.
结论:
- 正式化的理论基础支持在量子机器学习中使用量子电路进行连续分布.
- 资源界限为优化量子电路设计提供了指导,用于生成复杂的概率分布.
- 这项工作为探索生成模型和其他连续变量任务中的量子优势开辟了道路.
相关概念视频
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
127
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
127
Probability Distributions
7.9K
The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
7.9K
Multi-input and Multi-variable systems
150
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence...
In the absence...
150
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
101
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
101
Propagation of Uncertainty from Random Error
1.1K
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.1K
Random Variables
13.4K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
13.4K


