Non-adiabatic holonomic quantum computation, which recently attained a considerable attention, offers a promising approach for implementation of fast, universal, and robust quantum information processing. In this all-geometric approach, quantum gates are all based on non-adiabatic extensions of the geometric Berry phase effects. Apart from its fundamental and conceptual aspects, physical realizations of proposed mathematical structures play central role in the development of large-scale quantum computation. Here, we propose an experimentally feasible nano-engineered solid-state structure to realize geometric quantum computation via non-adiabatic quantum holonomies. We use a system of three coupled quantum dots containing a single electron, where two states of a double quantum-dot charge qubit interact through an intermediate quantum dot. Careful control of the inter-dot tunneling parameters makes it possible to create a geometric model system, which allows for robust and efficient quantum information processing.
Non-adiabatic holonomic quantum computation, which recently attained a considerable attention, offers a promising approach for implementation of fast, universal, and robust quantum information processing. In this all-geometric approach, quantum gates are all based on non-adiabatic extensions of the geometric Berry phase effects. Apart from its fundamental and conceptual aspects, physical realizations of proposed mathematical structures play central role in the development of large-scale quantum computation. Here, we propose an experimentally feasible nano-engineered solid-state structure to realize geometric quantum computation via non-adiabatic quantum holonomies. We use a system of three coupled quantum dots containing a single electron, where two states of a double quantum-dot charge qubit interact through an intermediate quantum dot. Careful control of the inter-dot tunneling parameters makes it possible to create a geometric model system, which allows for robust and efficient quantum information processing.
Reliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast, universal, and robust quantum logic gates particularly useful in nano-fabricated solid-state architectures, which typically have short coherence times. Here, we propose an experimentally feasible scheme to realize high-speed universal geometric quantum gates in nano-engineered pseudo-spin charge qubits. We use a system of three coupled quantum dots containing a single electron, where two computational states of a double quantum dot charge qubit interact through an intermediate quantum dot. The additional degree of freedom introduced into the qubit makes it possible to create a geometric model system, which allows robust and efficient single-qubit rotations through careful control of the inter-dot tunneling parameters. We demonstrate that a capacitive coupling between two charge qubits permits a family of non-adiabatic holonomic controlled two-qubit entangling gates, and thus provides a promising procedure to maintain entanglement in charge qubits and a pathway toward fault-tolerant universal quantum computation. We estimate the feasibility of the proposed structure by analyzing the gate fidelities to some extent.
A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
Geometrical phases acquired in cyclic quantum evolutions can be utilized as
natural resources for constructing robust logic gates for quantum information
processing, which was originally proposed through adiabatic changes of the
driving Hamiltonian. Practically, much efforts have been made to shorten the
construction times of geometrical gates, known as non-adiabatic holonomic
quantum computation (NHQC). However, previous NHQC gates require the driving
Hamiltonian to satisfy a set of rather restrictive conditions, reducing the
robustness of the resulting geometric gates against control errors. Here we
show that non-adiabatic geometric gates can be constructed in an alternative
way where the driving Hamiltonian can exhibit a high degree of flexibility for
retaining the robustness of the geometric phases. Consequently, this approach
makes it possible to incorporate most of the existing optimal control methods,
such as dynamical decoupling, composite pulses, and shortcut to adiabaticity,
into the construction of geometrical gates, to further address different types
of errors. Furthermore, this extensible approach of geometric quantum
computation can be applied to various physical platform such as superconducting
qubits and nitrogen-vacancy (NV) centers. Specifically, we performed numerical
simulation to show how the noise robustness in the recent experimental
implementations [Phys. Rev. Lett. 119, 140503 (2017)] and [Nat. Photonics 11,
309 (2017)] of NHQC with NV centers can be significantly improved by our
optimized NHQC approach. These results cover a large class of new techniques
combing the noise robustness of both geometric phase and optimal control
theory.
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.
Non-adiabatic geometric quantum computation (NGQC) and non-adiabatic holonomic quantum computation (NHQC) have been proposed to reduce the run time of geometric quantum gates. However, in terms of robustness against experimental control errors, the existing NGQC and NHQC scenarios have no advantage over standard dynamical gates in most cases. Here, we give the reasons of why non-adiabatic geometric gates are sensitive to the control errors, and further, we propose a new class of geometric property condition (GPC)-based non-adiabatic geometric gates, in which the global control condition can guarantee both high speed and robustness of geometric gate. To illustrate the working mechanism of GPC-based geometric gates, we give two simple examples of GPC-NGQC and GPC-NHQC for two- and three-level quantum systems, respectively. Theoretical and numerical results with the experimental parameters indicate that our scheme can significantly improve the gate performance comparing with the previous NGQC, NHQC and standard dynamical schemes. GPC-based geometric quantum computation can be applied to various physical platforms such as superconducting qubits, quantum dots, and trapped ions. All of these sufficiently show that our scheme provides a promising way towards robust geometric quantum computation.