Abstract
Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits.
Highlights
A number of proposals have been presented for realizing both conventional and unconventional geometric phase gates[37,38,39,40,41,42,43,44,45,46,47,48,49,50,51]
Equation (1) shows that when the control qubit A is in the state + ( − ), a phase shift eiθj happens to the state + ( − ) but nothing happens to the state − ( + ) of the target qubit j (j = 1, 2, ..., n)
Which implies that when and only when the control qubit A is in the state −, a phase shift ei2θj happens to the state − of the target qubit j but nothing otherwise
Summary
A number of proposals have been presented for realizing both conventional and unconventional geometric phase gates[37,38,39,40,41,42,43,44,45,46,47,48,49,50,51]. Such a multiqubit phase or CNOT gate is useful in QIP This multiqubit gate is an essential ingredient for implementation of quantum algorithm (e.g., the discrete cosine transform20), the gate plays a key role in quantum cloning[24] and error correction[23], and it can be used to generate multiqubit entangled states such as Greenberger-Horne-Zeilinger states[25]. It is noted that this multi-target-qubit gate is equivalent to a multiqubit gate with different control qubits acting on the same target qubit (see Fig. 2), which is a key element in quantum Fourier transform[1,19]. Our goal is propose a simple method for implementing a generic unconventional geometric (UG) multi-target-qubit gate described by Eq (1), with one qubit (qubit A) simultaneously controlling n target qubits (1, 2, ..., n) distributed in n cavities (1, 2, ..., n). It is important and imperative to explore how to realize multiqubit gates performed on qubits that are spatially-separated and distributed in different cavities
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