What is Quantum Machine Learning?

The Synergy of Quantum Computing and Machine Learning Quantum computing is rapidly advancing and finding applications across various fields, particularly in machine learning. The connection between quantum computing and machine learning is significant; both can enhance each other’s capabilities. In this context, neural networks process information similarly to quantum circuits, allowing for tuning to achieve desired outcomes. Machine learning encompasses supervised and unsupervised methods with generative models gaining traction due to their ability to create new data.

Harnessing Generativity: A Focus on Quantum Models Generative models are a key focus in the realm of quantum machine learning because they align well with the strengths of quantum computers that excel at generating random numbers without needing defined inputs. Classical computers perform better on supervised tasks where input-output relationships are clear while generative tasks fit more naturally within the framework provided by quantum systems. Various classical models like GANs exist alongside their counterparts in quantized forms such as Quantum Generative Adversarial Networks (QGANs) which leverage these unique properties for advanced data generation.

Quantum Circuit Board Machines (QCBM) connect quantum computing and machine learning through probability. Using a coin flip as an example, the likelihood of heads or tails can be modeled to understand data patterns. Given two biased coins, one with a 60% chance for heads and another with only 10%, the first is more likely to produce results similar to observed flips of six heads and four tails. This illustrates how generative models learn from data distributions; they identify underlying probabilities that generated existing data before creating new samples resembling it.

A qubit, or quantum bit, is the fundamental building block of quantum computers and differs from a classical bit. While a classical bit functions like a light switch with two states (on/off), represented as 0 and 1, a qubit behaves more like a slider that can exist in any superposition between these states. This means it can represent not just pure zero or one but also combinations such as half-zero/half-one. The concept of the Bloch sphere illustrates this further; its poles represent the binary states while points along its surface signify various superpositions. Although qubits have infinitely many potential configurations compared to bits' limited options, they do not equate to infinite information capacity due to inherent constraints.

Quantum measurement causes a qubit to collapse into one of two states, either 0 or 1. When observed, the original state information is lost; only the outcome remains. The likelihood of collapsing into each state depends on its current position: closer to north pole increases chances for state zero and vice versa for south pole leading to state one. For instance, if positioned at the equator, there’s an equal probability (50-50) for both outcomes. Visualizing this with magnets illustrates that higher positions favor certain probabilities while definitive certainty exists only when fully aligned with either pole.

Qubits can function as generative models in machine learning, particularly within the realm of generative machine learning. Each qubit represents a probabilistic model; for instance, it can simulate a biased coin flip. By preparing specific states, one can create qubits that reflect different probabilities—such as a coin landing heads 60% or only 10% of the time.

Qubits: Superposition vs Determinism A qubit exists in a superposition of states, unlike classical objects like coins that have defined states. When observing a qubit, the act of measurement alters its state rather than revealing an already determined one. This challenges our understanding and leads to paradoxes if we assume determinism in quantum mechanics.

The Impact of Measurement Bases Using thought experiments with gloves illustrates how measurements affect outcomes based on chosen bases. Observing color or shape requires different approaches; measuring one property can erase certainty about another due to the nature of superpositions within quantum systems.

Understanding Quantum Measurement Bases Three primary measurement bases exist: Z (zero-one), X (plus-minus), and Y (plus i/minus i). Each basis reveals distinct properties but cannot be measured simultaneously without altering results. Understanding these concepts is crucial for grasping quantum computing fundamentals and algorithms related to machine learning applications.

Quantum gates are essential for manipulating qubits, similar to how classical gates operate on bits. Preparing a qubit in a specific state requires using rotation and entangling gates. Rotation gates allow the adjustment of a qubit's position on its Bloch sphere along three axes (x, y, z) by an angle theta. For instance, applying an ry gate can create superposition states like 50/50 between |0⟩ and |1⟩—akin to flipping a fair coin. By adjusting the rotation angle further, one can simulate biased coin tosses with different probabilities.

Modeling Coin Tosses with Quantum Circuits Quantum computing can simulate biased coin tosses, demonstrating how two independent coins yield predictable outcomes. For instance, flipping a pair of fair coins results in equal probabilities for all combinations: heads-heads, heads-tails, tails-heads, and tails-tails. This independence allows the use of quantum circuits with qubits to replicate these probabilities accurately through rotations that reflect their unbiased nature.

Understanding Bias Through Probability Models When analyzing more complex scenarios involving biased coins yielding specific outcomes like 72% heads-heads and 18% heads-tails from repeated flips reveals deeper insights into probability models. The data aligns perfectly with a model using highly biased coins (90% and 80%), showcasing how quantum circuits can represent such correlations effectively by adjusting rotation angles accordingly during measurement.

Exploring Quantum Entanglement The concept of entanglement emerges when tossing two hypothetical correlated coins resulting only in extremes—either both showing heads or both showing tails—with no mixed results possible. This suggests an underlying connection between the measurements rather than mere chance; they are not independent but instead exhibit correlation akin to quantum entangled states where actions on one affect another instantaneously across distances—a phenomenon famously termed 'spooky action at a distance.'

The yy gate is essential for creating entanglement between two qubits. By applying the correct angle, specifically the highest angle, full entanglement can be achieved. Upon measurement, outcomes will consistently yield either both heads or both tails. This results in a histogram showing equal probabilities of obtaining zeroes and ones from the qubit pair.

Quantum machine learning explores the challenge of creating specific entangled states with qubits. When dealing with four special coins that always land in either all heads or all tails, constructing a quantum circuit to achieve this state becomes complex due to limitations on rotation and entangling gates. A systematic approach involves selecting a fixed architecture for the circuit while adjusting parameters like angles, similar to how traditional neural networks operate. Three topologies are considered: star topology connecting one qubit to others, line topology linking each qubit sequentially, and complete connectivity through old topology where every pair is connected. The objective is finding angle configurations that yield desired measurement outcomes.

Utilizing Bars and Stripes Dataset for Quantum Model Training To train a quantum circuit-based model (QCBM), we utilize the bars and stripes dataset, which consists of images representing vertical bars or horizontal stripes within rectangles. This toy dataset is essential for testing generative models due to its defined probability distribution where specific configurations appear with equal likelihood while others do not. The encoding process translates these visual patterns into bit strings, facilitating their use in modeling through QCBMs.

Optimizing Circuit Architecture and Parameters in QCBM Training The architecture selection for QCBMs mirrors classical machine learning approaches; simpler architectures are preferred but may require more layers to capture complex data distributions effectively. Finding optimal angles that define the circuit's behavior involves training akin to traditional methods—iteratively adjusting parameters based on performance against desired outcomes until convergence towards an accurate representation of the target histogram occurs.

Iterative Optimization Techniques for Effective Learning Training employs iterative optimization techniques similar to those used in classical settings, focusing on minimizing discrepancies between generated histograms from measurements versus targeted distributions like that of bars and stripes. Various statistical measures such as KL divergence help assess differences between these distributions while angle adjustments can be made using gradient descent or derivative-free strategies like covariance matrix adaptation evolution strategy (CMA-ES) or particle swarm optimization (PSO).

KL divergence is an effective method for comparing two distributions, yielding a small value when they are similar and a large one when they differ. The formula resembles that of entropy, representing the difference between cross-entropy and entropy; it remains non-negative with zero indicating identical distributions. Updating angles in this context often relies on non-gradient methods due to challenges in finding derivatives for certain circuits. This iterative training process parallels machine learning techniques, progressively refining results until optimal angles are achieved.

Explore a flexible lab environment where QCBMS coding allows for easy modifications to datasets and error functions. The platform, Orchestra, facilitates quantum workflows with demos available that illustrate parsing strategies. For those interested in quantum machine learning or computing, resources are accessible through Zapata Computing's website and documentation. Additionally, the speaker promotes their book on machine learning along with a discount code for purchases made online.