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

Transformation rules for CNOT-based quantum circuits and their applications

Kazuo Iwama, Shigeru Yamashita

New Generation ComputingDec 1, 20035 citations

Controlled-NOT gate design for Josephson phase qubits with tunable inductive coupling: Weyl chamber steering and area theorem

Andrei Galiautdinov, Michael R. Geller

Superconducting qubits with tunable coupling are ideally suited for fast and accurate implementation of quantum logic. Here we present a simple approach, based on Weyl chamber steering, to CNOT gate design for inductively coupled phase qubits with tunable coupling strength g. In the presence of simultaneous rf pulses on the individual qubits that appropriately track the coupling strength as it is varied, we show that an infinite family of switching sequences preserving the time integral or "area" of g can be used to generate CNOT logic. We demonstrate our approach by considering time-dependencies most likely to be used in actual implementations: trapezoidal, sine, and soft quartic (also known as Landau's hat).Superconducting qubits with tunable coupling are ideally suited for fast and accurate implementation of quantum logic. Here we present a simple approach, based on Weyl chamber steering, to CNOT gate design for inductively coupled phase qubits with tunable coupling strength g. In the presence of simultaneous rf pulses on the individual qubits that appropriately track the coupling strength as it is varied, we show that an infinite family of switching sequences preserving the time integral or "area" of g can be used to generate CNOT logic. We demonstrate our approach by considering time-dependencies most likely to be used in actual implementations: trapezoidal, sine, and soft quartic (also known as Landau's hat).

arXiv:quant-ph/0703208Mar 22, 20071 citation

Coupled Josephson phase qubits

Tobias Wirth, Jürgen Lisenfeld, Alexander V. Lukashenko +2 more

Verhandlungen der Deutschen Physikalischen GesellschaftJan 1, 20060 citations

Tunneling qubit operation on a protected Josephson junction array

Zhi Yin, Sheng-Wen Li, Yi-Xin Chen

We propose a complete quantum computation process on a topologically protected Josephson junction array system, originally proposed by Ioffe and Feigel'man [Phys. Rev. B 66, 224503 (2002)]. Logical qubits for computation are encoded in the punctured array. The number of qubits is determined by the number of holes. The topological degeneracy is lightly shifted by tuning the flux along specific paths. We show how to perform both single-qubit and basic quantum-gate operations in this system, especially the controlled-NOT (CNOT) gate.We propose a complete quantum computation process on a topologically protected Josephson junction array system, originally proposed by Ioffe and Feigel'man [Phys. Rev. B 66, 224503 (2002)]. Logical qubits for computation are encoded in the punctured array. The number of qubits is determined by the number of holes. The topological degeneracy is lightly shifted by tuning the flux along specific paths. We show how to perform both single-qubit and basic quantum-gate operations in this system, especially the controlled-NOT (CNOT) gate.

arXiv:0908.3358Physical Review AJan 27, 20102 citations

\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.