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3361 results in Quantum Physics, Quantum Information and Quantum Computation

Page 51 of 169

  • 1 - The Mathematical Minimum

  • Robert Hundt
  • Book:
    Quantum Computing for Programmers
    Published online:
    28 March 2022
    Print publication:
    31 March 2022, pp 1-8

  • Summary

    This brief chapter discusses the minimum mathematical background required to understand the mathematical derivations in this text fully. A basic familiarity with matrices and vectors is assumed. The chapter introduces and reviews key properties of complex numbers, the Dirac notation with inner and outer products, the Kronecker product, unitary and Hermitian matrices, eigenvalues and eigenvectors, the matrix trace, and how to construct the Hermitian adjoint of matrix-vector expressions.

  • 4 - Scalable, Fast Simulation

  • Robert Hundt
  • Book:
    Quantum Computing for Programmers
    Published online:
    28 March 2022
    Print publication:
    31 March 2022, pp 122-148

  • Summary

    The basic infrastructure developed so far is sufficient for small-scale quantum algorithms. It is also a great learning tool. However, for complex algorithms with many more qubits and gates, this matrix-based infrastructure does not scale. This chapter improves the infrastructure to scale to problems with up to 30 qubits and tens of thousands of gates.

    First, the chapter introduces an elegant circuit abstraction. A method to apply operators with linear complexity comes next, which is a significant improvement over the cubic or quadratic methods presented previously. Acceleration with C++ enables another 100x speedup. Finally, a sparse state representation is being discussed at length, which can be the best-performing implementation for many circuits.

  • 2 - Quantum Computing Fundamentals

  • Robert Hundt
  • Book:
    Quantum Computing for Programmers
    Published online:
    28 March 2022
    Print publication:
    31 March 2022, pp 9-77

  • Summary

    This chapter introduces the fundamental concepts and rules of quantum computing. In parallel, it develops an initial, easy-to-understand codebase in Python for building and simulating small-scale quantum circuits and algorithms.

    The chapter details single qubits, superposition, quantum states with many qubits, operators, including a sizable set of important single-qubit gates and controlled gates. The Bloch sphere and the quantum circuit notation are introduced. Entanglement follows, that fascinating “spooky action at a distance,” as Einstein called it. With this background, the chapter discusses maximally entangled Bell states, the no-cloning theorem, the noneffect of global phases, the partial trace and reduced density matrix, and uncomputation. The quantum postulates are discussed in a nonphilosophical way, leading to measurement and how to simulate it.

Page 51 of 169