Binary decisions are the simplest form of decisions that are made in our daily lives. Examples include choosing a two-way path in a maze, accepting or declining an offer, etc. These decisions are also made by computers, machines and various electronic components. But decisions made on these devices can be partial and deterministic, and hence compromised. In this paper, a simple framework to implement binary decisions using one or many qubits is presented. Such systems are based on a separate hardware infrastructure rather than computer codes. This helps enable true randomness and impartial decision making. The multi-armed bandit problem is used to highlight the decision making ability of qubits by predictive modelling based on quantum Bayesianism. Bipartite and multipartite entangled states are also used to solve specific cases of the problem.
Binary decisions are the simplest form of decisions that are made in our daily lives. Examples include choosing a two-way path in a maze, accepting or declining an offer, etc. These decisions are also made by computers, machines and various electronic components. But decisions made on these devices can be partial and deterministic, and hence compromised. In this paper, a simple framework to implement binary decisions using one or many qubits is presented. Such systems are based on a separate hardware infrastructure rather than computer codes. This helps enable true randomness and impartial decision making. The multi-armed bandit problem is used to highlight the decision making ability of qubits by predictive modelling based on quantum Bayesianism. Bipartite and multipartite entangled states are also used to solve specific cases of the problem.
This work focuses on quantum machine learning and analyzes the power of one single qubit to solve classical machine learning problems. We explore possible strategies to address traditional supervised, unsupervised, and reinforcement learning tasks. In particular, we study binary and multinomial classification, regression problems, time series forecasting, clustering, and quantum reinforcement learning. Our results suggest that the same methodology could be used to address all three types of learning with different measurement strategies and, despite the strong limitation of reduced data dimensionality of the candidate problems, a single qubit can achieve similar or even improved performance with respect to state-of-the-art classic machine learning methods in many cases. As simulating the evolution of one qubit state is computationally efficient, our study enables the possibility to use the qubit model as a candidate solution to implement simple decision-making machine learning models in hardware with extremely low memory resources such as embedded systems or edge devices. The outcomes provided could be also of interest in academia and for the construction of demonstrators using low-scale contemporary quantum hardware.
It is well known, and appreciated, that quantum computers have the potential to be the most powerful computational devices ever created. This newfound power comes from a quantum parallelism effect that allows the computer to be in multiple states at the same time. This property of quantum parallelism, while suited to handle common problems such as factoring and searching an unorganized database, is extremely well-suited to handle the task of solving a binary maze. I propose an algorithm that can be used to solve a binary maze on a quantum computer, with guaranteed accuracy. While it does work, it does come with a few setbacks, in that the maze must have no flaws, and that the computer requires a number of qubits equal to the number of decisions in the maze, plus log 2 of the decisions.
Quantum computing is the theory of quantum bits, or qubits, and their associated linear transformations. A quantum computer is more powerful than classical computers, with the problems being solvable. Quantum computing is expected to play an increasingly important role in building more compact and less power-consuming computers. Quantum Computing has emerged to be a very effective field where numerous scientists are doing research in this area. It is true that quantum computing system is now in its initial theoretical state, a lot of aspects of this logic has been proposed by scientists over the years. Quantum computing promises to compute a whole set of intractable problems easily and within a very small amount of time. From binary to multi-valued logic quantum computing systems have a lot of properties to be explored, but mainly theoretically and not in a form of some tangible hardware logic. In the present study the authors have made a thorough study of the properties of binary and multi-valued quantum logic along with the impact of Quantum Information Decision Diagram (QUIDD), Quantum Multi-Valued Decision Diagrams in quantum logic.
Machine Learning (ML) aims at designing models that learn from previous experience, without being explicitly formulated. Applications of machine learning are inexhaustible, including recognizing patterns, predicting future trends and making decisions, and they are capable of handling sizable quantities of multi-dimensional data in the form of large vectors and tensors. To perform these operations on classical computers, however, requires vast time and computational resources. Unlike the classical computers that rely on computations using binary bits, Quantum Computers (QC) benefit from qubits which can hold combinations of 0 and 1 at the same time via superposition and entanglement. This makes QCs powerful at handling and post processing large tensors, making them a prime target for implementing ML algorithms. While several models used for ML on QCs are based on concepts from their classical computing counterparts, utilization of the QC's potential has made them the superior of the two. This paper presents an overview of the current state of knowledge in application of ML on QC, and evaluates the speed up, and complexity advantages of using quantum machines.
This paper demonstrates that some non-classical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed in a survey affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can, however, be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020s, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, by representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modeling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.
As we have seen, even a single qubit is a surprisingly interesting object. However, the real power of quantum information processing begins with systems of two or more qubits. Before studying these in detail we need to expand our notation a little. Consider a system of two qubits, labeled a and b , each of which has two basis states, |0⧽ and |1⧽. The whole system then has four basis states, which can be written as |0 a 0 b ⧽, |0 a 1 b ⧽, |1 a 0 b ⧽ and |1 a 1 b ⧽, and can be found in any general superposition of these states, so that it occupies a four-dimensional Hilbert space. In the same way, a system of three qubits inhabits an eight-dimensional Hilbert space, and so on. This exponential increase in the size of the Hilbert space with a linear increase in the number of qubits underlies the power of quantum computers. Direct products The size of the Hilbert spaces involved can also be a huge problem, however, making it difficult to describe states of systems with many qubits. A partial solution is to note that some states can be described in a simpler way, using the concept of direct products . These states, in which the individual qubits can in principle be discussed separately, make up a tiny minority of the states accessible to a multi-qubit system, but include many important states, most notably the basis states. States of this kind are said to be separable , and states which are not separable are said to be entangled . Entangled states are much more interesting than separable ones, but it is wise to begin with the simpler case.