Basics of Quantum Computation

Abstract

Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic principles of quantum computation, including the construction of basic gates, and networks. We illustrate the power of quantum algorithms using the simple problem of Deutsch, and explain, again in very simple terms, the well known algorithm of Shor for factorisation of large numbers into primes. We then describe physical implementations of quantum computers, focusing on one in particular, the linear ion-trap realization. We explain that the main obstacle to building an actual quantum computer is the problem of decoherence, which we show may be circumvented using the methods of quantum error correction.

28 pages including 17 figures, invited basic review article for Progress in Quantum Electronics

References in corpus (11)

• Experimental quantum teleportation
• Quantum Mechanics helps in searching for a needle in a haystack
• Quantifying Entanglement
• Entanglement Measures and Purification Procedures
• Quantum Algorithms Revisited
• On the Improvement of Frequency Stardards with Quantum Entanglement
• A Multiparticle Generalization of Entanglement Swapping
• Implementation of a Quantum Algorithm to Solve Deutsch's Problem on a Nuclear Magnetic Resonance Quantum Computer
• Statistical Inference, Distinguishability of Quantum States, And Quantum Entanglement
• Quantum Physics and Computers
• A nonadditive quantum code

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• Cavity Loss Induced Generation of Entangled Atoms
• Optimal local implementation of non-local quantum gates
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• A Survey on Quantum Channel Capacities
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• Efficient factorization with a single pure qubit and $logN$ mixed qubits
• Fluorescence control through multiple interference mechanisms
• Decoherence and Entanglement in Two-mode Squeezed Vacuum States
• The fully entangled fraction as an inclusive measure of entanglement applications
• Classical information and distillable entanglement
• Teleportation using coupled oscillator states
• Bounds on entanglement in qudit subsystems
• Local and Nonlocal Properties of Werner States
• Typical entanglement in multi-qubit systems
• Nonextensive approach to decoherence in quantum mechanics
• A Novel Clustering Algorithm Based on Quantum Games
• Quantum synthesis of arbitrary unitary operators
• Entangling power of two-qubit gates on mixed states
• Entanglement Creation Using Quantum Interrogation
• Multi-Receiver Quantum Dense Coding with Non-Symmetric Quantum Channel
• Hückel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding
• Number Partitioning on a Quantum Computer
• Physics at the FQMT'04 conference
• Nonlinear Qubit Transformations
• Quantum Gravity from the Composition of Spacetime Constructed through Generalised Proper Time
• Quantum computation in the neuronal microtubules: quantum gates, ordered water and superradiance
• Quantum Computing: an undergraduate approach using Qiskit
• Finding Solutions to NP Problems: Philosophical Difference Between Quantum and Evolutionary Search Algorithms
• Measurement-Disturbance Tradeoff Outperforming Optimal Cloning
• Coherent manipulation of two dipole-dipole interacting ions
• Resource state generation for a multispin register in a hybrid matter-photon quantum information processor
• A Theory of Computation Based on Quantum Logic (I)
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics
• Deutsch and Jozsa's Algorithm Revisited
• Creating long-range entangled Majorana pairs: from spin-1/2 twisted Kitaev to generalized XY chains