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arXiv:2202.08061

Holonomic control of a three-qubits system in an NV center using a near-term quantum computer

Shaman Bhattacharyya, Somnath Bhattacharyya

Published Feb 16, 2022• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.2202.08061

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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.
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. Considering 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 (~85%) of three-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate's dark state with the qubit's initial state hence decoherence of the multi-qubit system is well-controlled through a π/3 rotation.
Although geometric phases in quantum evolution are 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 nonadiabatic 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.
A microwave shares a nonintuitive phase called the geometric phase with an interacting electron spin after an elastic scattering. The geometric phase, generally discarded as a global phase, allows universal holonomic gating of an ideal logical qubit, which we call a geometric spin qubit, defined in the degenerate subspace of the triplet spin qutrit. We here experimentally demonstrate nonadiabatic and non-abelian holonomic quantum gates over the geometric spin qubit on an electron or nitrogen nucleus. We manipulate purely the geometric phase with a polarised microwave in a nitrogen-vacancy centre in diamond under a zero-magnetic field at room temperature. We also demonstrate a two-qubit holonomic gate to show universality by manipulating the electron-nucleus entanglement. The universal holonomic gates enable fast and fault-tolerant manipulation for realising quantum repeaters interfacing between universal quantum computers and secure communication networks.
We present a theoretical scheme that allows one to perform a universal set of holonomic gates on a two-qubit register, formed by a 13C^{13}\mathrm{C}13C 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 13C^{13}\mathrm{C}13C atoms allows one 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.
Geometric phase gates are promising tools toward robust quantum computing owing to their robustness against certain control errors and decoherence. Here, we propose a multiqubit architecture with a nonadiabatic geometric phase gate scheme that is feasible in widely used superconducting qubit designs such as transmon and fluxonium. Through segmented microwave drive on multiple qubits coupled off-resonantly to a common resonator, the geometric phase gate is obtained from the qubit-state-dependent displacement of the resonator without fine-tuning the qubit frequencies. Fidelity above 99.99% is achieved in simulation under the available experimental parameters. Our scheme uses all-microwave control and only exploits the lowest qubit levels with long coherence time; thus it is desirable for experiments. Together with the single-qubit holonomic gates demonstrated in earlier experiments, our scheme can realize universal all-geometric quantum computing, and it also finds applications in quantum simulation with many-body interactions.
At its most fundamental level, circuit-based quantum computation relies on the application of controlled phase shift operations on quantum registers. While these operations are generally compromised by noise and imperfections, quantum gates based on geometric phase shifts can provide intrinsically fault-tolerant quantum computing. Here we demonstrate the high-fidelity realization of a recently proposed fast (non-adiabatic) and universal (non-Abelian) holonomic single-qubit gate, using an individual solid-state spin qubit under ambient conditions. This fault-tolerant quantum gate provides an elegant means for achieving the fidelity threshold indispensable for implementing quantum error correction protocols. Since we employ a spin qubit associated with a nitrogen-vacancy colour centre in diamond, this system is based on integrable and scalable hardware exhibiting strong analogy to current silicon technology. This quantum gate realization is a promising step towards viable, fault-tolerant quantum computing under ambient conditions. Quantum gates based on geometric phase shifts offer a promising approach for the realization of fault-tolerant quantum computing. Using nitrogen-vacancy centre qubits in diamond, this study experimentally realises a high-fidelty, non-adiabatic, non-Abelian holonomic single-qubit gate at room temperature.