Assignments

These comprehensive problem sets bring together foundational models, mathematical proofs, circuit constructions, and physical principles from across multiple chapters. Unlike isolated exercises, each assignment asks you to synthesize ideas: tracing how classical reversibility grounds quantum gate models, how geometry dictates state distinguishability, and how composite entanglement sets the boundary between classical and quantum information processing.

Work through each assignment after completing its prerequisite chapters. Attempt every problem independently by hand, showing all intermediate algebraic steps, before expanding the complete worked solutions to verify your reasoning.

Work from first principles. Rather than memorizing formulas, derive state evolutions, inner products, and operator identities step by step. When calculating state transformations, write down the full tensor product representation or state sum before applying gates.

Distinguish mathematical definitions from physical postulates. State clearly when a property follows from the mathematics of vector spaces (such as linearity or the Cauchy–Schwarz inequality) versus when it relies on a physical postulate of quantum mechanics (such as unitarity of closed evolution or the Born rule for projective measurement).

Compare with physical intuition. Check limiting cases whenever possible: what happens when \(\theta = 0\) or \(\theta = \pi/4\)? Does an entangled state reduce to a product state? Does an unconditioned marginal density matrix reflect the no-signalling principle? Checking these boundaries will quickly catch algebraic errors.