1 A few words about quantum computing

Quantum computing is presented as a fundamentally different paradigm from classical computing, one that relies on quantum-mechanical phenomena and therefore resists day-to-day intuition. The chapter lowers the barrier to entry by advocating a physics-light, learn-by-doing approach: build understanding through solving problems and writing quantum programs. It targets readers who already know the basics—quantum states, gates, Dirac notation, control and adjoint operations, and measurement—along with comfort in linear algebra and some trigonometry. Brief refreshers appear where needed, while more thorough introductions can be paired from external resources. The overarching goal is to transition from abstract concepts to practical, program-oriented reasoning about quantum computation.

The discussion separates hype from reality: quantum computers will not replace classical machines, but can offer advantages on specific, hard problems. Practical quantum advantage requires that the best classical methods are too slow, the quantum solution is fast enough to matter, and the task itself is meaningful. Promising domains include simulating quantum systems and materials science, where “small-data, big-compute” structures can be exploited and speedups beyond quadratic are plausible. At the same time, the chapter stresses practicality: theoretical improvements (for example, quadratic search speedups) may be eclipsed by structured classical methods or by the high cost of quantum subroutines, so careful algorithmic and implementation-level analysis is essential to identify truly useful advantages.

The chapter then peeks inside modern quantum systems, organized around three components that coevolve: algorithms, hardware, and software. Hardware remains in the noisy intermediate-scale era, progressing toward fault tolerance via error correction and scale, with milestones moving from proofs of concept to demonstrations of advantage and ultimately to solving practical problems. The software stack mirrors classical computing, from high-level languages and libraries through compilation, optimization, and error-correction layers down to platform-specific control, with simulators playing a central role in development and testing. A developer-oriented workflow follows four steps—implement (often in hybrid quantum-classical form), test and debug (largely via simulators), estimate resources, and run on hardware—and this book focuses on the first three, using Qiskit and Q# to build hands-on proficiency amid a rapidly growing ecosystem and job market for quantum technologies.

Quantum advantage: the time a quantum computer takes to solve a problem grows at a slower rate than the time a classical computer takes as the problem size increases. The problems for which crossover time is months or more offer no practical advantage, since the problem instances that have practical value are much larger than the crossover size and take much longer to solve, and running a quantum computer for months or years to solve a single problem instance is not really practical.

The major milestones of quantum hardware development. The first two, showing the use of quantum mechanics to perform a computation and having a quantum computer solve an artificial problem that a classical computer can not, have already been achieved. The next milestone, building a fault-tolerant quantum computer that can run long computations, is the current focus. The final goal is to build a quantum computer that can solve practical problems that a classical computer can not.

Quantum software stack serves as an interface between the quantum algorithms and the hardware running them. Its components mirror those of the classical software stack.

Quantum application software development workflow. From the developer perspective it is similar to the classical software development workflow, with some differences to account for the nature of quantum computing. For example, using quantum simulators instead of the hardware makes testing the software on small problems faster and easier, since it eliminates the need to account for noise.

• Quantum computing cannot speed up arbitrary classical computing tasks; instead, it will let us solve some highly specialized problems such as quantum systems simulations that are too complicated for classical (super)computers.
• To yield practical advantage over the best classical algorithms for the same problem, quantum algorithms have to offer significant speedups, featuring at least exponentially better asymptotic complexity compared to that of the classical algorithms.
• Quantum hardware is in its "noisy intermediate-scale era", with devices too large to be simulated classically but too small and too noisy to solve practical problems.
• The software stack plays a critical role for quantum computers, enabling the execution of algorithms on hardware and accessing the quantum systems via the cloud, accelerating algorithms research and driving the requirements for hardware design.
• Governments and companies worldwide pay increasing attention to quantum computing and invest in its continued development.
• Learning quantum computing can give you a lot of opportunities to contribute to this domain and, like learning any new computing paradigm, make you a better thinker!

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