Quantum Computing

Overview

Quantum computing studies how information can be processed using quantum-mechanical systems. It includes the design of quantum algorithms, software, and hardware, and their applications in communication, learning, and simulation of physical systems using quantum computers.

Quantum computing ≠ Computing quantum phenomena

Quantum computing is distinct from the classical simulation of quantum phenomena. Instead, it involves the use of quantum computational primitives - such as qubits and qudits - which are fundamentally different from the classical bit. This shift enables new forms of computation and gives rise to the notion of the quantum computational stack:

• Quantum hardware: physical quantum computers built using superconducting qubits, trapped ions, photonic, neutral atoms, or spin qubits - fundamentally different from classical silicon-based technology.
• Quantum software: languages, compilers, and programming environments designed to run on and interface with quantum hardware. Examples include quantum programming languages (e.g. Qiskit), quantum circuit compilers (e.g. Qiskit transpiler), quantum error correction libraries (e.g. Stim).
  
• Quantum algorithms: algorithms such as Shor’s Factorization and Grover’s Search that exploit quantum phenomena like superposition and interference to solve problems more efficiently than is possible classically. These breakthroughs enable exponential or quadratic speedups for tasks such as factoring large integers or searching unstructured datasets.
• Quantum verification: formal methods for reasoning about the correctness and reliability of quantum programs and circuits. This includes techniques from automata theory, logic, and model checking, adapted to the quantum setting to ensure that quantum software behaves as intended.

As a final clarifying note, we also include classical computing research that directly supports the development and understanding of quantum computation. This includes:

• Classical simulation of quantum computers (e.g., for prototyping quantum circuits).
• Quantum error correction codes and frameworks implemented on classical hardware.
• Formal verification of quantum programs and circuits.

We aim to develop quantum algorithms, languages, and systems grounded in the science of computing. Our long-term goal is to build a sustainable ecosystem for quantum computing - spanning theory, software, hardware, and education.