Deutsch–Jozsa algorithm

E349464

The Deutsch–Jozsa algorithm is a foundational quantum algorithm that demonstrates how quantum computation can solve certain decision problems exponentially faster than any classical deterministic algorithm.

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Statements (50)

Predicate Object
instanceOf quantum algorithm
quantum computing protocol
algorithmType exact quantum algorithm
assumesAccessTo black-box oracle implementing U_f
complexityClassicalDeterministic O(2^n)
complexityQuantum O(n)
demonstrates advantage of quantum computation over classical computation
power of quantum interference
power of quantum superposition
errorProbability 0
field quantum computing
quantum information theory
finalMeasurementRegister first n qubits
generalizationOf Deutsch–Jozsa algorithm self-linksurface differs
surface form: Deutsch algorithm
guaranteeOnOracle function is either constant or balanced
implementationStatus implemented on small-scale quantum processors
initialState |0⟩^⊗n ⊗ |1⟩
inputType oracle function
keyResource Walsh–Hadamard transform
surface form: Hadamard transform

quantum interference
quantum parallelism
measurementOutcomeForBalanced any non-zero bit string
measurementOutcomeForConstant all-zero bit string
modelOfComputation quantum circuit model
namedAfter David Deutsch
Richard Jozsa
numberOfOracleQueriesClassicalDeterministicWorstCase 2^(n-1)+1
numberOfOracleQueriesQuantum 1
numberOfQubitsRequired n+1
oracleFunctionCodomain single bit
oracleFunctionDomain n-bit strings
oraclePropertyTested constant or balanced
originalPublicationTitle Deutsch–Jozsa algorithm self-linksurface differs
surface form: Rapid solution of problems by quantum computation
originalPublicationVenue Proceedings of the Royal Society
surface form: Proceedings of the Royal Society of London A
outputType decision whether function is constant or balanced
pedagogicalRole introductory example in quantum computing courses
problemTypeSolved Deutsch–Jozsa algorithm self-linksurface differs
surface form: Deutsch–Jozsa problem

black-box decision problem
relatedTo Bernstein–Vazirani algorithm
Deutsch
surface form: Deutsch problem

Grover’s algorithm
Simon’s algorithm
surface form: Shor’s algorithm

Simon’s algorithm
requires coherent control over multiple qubits
significance first example of exponential quantum speedup in query complexity model
speedupType exponential separation between quantum and classical deterministic query complexity
typicalUse theoretical demonstration rather than practical application
usesGate Hadamard gate
oracle unitary U_f
yearProposed 1992

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Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

David Deutsch knownFor Deutsch–Jozsa algorithm
Deutsch–Jozsa algorithm originalPublicationTitle Deutsch–Jozsa algorithm self-linksurface differs
this entity surface form: Rapid solution of problems by quantum computation
Deutsch–Jozsa algorithm problemTypeSolved Deutsch–Jozsa algorithm self-linksurface differs
this entity surface form: Deutsch–Jozsa problem
Deutsch–Jozsa algorithm generalizationOf Deutsch–Jozsa algorithm self-linksurface differs
this entity surface form: Deutsch algorithm