Two-qubit quantum gate and entanglement protected by circulant symmetry

Abstract

We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not depend on the magnitude of the Hamiltonian elements as long as the circulant symmetry is preserved. The QFT implementation relies on the adiabatic transition from each of the spin product states to the respective quantum Fourier superposition states. We show that in ion traps one can obtain a Hamiltonian with the circulant symmetry by tuning the spin-spin interaction between the trapped ions. We present numerical results which demonstrate that very high fidelity can be obtained with realistic experimental resources. We also describe how the gate can be accelerated by using a "shortcut-to-adiabaticity" field.

Quantum Fisher Information and Bures Distance Correlations of Coupled Two Charge-Qubits Inside a Coherent Cavity with the Intrinsic Decoherence

“…Quantum simulations are needed to manipulate the quantum information processing in various two-qubit systems such as quantum dots and quantum superconducting circuits. Some recent examples can be cited as the preparation of entanglement via Pauli-spin blockade [65], the realization of two-qubit quantum Fourier, circulant symmetry-protected entanglement [66], and the design of a scalable qubit-coupled dispersive communication architecture [43].…”

Maintaining Entanglement for Three Qubit Gate System via Circulant Symmetry

“…Concerning the physical implementation of logical QFT, the circulant Hamiltonians are addressed [10], which due to the fact that the eigenspectrum of circulant matrix is spanned by the Fourier modes [11,12]. Recently, Ivanov and Vitanov [13] have constructed a Hamiltonian based on two spins emerged in a magnetic field, generating a Rabi oscillations, and by adjusting the coupling strength of the spin-spin interaction a circulant symmetry was obtained. Consequently, they showed that the eigenvectors do not depend on the magnitude of the physical parameters, which entails the protection of entanglement and then the obtained system can be used as a logical QFT.…”

“…Motivated by the results developed in [13], we study a Hamiltonian describing three spins in a magnetic field, coupled via linear and non-linear interactions. The last coupling generally arises when the interaction medium is non-linear [16][17][18] and remains an important ingredient to generate a circulant Hamiltonian.…”

“…These allow us to combine our gate with the short-cut to adiabacity scheme in order to accelerate the gate. To physically implement the gate, we suggest an extension of the proposal described in [13].…”

Optimal Robust Quantum Control by Inverse Geometric Optimization

“…[30], one can compensate the error in the phase of a two-qubit controlled-PHASE gate (e.g. implemented in an ion trap) using interactions of the form T 1 ⌘ 1 2 x ⌦ x , T 2 ⌘ 1 2 x ⌦ y and T 3 ⌘ 1 2 1 1 ⌦ z , which feature SU(2) symmetry; (iii) Qudit gate (with an arbitrary dimension d), at the heart of quantum Fourier transform (a key ingredient of many quantum algorithms), in a multi-pod configuration with some overlapping controls [31] or with circulant symmetries [32].…”