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Although geometric phases in quantum evolution were historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary single-qubit holonomic gates from a single cycle of non-adiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.Besides its central role in the understanding of contemporary physics [1,2], the quantum geometric phase is gaining recognition as a powerful resource for practical applications using quantum systems [3][4][5]. The manipulation of nanoscale systems has progressed rapidly towards realizing quantum-enhanced information processing and sensing, but also revealed the necessity for new methods to combat noise and decoherence [6][7][8]. Due to their intrinsic tolerance to local fluctuations [9,10], geometric phases offer an attractive route for implementing high-fidelity quantum logic. This approach, termed holonomic quantum computation (HQC) [3,[11][12][13][14][15], employs the cyclic evolution of quantum states and derives its resilience from the global geometric structure of the evolution in Hilbert space. Arising both for adiabatic [16] and non-adiabatic [17] cycles, geometric phases can be either Abelian (phase shifts) or non-Abelian (matrix transformations) [18] by acting on a single state or a subspace of states, respectively.Recently, non-Abelian, non-adiabatic holonomic gates using three-level dynamics [19] were proposed to match the computational universality of earlier adiabatic schemes [3,[11][12][13], but also eliminate the restriction of slow evolution. By reducing the run-time of holonomic gates, and thus their exposure to decoherence, this advance enabled experimental demonstration of HQC in superconducting qubits [20], nuclear spin ensembles in liquid [21], and nitrogen-vacancy (NV) centers in diamond [22,23]. However, these initial demonstrations were limited to fixed rotation angles about arbitrary axes, and thus required two non-adiabatic loops of evolution, from two iterations of experimental control, to execute an arbitrary gate [20][21][22][23]. Alternatively, variable angle rotations from a single non-adiabatic loop can be achieved using Abelian geometric phases [14,24] or hyperbolic secant pulses [25][26][27], but these approaches are complicated by a concomitant dynamic phase. To address these shortcomings, non-Abelian, non-adiabatic single-loop schemes * awsch@uchicago.edu [28,29] were designed to allow purely geometric, arbitrary angle rotations about arbitrary axes with a single experimental iteration.In this Letter, we realize single-loop, single-qubit holonomic gates by implementing th...

The interaction of solid-state electronic spins with deformations of their host crystal is an important ingredient in many experiments realizing quantum information processing schemes. Here, we theoretically characterize that interaction for a nitrogen-vacancy (NV) center in diamond. We derive the symmetry-allowed Hamiltonian describing the interaction between the ground-state spin-triplet electronic configuration and the local strain. We numerically calculate the six coupling-strength parameters of the Hamiltonian using density functional theory, and propose an experimental setup for measuring those coupling strengths. The importance of this interaction is highlighted by the fact that it enables to drive spin transitions, both magnetically allowed and forbidden, via mechanically or electrically driven spin resonance. This means that the ac magnetic field routinely used in a wide range of spin-resonance experiments with NV centers could in principle be replaced by ac strain or ac electric field, potentially offering lower power requirements, simplified device layouts, faster spin control, and local addressability of electronic spin qubits.

We describe fabrication and testing of composite flux qubits combining Nb-and Al-based superconducting circuit technology. This hybrid approach to making qubits allows for employing π-phase shifters fabricated using well-established Nbbased technology of superconductor-ferromagnet-superconductor Josephson junctions. The important feature here is to obtain high interface transparency between Nb and Al layers without degrading sub-micron shadow mask. We achieve this by in-situ Ar etching using e-beam gun. Shadow-evaporated Al/AlO x /Al Josephson junctions with Nb bias pads show the expected current-voltage characteristics with reproducible critical currents. Using this technique, we fabricated composite Nb/Al flux qubits with Nb/CuNi/Nb π-shifters and measured their magnetic field response. The observed offset between the field responses of the qubits with and without πjunction is attributed to the π phase shift. The reported approach can be used for implementing a variety of hybrid Nb/Al superconducting quantum circuits.

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Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number n of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size 2n−2 can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such "complete" pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.

In search of two level quantum systems that implement a qubit, the nitrogen-vacancy (NV) center in diamond has been intensively studied for years. Despite favorable properties such as remarkable defect spin coherence times, the addressability of NV centers raises some technical issues. The coupling of a single NV center to an external driving field is limited to short distances, since an efficient coupling requires the NV to be separated by only a few microns away from the source. As a way to overcome this problem, an enhancement of coherent coupling between NV centers and a microwave field has recently been experimentally demonstrated using spin waves propagating in an adjacent yttrium iron garnet (YIG) film 1 . In this paper we analyze the optically detected magnetic resonance spectra that arise when an NV center is placed on top of a YIG film for a geometry similar to the one in the experiment. We analytically calculate the oscillating magnetic field of the spin wave on top of the YIG surface to determine the coupling of spin waves to the NV center. We compare this coupling to the case when the spin waves are absent and the NV center is driven only with the antenna field and show that the calculated coupling enhancement is dramatic and agrees well with the one obtained in the recent experiment.

In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic evolution can be viewed as a conventional Hamiltonian dynamics in an appropriately chosen extended Hilbert space. In contrast to the existing approaches, our method does not require the calculation of the non-Abelian Berry connection and can be applied without any parametrization of the dark subspace, which becomes a challenging problem with increasing system size.