Two-qubit logic gate

Ahmet Gün, İrfan Şaka, Azmi Gençten

In NMR quantum computing, spin states of spin-1/2 nuclei are called qubits. Quantum logic gates are represented by unitary matrices. As a universal gate, controlled-NOT (CNOT) is a two-qubit gate. For the IS (I = 1/2 and S = 1/2) spin system, two-qubit CNOT gate is represented by a 4 × 4 matrix. SWAP logic gate, which exchanges two quantum states, is constructed by CNOT gates. In this study, first, four-qubit CNOT gates are constructed for the IS (I = 3/2, S = 3/2) spin system. Then, by using these CNOT gates, a four-qubit SWAP logic gate is found. As an application and verification, an obtained SWAP logic gate is applied to the matrix representation of product operators for the IS (I = 3/2, S = 3/2) spin system. SWAP logic gate can also be presented by an NMR pulse sequence. By using the product operator theory, the pulse sequence of the SWAP logic gate is applied to product operators of the IS (I = 3/2, S = 3/2) spin system. The expected exchange results are obtained for both the matrix representation and the pulse sequence of SWAP logic gate.

Christopher J. Ballance

Christopher J. Ballance

Jia-Xiu Han, Jiang Zhang, Guangming Xue +2 more

Demonstrating that logical qubits outperform their physical counterparts represents a milestone in achieving reliable quantum computation. Here, we propose to protect logical qubits with a dynamical decoupling scheme that implements i gates on nearest-neighbor physical qubits, and we experimentally demonstrate this scheme on superconducting transmon qubits. In our scheme, each logical qubit requires only two physical qubits. A universal set of quantum gates on the logical qubits can be achieved such that each logical gate comprises only one or two physical gates. Our experiments reveal that the coherence time of a logical qubit is extended by up to 357% compared to the better-performing physical qubit. Moreover, we demonstrate—to the best of our knowledge, for the first time—that multiple logical qubits can outperform their physical superconducting counterparts. We illustrate a set of universal gates through a logical Ramsey experiment and the creation of a logical Bell state. Given its scalable nature, our scheme holds promise as a component for future reliable quantum computation.

Chui‐Ping Yang, Siyuan Han

A novel approach is proposed for realizing an arbitrary-operation gate with a SQUID qubit via pulsed-microwave manipulation. In this approach, the two logical states of the qubit are represented by the two lowest levels of the SQUID and an intermediate level is utilized for the gate manipulation. The method does not involve population in the intermediate level or tunneling between the two logical qubit states during the gate operation. Morever, we show that the gate can be much faster than the conventional two-level gate. In addition, to take the advantage of geometric quantum computing, we further show how the method can be extended to implement an arbitrary quantum logic operation in a SQUID qubit via geometric manipulation.

徐晶