Quantum computing

G. Brassard, I. Chuang, S. Lloyd, C. Monroe
1998 Proceedings of the National Academy of Sciences of the United States of America  
Quantum computation is the extension of classical computation to the processing of quantum information, using quantum systems such as individual atoms, molecules, or photons. It has the potential to bring about a spectacular revolution in computer science. Current-day electronic computers are not fundamentally different from purely mechanical computers: the operation of either can be described completely in terms of classical physics. By contrast, computers could in principle be built to profit
more » ... from genuine quantum phenomena that have no classical analogue, such as entanglement and interference, sometimes providing exponential speed-up compared with classical computers. Quantum Information. All computers manipulate information, and the unit of quantum information is the quantum bit, or qubit. Classical bits can take either value 0 or 1, but qubits can be in a linear superposition of the two classical states. If we denote the classical bits by ͉0͘ and ͉1͘, a quantum bit can be in any state ␣͉0͘ ϩ ␤͉1͘, where ␣ and ␤ are complex numbers called amplitudes subject to ͉␣͉ 2 ϩ ͉␤͉ 2 ϭ 1. Any attempt at measuring qubits induces an irreversible disturbance. For example, the most direct measurement on ␣͉0͘ ϩ ␤͉1͘ results in the qubit making a probabilistic decision: with probability ͉␣͉ 2 , it becomes ͉0͘ and with complementary probability ͉␤͉ 2 , it becomes ͉1͘; in either case the measurement apparatus tells us which choice has been taken, but all previous memory of the original amplitudes ␣ and ␤ is lost. Unlike classical bits, where a single string of n zeros and ones suffices to describe the state of n bits, a physical system of n qubits requires 2 n complex numbers to describe its state. For example, two qubits can be in the state ␣͉00͘ ϩ ␤͉01͘ ϩ ␥͉10͘ ϩ ␦͉11͘ for arbitrary complex numbers ␣, ␤, ␥, and ␦ subject only to the constraint ͉␣͉ 2 ϩ ͉␤͉ 2 ϩ ͉␥͉ 2 ϩ ͉␦͉ 2 ϭ 1. Another feature of qubits is the property of entanglement. Consider the two-qubit state (͉00͘ Ϫ ͉01͘ Ϫ ͉10͘ ϩ ͉11͘)͞2. This state is less complicated than it actually looks, because it can be factored into the product of two one-qubit states, each of which is (͉0͘ Ϫ ͉1͘)͞ ͌ 2. Similarly, many n-qubit states can be written in factored form and thus require only 2n numbers for their description, which is much less than the 2 n numbers generally required. However, some special states such as (͉01͘ Ϫ ͉10͘)͞ ͌ 2 cannot be factored. When these two qubits are measured, they yield either 0 and 1 or 1 and 0, with equal probability (1͞ ͌ 2) 2 ϭ 1͞2, but which of these two outcomes will occur is not determined until the measurement is actually performed. This has no classical analogue. Quantum Computing. Computers that thrive on entangled quantum information could run exponentially faster than classical computers because n qubits require 2 n numbers for their description. A few simple operations on these qubits can affect all 2 n numbers through the use of quantum parallelism and quantum interference.
doi:10.1073/pnas.95.19.11032 pmid:9736681 pmcid:PMC33891 fatcat:lxsvnv52pnckdomhjlvgw3vtni