Arbitrary two-qubit computation in 23 elementary gates

Journal Article · Tue Jul 01 00:00:00 EDT 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.68.012318· OSTI ID:20639884

Bullock, Stephen S; Markov, Igor L ^[1]

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1. Department of Mathematics, The University of Michigan, Ann Arbor, Michigan 48109-2122, USA (United States)

We address the problem of constructing quantum circuits to implement an arbitrary two-qubit quantum computation. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2 controlled-NOT (CNOT) gates. We also constructively prove a worst-case upper bound of 23 elementary gates, of which at most four (CNOT gates) entail multiqubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail larger quantum circuits than ours in the special case of two qubits. One such algorithm has a worst case of 61 gates, of which 18 may be CNOT gates.

• OSTI ID: 20639884
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 68; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ALGORITHMS
BASIC INTERACTIONS
ENERGY LEVELS
GATING CIRCUITS
INFORMATION THEORY
QUANTUM MECHANICS
ROTATION
SYNTHESIS