The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers with more than two qubits describing the transition between the dark states. In light of this, we have been experimenting with the IBM Quantum Experience technology to determine the capabilities of simulating holonomic control of NV-centers for three qubits describing an eight-level system that produces a non-Abelian geometric phase. The tunability of the geometric phase via the detuning frequency is demonstrated through the high fidelity (about 80%) of 3-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate dark state with the qubits initial state hence decoherence of the multi-qubit system is well-controlled through a 0.33pi rotation. The electron return probability can exhibit spin-orbit coupling-like behavior as observed in topological materials based on the extra geometric phase.
Nonadiabatic holonomic quantum computation has attracted increasing interest because of its robustness. In this paper, based on the shortcuts to adiabaticity (STA), we propose a scheme to construct a three-qubit nonadiabatic holonomic gate in a cavity quantum electrodynamics system. In the scheme, the three-qubit holonomic gate is implemented in a single step. Besides, numerical simulations show that the constructed holonomic quantum gate holds the characteristics of high-fidelity, decoherence-resistance and error-immunity.
We investigate a non-adiabatic holonomic operation that enables us to entangle two fixed-frequency superconducting transmon qubits attached to a common bus resonator. Two coherent microwave tones are applied simultaneously to the two qubits and drive transitions between the first excited resonator state and the second excited state of each qubit. The cyclic evolution within this effective 3-level $Λ$-system gives rise to a holonomic operation entangling the two qubits. Two-qubit states with 95\% fidelity, limited mainly by charge-noise of the current device, are created within $213~\rm{ns}$. T…
Geometric phases are noise-resilient, and thus provide a robust way towards high fidelity quantum manipulation. Here we experimentally demonstrate arbitrary non-adiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmark…
Geometric phase is an indispensable element for achieving robust and high-fidelity quantum gates due to its built-in noise-resilience feature. However, due to the complexity of manipulation and the intrinsic leakage of the encoded quantum information to non-logical-qubit basis, the experimental realization of universal nonadiabatic holonomic quantum computation is very difficult. Here, we propose to implement scalable nonadiabatic holonomic quantum computation with decoherence-free subspace encoding on a two-dimensional square superconducting transmon-qubit lattice, where only the two-body int…
The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.
Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault tolerant quantum computation, due to its robustness against operational noises. However, because of the parametric restriction of previous schemes, the main robust advantage of holonomic quantum gates is smeared. Here, we experimentally demonstrate a solution scheme, demonstrating nonadiabatic holonomic single qubit quantum gates with optimal control in a trapped Yb ion based on three level systems with resonant drives, which also hold the advantages of fast evolution and convenient …
The non-adiabatic holonomic quantum computation with the advantages of fast and robustness attracts widespread attention in recent years. Here, we propose the first scheme for realizing universal single-qubit gates based on an optomechanical system working with the non-adiabatic geometric phases. Our quantum gates are robust to the control errors and the parameter fluctuations, and have unique functions to achieve the quantum state transfer and entanglement generation between cavities. We discuss the corresponding experimental parameters and give some simulations. Our scheme may have the pract…
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated with superconducting transmon qutrit. However, the original protocol requires two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources and therefore makes the gates vulnerable to environment-induced decoherence. Single-shot protocol was subsequently proposed to realize an arbit…
In recent years qubit designs such as transmons approached the fidelities of up to 0.999. However, even these devices are still insufficient for realizing quantum error correction requiring better than 0.9999 fidelity. Topologically protected superconducting qubits are arguably most prospective for building a realistic quantum computer as they are intrinsically protected from noise and leakage errors that occur in transmons. We propose a topologically protected qubit design based on a $π$-periodic Josephson element and a universal set of gates: protected Clifford group and highly robust (with …
We present a theoretical scheme that allows to perform a universal set of holonomic gates on a two qubit register, formed by a $^{13}$C nuclear spin coupled to the electron spin of a nitrogen-vacancy center in diamond. Strong hyperfine interaction between the electron spin and the spins of the first three shells of $^{13}$C atoms allows to operate the state of the register on the submicrosecond timescale using microwave pulses only. We describe the system and the operating regime analytically and numerically, as well as simulate the initialization protocols.
Surface codes can protect quantum information stored in qubits from local errors as long as the per-operation error rate is below a certain threshold. Here we propose holonomic surface codes by harnessing the quantum holonomy of the system. In our scheme, the holonomic gates are built via auxiliary qubits rather than the auxiliary levels in multilevel systems used in conventional holonomic quantum computation. The key advantage of our approach is that the auxiliary qubits are in their ground state before and after each gate operation, so they are not involved in the operation cycles of surface…
Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here, we report a systematic, scalable approach based on dynamical invariants to realize HQGs without using additional Hilbert spaces. While presenting the theoretical framework of our approach, we design and experimentally evaluate single-qubit and two-qubits HQGs for the nuclear magnetic resonance system. The single-qubit gates acquire average fidelity 0.9972 by…
The physical implementation of holonomic quantum computation is challenging due to the needed complex controllable interactions in multilevel quantum systems. Here we propose to implement nonadiabatic holonomic quantum computation with conventional capacitive coupled superconducting transmon qubits. A universal set of holonomic gates is constructed with the help of the interaction with an auxiliary qubit rather than relying on delicate control over an auxiliary level of multilevel quantum systems. Explicitly, these quantum gates are realized by tunable interactions in an all-resonant way, whic…
Previous schemes of nonadiabatic holonomic quantum computation were focused mainly on realizing a universal set of elementary gates. Multiqubit controlled gates could be built by decomposing them into a series of the universal gates. In this article, we propose an approach for realizing nonadiabatic holonomic multiqubit controlled gates in which a $(n+1)$-qubit controlled-$(\boldsymbol{\mathrm{n}\cdot \mathrmσ})$ gate is realized by $(2n-1)$ basic operations instead of decomposing it into the universal gates, whereas an $(n+1)$-qubit controlled arbitrary rotation gate can be obtained by combin…
Scalable universal holonomic quantum computation realized with an adiabatic quantum data bus and potential implementation using superconducting flux qubits
Geometric phases are well known to be noise-resilient in quantum evolutions/operations. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced by nonabelian geometric phases. Here we propose and elaborate how to efficiently implement universal nonadiabatic holonomic quantum gates on simpler superconducting circuits, with a single transmon serving as a qubit. In our proposal, an arbitrary single-qubit holonomic gate can be realized in a single-loop scenario, by varying the amplitudes and phase difference of two mic…
The high-speed implementation and robustness against of non-adiabatic holonomic quantum computation provide a new idea for overcoming the difficulty of quantum system interacting with the environment easily decoherence, which realizing large-scale quantum computer construction. Here, we show that a high-fidelity quantum gates to implement non-adiabatic holonomic quantum computation under solid-state spin in Nitrogen-Vacancy(NV) centers, providing an extensible experimental platform that has the potential for room-temperature quantum computing, which has increased attention recent years. Compar…
Quantum computing has been attracting tremendous efforts in recent years. One prominent application is to perform quantum simulations of electron correlations in large molecules and solid-state materials, where orbital degrees of freedom are crucial to quantitatively model electronic properties. Electron orbitals unlike quantum spins obey crystal symmetries, making the atomic orbital in optical lattices a natural candidate to emulate electron orbitals. Here, we construct atom-orbital qubits by manipulating $s$- and $d$-orbitals of atomic Bose-Einstein condensation in an optical lattice. Noise-…
Obtaining high-fidelity and robust quantum gates is the key for scalable quantum computation, and one of the promising ways is to implement quantum gates using geometric phases, where the influence of local noises can be greatly reduced. To obtain robust quantum gates, we here propose a scheme for quantum manipulation by combining the geometric phase approach with the dynamical correction technique, where the imperfection control induced X-error can be greatly suppressed. Moreover, to be robust against the decoherence effect and the randomized qubit-frequency shift Z-error, our scheme is also …
Nonadiabatic holonomic quantum computation~(NHQC) provides an essential way to construct robust and high-fidelity quantum gates due to its geometric features. However, NHQC is more sensitive to the decay and dephasing errors than conventional dynamical gate since it requires an ancillary intermediate state. Here, we utilize the Hamiltonian reverse engineering technique to study the influence of the intermediate state-decoherence on the NHQC gate fidelity, and propose the novel schemes to construct the arbitrary single-qubit holonomic gate and nontrivial two-qubit holonomic gate with high fidel…
We investigate an all-out optical setup allowing for generation of non-Abelian geometric phases on its large degenerate eigenspaces. The proposal has the form of an M -pod system and can be implemented in terms of integrated photonic waveguide structures. We show that by injecting a larger number of photons into the optical setup, the degeneracy of eigenspaces scales rapidly. After studying the spectral properties of our system for the general case, we show how arbitrary U(4) transformations can be generated on the dark subspace of an optical tripod filled with two photons. Moreover, a degener…
Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits
为了实现一组基于非阿贝尔几何相位的通用量子逻辑门，传统的观点是需要超过两个能级的量子系统，这对于超导量子比特来说是非常困难的，这似乎是为什么在最近的实验中只实现单量子比特门的主要原因[A. A. Abdumalikov Jr \emph{et al} .，Nature 496，482（2013）]。本文提出在无消相干子空间中利用电路QED实现非绝热完整量子计算，其中只需要传输子比特中的两个能级，一个通常的相互作用，以及一个最小的无消相干子空间编码资源.特别是，我们的方案不仅克服了以往研究中遇到的困难，而且仍然可以获得相当大的有效耦合强度，从而可以实现高保真度的量子门。因此，本方案为利用超导电路实现鲁棒完整量子计算提供了一条很有前途的途径。
