Quantum Computing Algorithms and Architecture
Research Guide

A quantum algorithm specifies an abstract procedure—often as a circuit model—for solving a computational problem using qubits and quantum gates, as exemplified by "A fast quantum mechanical algorithm for database search" (1996) and "Algorithms for quantum computation: discrete logarithms and factoring" (2002). A quantum computing architecture specifies how those gates and qubits are realized, connected, controlled, and protected from noise, which is central to the device limitations discussed in "Quantum Computing in the NISQ era and beyond" (2018).

"A fast quantum mechanical algorithm for database search" (1996) motivates architectures that can implement repeated oracle-and-diffusion iterations efficiently, making multi-qubit gate synthesis and routing overhead critical. "Algorithms for quantum computation: discrete logarithms and factoring" (2002) motivates architectures that can sustain long, structured computations, which increases the importance of error correction and compilation strategies that reduce depth and noise accumulation.

"Quantum entanglement" (2009) summarizes entanglement as a core feature of quantum theory that must be realized in the laboratory, making its generation and preservation a hardware-level requirement. "Entanglement of Formation of an Arbitrary State of Two Qubits" (1998) formalizes entanglement quantification for two-qubit states, which connects directly to architecture because two-qubit entangling gates are typically the dominant error and calibration bottleneck in quantum processors.

Nielsen, Chuang, and Grover’s "Quantum Computation and Quantum Information" (2002) is a central reference for circuit models, algorithmic primitives, and the information-theoretic framing used across the field. Preskill’s "Quantum Computing in the NISQ era and beyond" (2018) complements that foundation by emphasizing how noise and limited qubit counts constrain which circuits can be executed in practice.

"Quantum Computing in the NISQ era and beyond" (2018) characterizes near-term devices as noisy intermediate-scale quantum systems where noise limits circuit size even when qubit counts reach roughly 50–100. Under this framing, architecture-aware compilation and error mitigation are necessary to extract utility from algorithms that would otherwise be impractical at available fidelities and depths.