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arXiv:2112.03643

QKSA: Quantum Knowledge Seeking Agent -- resource-optimized reinforcement learning using quantum process tomography

Aritra Sarkar, Zaid Al-Ars, Harshitta Gandhi, Koen Bertels

Published Dec 7, 2021• 1 citation

Abstract

In this research, we extend the universal reinforcement learning (URL) agent models of artificial general intelligence to quantum environments. The utility function of a classical exploratory stochastic Knowledge Seeking Agent, KL-KSA, is generalized to distance measures from quantum information theory on density matrices. Quantum process tomography (QPT) algorithms form the tractable subset of programs for modeling environmental dynamics. The optimal QPT policy is selected based on a mutable cost function based on algorithmic complexity as well as computational resource complexity. Instead of Turing machines, we estimate the cost metrics on a high-level language to allow realistic experimentation. The entire agent design is encapsulated in a self-replicating quine which mutates the cost function based on the predictive value of the optimal policy choosing scheme. Thus, multiple agents with pareto-optimal QPT policies evolve using genetic programming, mimicking the development of physical theories each with different resource trade-offs. This formal framework is termed Quantum Knowledge Seeking Agent (QKSA). Despite its importance, few quantum reinforcement learning models exist in contrast to the current thrust in quantum machine learning. QKSA is the first proposal for a framework that resembles the classical URL models. Similar to how AIXI-tl is a resource-bounded active version of Solomonoff universal induction, QKSA is a resource-bounded participatory observer framework to the recently proposed algorithmic information-based reconstruction of quantum mechanics. QKSA can be applied for simulating and studying aspects of quantum information theory. Specifically, we demonstrate that it can be used to accelerate quantum variational algorithms which include tomographic reconstruction as its integral subroutine.

DOI: 10.48550/arxiv.2112.03643

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In this research, we extend the universal reinforcement learning (URL) agent models of artificial general intelligence to quantum environments. The utility function of a classical exploratory stochastic Knowledge Seeking Agent, KL-KSA, is generalized to distance measures from quantum information theory on density matrices. Quantum process tomography (QPT) algorithms form the tractable subset of programs for modeling environmental dynamics. The optimal QPT policy is selected based on a mutable cost function based on algorithmic complexity as well as computational resource complexity. Instead of Turing machines, we estimate the cost metrics on a high-level language to allow realistic experimentation. The entire agent design is encapsulated in a self-replicating quine which mutates the cost function based on the predictive value of the optimal policy choosing scheme. Thus, multiple agents with pareto-optimal QPT policies evolve using genetic programming, mimicking the development of physical theories each with different resource trade-offs. This formal framework is termed Quantum Knowledge Seeking Agent (QKSA). Despite its importance, few quantum reinforcement learning models exist in contrast to the current thrust in quantum machine learning. QKSA is the first proposal for a framework that resembles the classical URL models. Similar to how AIXI-tl is a resource-bounded active version of Solomonoff universal induction, QKSA is a resource-bounded participatory observer framework to the recently proposed algorithmic information-based reconstruction of quantum mechanics. QKSA can be applied for simulating and studying aspects of quantum information theory. Specifically, we demonstrate that it can be used to accelerate quantum variational algorithms which include tomographic reconstruction as its integral subroutine.

Reinforcement learning is a subfield of machine learning that studies how an agent interacts with an environment in order to extract as large a reward as possible. A standard approach to study such interaction is through Markov Decision Processes (MDPs) and the task of choosing an optimal policy --- a function that tells the agent which action to take. In this work, we study two types of MDPs --- finite-horizon and infinite-horizon discounted --- and propose new quantum algorithms for computing approximate optimal policies. Our quantum algorithms are based on a new combination of standard value iteration and quantum subroutines like quantum mean estimation and quantum maximum finding, overall enhanced with techniques from sample-optimal classical algorithms. Our resulting query complexities improve upon previous works, thus approaching already established quantum lower bounds.

In this article we present the motivation and the core thesis towards the implementation of a Quantum Knowledge Seeking Agent (QKSA). QKSA is a general reinforcement learning agent that can be used to model classical and quantum dynamics. It merges ideas from universal artificial general intelligence, constructor theory and genetic programming to build a robust and general framework for testing the capabilities of the agent in a variety of environments. It takes the artificial life (or, animat) path to artificial general intelligence where a population of intelligent agents are instantiated to explore valid ways of modelling the perceptions. The multiplicity and survivability of the agents are defined by the fitness, with respect to the explainability and predictability, of a resource-bounded computational model of the environment. This general learning approach is then employed to model the physics of an environment based on subjective observer states of the agents. A specific case of quantum process tomography as a general modelling principle is presented. The various background ideas and a baseline formalism are discussed in this article which sets the groundwork for the implementations of the QKSA that are currently in active development.

Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an optimal policy for a

γ

-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy (

π^*

), the optimal value function (

v^*

), and the optimal

Q

-function (

q^*

), assuming the algorithms can access samples from the environment in quantum superposition. This assumption is justified whenever there exists a simulator for the environment; for example, if the environment is a video game or some other program. Our quantum algorithms, inspired by value iteration, achieve quadratic speedups over the best-possible classical sample complexities in the approximation accuracy (

ε

) and two main parameters of the MDP: the effective time horizon (

\frac{1}{1-γ}

) and the size of the action space (

A

). Moreover, we show that our quantum algorithm for computing

q^*

is optimal by proving a matching quantum lower bound.

Quantum process tomography (QPT) is a fundamental tool for fully characterizing quantum systems. It relies on querying a set of quantum states as input to the quantum process. Previous QPT methods typically employ a straightforward strategy for randomly selecting quantum states, overlooking differences in informativeness among them. In this work we propose a general active learning (AL) framework that adaptively selects the most informative subset of quantum states for reconstruction. We design and evaluate various AL algorithms and provide practical guidelines for selecting suitable methods in different scenarios. In particular, we introduce a learning framework that leverages the widely used variational quantum circuits to perform the QPT task and integrate our AL algorithms into the query step. We demonstrate our algorithms by reconstructing the unitary quantum processes resulting from random quantum circuits with up to seven qubits. Numerical results show that our AL algorithms achieve significantly improved reconstruction and the improvement increases with the size of the underlying quantum system. Our work opens new avenues for further advancing existing QPT methods.

In recent years, advancements in brain science and neuroscience have significantly influenced the field of computer science, particularly in the domain of reinforcement learning (RL). Drawing insights from neurobiology and neuropsychology, researchers have leveraged these findings to develop novel mechanisms for understanding intelligent decision-making processes in the brain. Concurrently, the emergence of quantum computing has opened new frontiers in artificial intelligence, leading to the development of quantum machine learning (QML). This study introduces a novel model that integrates Quantum Spiking Neural Networks (QSNN) and Quantum Long Short-Term Memory (QLSTM) architectures, inspired by the complex workings of the human brain. Specifically designed for reinforcement learning tasks in energy-efficient environments, our approach progresses through two distinct stages mirroring sensory and memory systems. In the initial stage, analogous to the brain’s hypothalamus, low-level information is extracted to emulate sensory data processing patterns. Subsequently, resembling the hippocampus, this information is processed at a higher level, capturing and memorizing correlated patterns. We conduct a comparative analysis of our model against existing quantum models such as Quantum Neural Networks and their classical counterparts, elucidating its unique contributions. Through empirical results, we aim to underscore the effectiveness of our approach in optimizing energy consumption in practical scenarios.

Quantum machine learning (QML) has been identified as one of the key fields that could reap advantages from near-term quantum devices, next to optimization and quantum chemistry. Research in this area has focused primarily on variational quantum algorithms (VQAs), and several proposals to enhance supervised, unsupervised and reinforcement learning (RL) algorithms with VQAs have been put forward. Out of the three, RL is the least studied and it is still an open question whether VQAs can be competitive with state-of-the-art classical algorithms based on neural networks (NNs) even on simple benchmark tasks. In this work, we introduce a training method for parametrized quantum circuits (PQCs) that can be used to solve RL tasks for discrete and continuous state spaces based on the deep Q-learning algorithm. We investigate which architectural choices for quantum Q-learning agents are most important for successfully solving certain types of environments by performing ablation studies for a number of different data encoding and readout strategies. We provide insight into why the performance of a VQA-based Q-learning algorithm crucially depends on the observables of the quantum model and show how to choose suitable observables based on the learning task at hand. To compare our model against the classical DQN algorithm, we perform an extensive hyperparameter search of PQCs and NNs with varying numbers of parameters. We confirm that similar to results in classical literature, the architectural choices and hyperparameters contribute more to the agents' success in a RL setting than the number of parameters used in the model. Finally, we show when recent separation results between classical and quantum agents for policy gradient RL can be extended to inferring optimal Q-values in restricted families of environments.