Quantum gates are the basic building blocks in the quantum circuits model. These gates can be implemented using adiabatic or non adiabatic processes. Adiabatic models can be controlled using auxiliary qubits, whereas non adiabatic models can be simplified by using one single-shot implementation. In this paper, the controlled adiabatic evolutions is combined with the single-shot implementation to obtain quantum gates with controlled non adiabatic evolutions. This is an important improvement which can speed the implementation of quantum gates and reduce the errors due to the long run in the adiabatic model. The robustness of our scheme to different types of errors is also investigated.
Quantum gates are the basic building blocks in the quantum circuits model. These gates can be implemented using adiabatic or non adiabatic processes. Adiabatic models can be controlled using auxiliary qubits, whereas non adiabatic models can be simplified by using one single-shot implementation. In this paper, the controlled adiabatic evolutions is combined with the single-shot implementation to obtain quantum gates with controlled non adiabatic evolutions. This is an important improvement which can speed the implementation of quantum gates and reduce the errors due to the long run in the adiabatic model. The robustness of our scheme to different types of errors is also investigated.
Abstract Quantum gates can be implemented adiabatically and nonadiabatically. Many schemes used at least two sequentially implemented gates to obtain an arbitrary one-qubit gate. Recently, it has been shown that nonadiabatic gates can be realized by single-shot implementation. It has also been shown that quantum gates can be implemented with controlled adiabatic evolutions. In this paper, we combine the advantage of single-shot implementation with controlled adiabatic evolutions to obtain controlled nonadiabatic evolutions. We also investigate the robustness to different types of errors. We find that the fidelity is close to unity for realistic decoherence rates.
Single quantum rotation gates can be perfectly implemented in a closed system using the controlled adiabatic evolutions process proposed by Itay Hen that may lead to build some quantum circuit blocks [Phys. Rev. A, 022309 (2015)]. These adiabatic evolutions yield to vanishing geometric phases. In this work, we extended Itay’s work by considering a more realistic model where the qubits are subjected to decoherence effects during the adiabatic evolution process. We demonstrate that, in the case of an open system, the decoherence leads to nonvanishing geometric phases and drastically reduces the performance of the quantum rotation gates bellow the fidelity target (0.999).
Fundamental quantum gates can be implemented effectively using adiabatic quantum computation or circuit model. Recently, Hen combined the two approaches to introduce a new model called controlled adiabatic evolutions [I. Hen, Phys. Rev. A, 91(2) (2015) 022309]. This model was specifically designed to implement one and two-qubit controlled gates. Later, Santos extended Hen’s work to implement [Formula: see text]-qubit controlled gates [A. C. Santos and M. S. Sarandy, Sci. Rep., 5 (2015) 15775]. In this paper, we discuss the implementation of each of the usual quantum gates, as well as demonstrate the possibility of preparing Bell’s states using the controlled adiabatic evolutions approach. We conclude by presenting the fidelity results of implementing single quantum gates and Bell’s states in open systems.
\n\nAdiabatic and superadiabatic controlled evolutions are used as universal models for quantum computations, where an auxiliary system is used as the main resource in the theory. While the adiabatic case demands a slow dynamics (so that the adiabatic theorem is satisfied), the superadiabatic model can speed up such process by spending more energy than the adiabatic one. In this paper, we explore a hybrid scheme of controlled evolutions and measurement in order to optimize the thermodynamic cost of implementing quantum gates. By adjusting a free parameter of the theory of controlled evolutions, we show that we can improve the energy cost of the evolution. To this end, we used a model of computation based on adiabatic/superadiabatic evolution and post-selection measurement on the auxiliary qubit. In both cases, adiabatic and superadiabatic, the probabilistic model allows for optimizing the thermodynamics cost of implementing gates. When the system reservoir interaction is taken into account, we show that the superadiabatic probabilistic model is more robust than the adiabatic one.\n
Quantum computation has been shown to be superior to classical computation in solving some problems, and therefore can substantially change our life. However, the realization of quantum computation is still challenging, even if quantum technologies have been improved significantly. Two main obstacles to the realization of practical quantum computation are control errors and decoherence. Control errors are caused by inaccurate manipulations of quantum systems and decoherence is caused by the inevitable interaction between the system and its environment. Geometric phases are only dependent on evolution paths of quantum systems but independent of the evolution details and therefore quantum computation based on geometric phases, i.e., geometric quantum computation, is robust against control errors, benefiting the realization of practical quantum computation. The early proposals of geometric quantum computation are based on adiabatic geometric phases. These proposals require quantum systems to undergo adiabatic evolution, which makes quantum systems evolve for a long time. To circumvent this, nonadiabatic geometric quantum computation based on nonadiabatic Abelian geometric phases was proposed soon after. In 2012, nonadiabatic holonomic quantum computation based on nonadiabatic non-Abelian geometric phases was proposed, which also circumvents long-time evolutions. Moreover, compared with nonadiabatic geometric quantum computation that uses the geometric phase as one parameter of a quantum gate, nonadiabatic holonomic quantum computation uses the holonomic matrix itself as a quantum gate. This makes nonadiabatic holonomic quantum computation possess whole-geometric property. Due to the merits of both geometric robustness and high-speed implementation without the limit of adiabatic evolution, nonadiabatic holonomic quantum computation has been attracting much attention. Until now, much progress has been achieved in the field of nonadiabatic holonomic quantum computation. On one hand, various methods have been proposed to design more efficient nonadiabatic holonomic gates. Nonadiabatic holonomic gates were first realized by using resonant laser fields to drive a three-level system. After this, the single-shot proposal and the single-loop proposal were proposed, allowing us to realize one-qubit gates by a shorter path and thereby reducing the exposure time of nonadiabatic holonomic gates to the environment. To further shorten the exposure time, the path-shortening protocol was put forward, where nonadiabatic holonomic gates can be realized based on a class of extended evolution paths that are shorter than the former ones. Recently, a general approach of constructing Hamiltonians for nonadiabatic holonomic quantum computation was put forward, by using which one can easily find a Hamiltonian making the quantum system evolve along a desired path so that nonadiabatic holonomic gates can be realized with an economical evolution time. On the other hand, various methods have been proposed to combine nonadiabatic holonomic gates and various decoherence-resilient methods, making the resulting schemes robust against both control errors and decoherence. The first proposal in this aspect is combining nonadiabatic holonomic gates and decoherence-free subspaces. Gradually, proposals combining nonadiabatic holonomic gates with noiseless subsystems, dynamical decoupling and surface codes were put forward. Last but not least, various proposals suitable for specific physical systems have been proposed and particularly various experimental platforms have been used to demonstrate nonadiabatic holonomic gates. This also significantly improves the development of nonadiabatic holonomic quantum computation. In this paper, we review the above research advances on nonadiabatic holonomic quantum computation, aiming to help readers understand the main developments of nonadiabatic holonomic quantum computation.
Quantum state preparation by adiabatic evolution is currently rendered ineffective by the long implementation times of the underlying quantum circuits, comparable to the decoherence time of present and near-term quantum devices. These implementation times can be significantly reduced by realizing these circuits with custom gates. Using classical computing, we model the output of a realistic two-qubit processor implementing the adiabatic evolution of a two-spin system by means of custom gates. This modeled output is then compared with the results of quantum simulations solving the same problem on IBM Quantum (IBMQ) systems. When used to emulate the behavior of the IBMQ quantum circuit, our realistic model yields state fidelities ranging from 65% to 85%, similar to the actual performance of a diverse set of IBMQ devices. When we reduced the implementation time by using custom gates, however, the loss of fidelity was reduced by at least a factor of 4, allowing us to accurately extract the energy of the target state. This improvement is enough to render adiabatic evolution useful for quantum state preparation for small systems or as a preconditioner for other state preparation methods.