by Vivek V. Shende A, Igor L. Markov A, Stephen S. Bullock B
http://www.eecs.umich.edu/~imarkov/pubs/conf/spie04-2qubits.pdf
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Abstract:
An important result from the mid nineties shows that any unitary evolution may be realized as a sequence of controlled-not and one-qubit gates. This work surveys especially efficient circuits in this library, in the special case of evolutions on two-quantum bits. In particular, we show that to construct an arbitrary two-qubit state from |00〉, oneCNOT gate suffices. To simulate an arbitrary two-qubit operator up to relative phases, twoCNOTs suffice. To simulate an arbitrary two-qubit operator up to global phase, three CNOTs suffice. In each case, we construct an explicit circuit and prove optimality in the generic case. We also contribute a procedure to determine the minimal number ofCNOT gates necessary to simulate a given two-qubit operator up to global phase. We use this procedure to discuss timing a given Hamiltonian to simulate the CNOT and to determine an optimal circuit for the two-qubit Quantum Fourier Transform. Our constructive proofs amount to circuit synthesis algorithms and have been coded inC++. 1.
Citations
|
75
|
Two-bit gates are universal for quantum computation
– DiVincenzo
- 1995
|
|
21
|
Basic Algebraic Geometry 1
– Shafarevich
- 1994
|
|
9
|
Approximation by Quantum Circuits
– Knill
- 1995
|
|
6
|
Entanglement of a Pair of Quantum Bits
– Hill, K
- 1997
|
|
5
|
et al., “Elementary Gates For Quantum
– Barenco
- 1995
|
|
4
|
An Elementary Two-Qubit Quantum Computation
– Bullock, Markov
- 2003
|
|
4
|
A Universal Quantum Circuit For Two-qubit Transformations With Three CNOT gates,” quant-ph/0307177
– Vidal, Dawson
- 2004
|
|
3
|
Nonlocal Properties of Two-qubit Gates and Mixed States and Optimization
– Makhlin
- 2002
|
|
2
|
Optimal Realization of an Arbitrary Two-Qubit Quantum Gate”,quant-ph/0308006
– Vatan, Williams
- 2004
|
|
2
|
et al., “Mixed State Entanglement and Quantum Error Correction
– Bennett
- 1996
|
|
2
|
Time Optimal Control
– Khaneja, Brockett, et al.
- 2001
|
|
2
|
et al., “Characterization of Separable States and Entanglement
– Lewenstein
- 2001
|
|
1
|
et al., “Exact two-qubit universal quantum circuit
– Zhang
|
|
1
|
et al., “Optimal quantum circuit synthesis from Controlled-U gates”,quant-ph/0308167
– Zhang
|
|
1
|
et al., “Computing Local Invariants of Qubit Systems
– Grassl
- 1998
|
|
1
|
Canonical Decompositions of n-qubit Quantum
– Bullock, Brennen
|
|
1
|
Experimental Issues in Coherent Quantum Manipulation of Trapped Atomic Ions
– al
- 1998
|
|
1
|
bounds on the complexity of simulating quantum gates
– al
- 2003
|
|
1
|
et al., “A geometric theory of non-local two-qubit operations
– Zhang
|
