Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the rotation axes can be tuned arbitrarily in a fixed plane, then two rotation steps are sufficient for implementing a single-qubit gate, and one rotation step is sufficient for implementing a state transformation. The results are relevant for "exchange-only" logical qubits encoded in three-spin blocks, which are important for universal quantum computation in decoherence free subsystems and subspaces.Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the rotation axes can be tuned arbitrarily in a fixed plane, then two rotation steps are sufficient for implementing a single-qubit gate, and one rotation step is sufficient for implementing a state transformation. The results are relevant for "exchange-only" logical qubits encoded in three-spin blocks, which are important for universal quantum computation in decoherence free subsystems and subspaces.

arXiv:1303.0297Mar 1, 20137 citations

Implementing Two-Qubit Gates

Ray LaPierre

The Materials Research Society seriesOct 24, 20250 citations

Controlled-NOT logic with nonresonant Josephson phase qubits

Andrei Galiautdinov

We establish theoretical bounds on qubit detuning for some of the previously proposed controlled-NOT (CNOT) logic gate implementations with weakly coupled Josephson phase qubits. It is found that in the two-step, $\sqrt{i\text{SWAP}}$ -based case the value of the detuning during the entangling operations must not exceed $2g$ , where $g$ is the characteristic coupling constant. In the single-step case we consider two practical, physically distinct implementations, in which one of the qubits is driven by a concurrent rf pulse of fixed frequency. We find that when the local drive is applied to the ``reference'' qubit (with which it is in resonance), the detuning should not exceed $g$ . If the drive is applied to the ``detuned'' qubit, generation of the perfect CNOT gate is possible at any value of detuning provided that the amplitude of the pulse can be made arbitrarily large.We establish theoretical bounds on qubit detuning for some of the previously proposed controlled-NOT (CNOT) logic gate implementations with weakly coupled Josephson phase qubits. It is found that in the two-step, $\sqrt{i\text{SWAP}}$-based case the value of the detuning during the entangling operations must not exceed $2g$, where $g$ is the characteristic coupling constant. In the single-step case we consider two practical, physically distinct implementations, in which one of the qubits is driven by a concurrent rf pulse of fixed frequency. We find that when the local drive is applied to the ``reference'' qubit (with which it is in resonance), the detuning should not exceed $g$. If the drive is applied to the ``detuned'' qubit, generation of the perfect CNOT gate is possible at any value of detuning provided that the amplitude of the pulse can be made arbitrarily large.

arXiv:0901.0001Physical Review AApr 13, 20098 citations

Implementing Two-Qubit Gates

Ray LaPierre

The Materials Research Society seriesJan 1, 20211 citation

\sqrt{i\text{SWAP}}

-based case the value of the detuning during the entangling operations must not exceed

2g

, where

g

is the characteristic coupling constant. In the single-step case we consider two practical, physically distinct implementations, in which one of the qubits is driven by a concurrent rf pulse of fixed frequency. We find that when the local drive is applied to the ``reference'' qubit (with which it is in resonance), the detuning should not exceed

g

. If the drive is applied to the ``detuned'' qubit, generation of the perfect CNOT gate is possible at any value of detuning provided that the amplitude of the pulse can be made arbitrarily large.