2007
DOI: 10.1103/physreva.76.022335
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Simplified approach to implementing controlled-unitary operations in a two-qubit system

Abstract: We introduce a scheme for realizing arbitrary controlled-unitary operations in a two-qubit system. If the 2 ϫ 2 unitary matrix is special unitary ͑has unit determinant͒, the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in our scheme will constitute varying one of the parameters of the system between an arbitrarily maximum and a "calculated" minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the… Show more

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Cited by 7 publications
(6 citation statements)
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“…In this work, we considered the Hamiltonian with Ising interactions, however, the proposed gates can be realized for Hamiltonians with XX and YY interactions by simply interchanging the tunneling and bias values while coupling values and other parameters remain unchanged [7,15]. Furthermore, here we considered an arbitrary size 2D array of qubits to represent the application of multi-qubit parity gates in Surface Code schemes.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…In this work, we considered the Hamiltonian with Ising interactions, however, the proposed gates can be realized for Hamiltonians with XX and YY interactions by simply interchanging the tunneling and bias values while coupling values and other parameters remain unchanged [7,15]. Furthermore, here we considered an arbitrary size 2D array of qubits to represent the application of multi-qubit parity gates in Surface Code schemes.…”
Section: Discussionmentioning
confidence: 99%
“…It is challenging to solve such a large matrix analytically in order to derive the system parameters. However, using a pulses bias scheme [14,15] and reduced Hamiltonian technique [16], we can solve the system parameters to realize a desired multi-qubit parity gate.…”
Section: Physical Model and The Simulation Methodsmentioning
confidence: 99%
“…This is because qubit A i is coupled to the |0〉 and the |1〉 qubits adjacent to it through the same coupling ξ 1 , and the relative phases due to the presence of each of these qubits cancel out. Next, we perform a Hadamard gate on qubit A i , where the bias on it is pulsed to a value Δ+ξ [43]. Again, no relative phases are picked up by qubit B i , now in the |0〉 state, since it is coupled to the |0〉 and |1〉 qubits on either side of it through the same coupling (−ξ 1 ).…”
Section: Hadamard Gatementioning
confidence: 99%
“…Further, to match our parameter values with those in [50], we used the following values in our simulations: A j = 1 GHz, K12 = K2 3 = 866 MHz (or, equivalently, f | 2 = £23 = 866 MHz), and T = 1.25 ns. These values were obtained by scaling up the values obtained in a weak-coupling regime [53] PHYSICAL REVIEW A 91, 042310 (2015) by multiplying each parameter by a scaling factor of 40. This is because in increasing Aj from 25 MHz (value of tunneling solved for in Sec.…”
Section: A Presence Of Unwanted Couplingsmentioning
confidence: 99%
“…This is because in increasing Aj from 25 MHz (value of tunneling solved for in Sec. II and in [53]) to 1 GHz we have increased it 40 times. Note that in scaling the time required for each gate operation (P gate and DCN gate), we used Eq.…”
Section: A Presence Of Unwanted Couplingsmentioning
confidence: 99%