Memory is a precious commodity across many different areas. I will present two ways in which quantum devices can lower memory requirements. The first application is the simulation of stochastic processes, i.e. processes that exhibit some randomness. We have experimentally realized quantum simulations of classical stochastic processes. Our simulators have lower memory requirements than the optimal classical simulators. The second type of quantum device I will discuss is a quantum autoencoder, which autonomously learns how to compress quantum data. We have developed and experimentally realized a photonic quantum autoencoder that is trained based on sets of quantum states.
Memory is a precious commodity across many different areas. I will present two ways in which quantum devices can lower memory requirements. The first application is the simulation of stochastic processes, i.e. processes that exhibit some randomness. We have experimentally realized quantum simulations of classical stochastic processes. Our simulators have lower memory requirements than the optimal classical simulators. The second type of quantum device I will discuss is a quantum autoencoder, which autonomously learns how to compress quantum data. We have developed and experimentally realized a photonic quantum autoencoder that is trained based on sets of quantum states.
With quantum resources a precious commodity, their efficient use is highly desirable. Quantum autoencoders have been proposed as a way to reduce quantum memory requirements. Generally, an autoencoder is a device that uses machine learning to compress inputs, that is, to represent the input data in a lower-dimensional space. Here, we experimentally realize a quantum autoencoder, which learns how to compress quantum data using a classical optimization routine. We demonstrate that when the inherent structure of the dataset allows lossless compression, our autoencoder reduces qutrits to qubits with low error levels. We also show that the device is able to perform with minimal prior information about the quantum data or physical system and is robust to perturbations during its optimization routine.
Abstract Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the stochastic process, which requires a memory system to propagate correlations between the past and future of the process. Here, we introduce a method of lossy quantum dimension reduction that allows this memory to be compressed, not just beyond classical limits, but also beyond current state-of-the-art quantum stochastic sampling approaches. We investigate the trade-off between the saving in memory resources from this compression, and the distortion it introduces. We show that our approach can be highly effective in low distortion compression of both Markovian and strongly non-Markovian processes alike. We further discuss the application of our results to quantum stochastic modelling more broadly.
Abstract Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x , to map x to a lower dimensional point y such that x can likely be recovered from y . The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.
Stochastic processes underlie a vast range of natural and social phenomena.Some processes such as atomic decay feature intrinsic randomness, whereas other complex processes, e.g., traffic congestion, are effectively probabilistic because we cannot track all relevant variables.To simulate a stochastic system's future behavior, information about its past must be stored, and thus memory is a key resource.Quantum information processing promises a memory advantage for stochastic simulation.Here, we report the first experimental demonstration that a quantum stochastic simulator can encode the required information in fewer dimensions than any classical simulator, thereby achieving a quantum advantage in minimal memory requirements using an individual simulator.This advantage is in contrast to recent proof-of-concept experiments, where the memory saving would only become accessible in the limit of a large number of parallel simulations.In those examples, the minimal memory registers of individual quantum simulators had the same dimensionality as their classical counterparts.Our photonic experiment thus establishes the potential of new, practical resource savings in the simulation of complex systems.
Since its inception, quantum information processing (QIP) has been branched into many new directions. As well as well-known applications such as teleportation and metrology, researchers are beginning to investigate interdisciplinary areas such as quantum machine learning. One of the interesting areas is where quantum information science meets stochastic modelling, from the field of complexity science. Recently, it has been shown theoretically that, for simulating classical systems, quantumassisted models and simulators are more efficient in terms of memory storage they require to do simulations, compared with classical computers. That is, for most systems, classical simulators demand an excessive amount of memory storage, while quantum simulators can do the same simulation with less memory. The main focus of this thesis is on experimental realisation of quantum simulators that are capable of simulating stochastic processes with a reduced amount of memory. To implement the (nearly) exact simulation of stochastic processes using quantum simulators, it is essential to have low-noise state preparation, robust unitary operations, and high-precision read-out. These requirements, and the flexibility and precision of photonic quantum optics, make photonics the ideal system for developing the science of this new quantum advantage and for making strides towards its technological realisation. In the context of stochastic simulation, I have experimentally studied three key problems that serve as stepping stones in advancing this new field. In the first experiment, an error-tolerant quantum simulator was designed, and realised to simulate a 1D Ising spin chain, using internal states that store less information than the corresponding classical approach. Furthermore, an interesting and fundamental phenomenon named the ambiguity of simplicity is witnessed. This is the inconsistency that we observe in the order of relative complexity of two systems when we change the simulators from classical to quantum. In the second experiment, a quantum simulator was built that can simulate classical processes for more than one step of the simulation at a time, storing the information from multiple steps coherently. In the third experiment, a new type of quantum memory advantage, which is based on the dimensionality of the memory register, rather than on information entropy measure, is demonstrated. This advantage is realisable in a single simulator, in contrast to previous works. Realising the dimensionality memory advantage in practical applications does not rely on running multiple simulators in parallel.In the field of optical QIP, realising an ideal single-photon source has been a longstanding challenge. In another part of my PhD, I have worked on a source that aims to tackle some of the existing issues in this context. We built a source of high-quality entangled photons with a high heralding efficiency, which has the potential to be used in multi-photon experiments. This source was also essential to demonstrate a fundamental task in quantum non-locality, one-way steering, which was performed conclusively for the first time.
As a ubiquitous aspect of modern information technology, data compression has a wide range of applications. Therefore, a quantum autoencoder which can compress quantum information into a low-dimensional space is fundamentally important to achieve automatic data compression in the field of quantum information. Such a quantum autoencoder can be implemented through training the parameters of a quantum device using classical optimization algorithms. In this paper, we demonstrate the condition of achieving a perfect quantum autoencoder and theoretically prove that a quantum autoencoder can losslessly compress high-dimensional quantum information into a low-dimensional space (also called latent space) if the number of maximum linearly independent vectors from input states is no more than the dimension of the latent space. Also, we experimentally realize a universal two-qubit unitary gate and design a quantum autoencoder device by applying a machine learning method. Experimental results demonstrate that our quantum autoencoder is able to compress two two-qubit states into two one-qubit states. Besides compressing quantum information, the quantum autoencoder is used to experimentally discriminate two groups of nonorthogonal states.