Producing and maintaining entanglement reside at the heart of the optimal construction of quantum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that allows the geometric implementation of entangling gates between the register qubits with any arbitrary entangling power. We show this by demonstrating a circuit through a spin chain, which performs universal nonadiabatic holonomic two-qubit entanglers. The proposed gates are all electric and geometric, which would help to realize fast and robust entangling gates on spin qubits. This family of entangling gates contains gates that are as efficient as the cnot gate in quantum algorithms. We examine the robustness of the circuit to some extent.
Producing and maintaining entanglement reside at the heart of the optimal construction of quantum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that allows the geometric implementation of entangling gates between the register qubits with any arbitrary entangling power. We show this by demonstrating a circuit through a spin chain, which performs universal nonadiabatic holonomic two-qubit entanglers. The proposed gates are all electric and geometric, which would help to realize fast and robust entangling gates on spin qubits. This family of entangling gates contains gates that are as efficient as the cnot gate in quantum algorithms. We examine the robustness of the circuit to some extent.
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.
Geometric phases are well known to be noise resilient in quantum evolutions and operations. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced by non-Abelian 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 microwave fields resonantly coupled to a transmon, while nontrivial two-qubit holonomic gates may be generated with a transmission-line resonator being simultaneously coupled to the two target transmons in an effective resonant way. Moreover, our scenario may readily be scaled up to a two-dimensional lattice configuration, which is able to support large scalable quantum computation, paving the way for practically implementing universal nonadiabatic holonomic quantum computation with superconducting circuits.
Abstract The nonadiabatic holonomic quantum computation has attracted much attention in recent years because of its fastness and robustness. Here, the first scheme to realize theoretically universal single‐qubit gates on an optomechanical system working with nonadiabatic geometric phases is proposed. These quantum gates are robust to the control errors and parameter fluctuations. They can be used to achieve efficiently both quantum state transfer and entanglement generation between two optical modes via the intermediate action of a mechanical mode, showing that they are useful in robust quantum information processing.
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.
Recent advances in the physical sciences and engineering have created great hopes for new computational paradigms and substrates. One such new approach is the quantum computer, which holds the promise of enhanced computational power. Analogous to the way a classical computer is built from electrical circuits containing wires and logic gates, a quantum computer is built from quantum circuits containing quantum wires and elementary quantum gates to transport and manipulate quantum information. Therefore, design of quantum gates and quantum circuits is a prerequisite for any real application of quantum computation.
In this dissertation we apply geometric control methods from differential geometry and Lie group representation theory to analyze the properties of quantum gates and to design optimal quantum circuits. Using the Cartan decomposition and the Weyl group, we show that the geometric structure of nonlocal two-qubit gates is a 3-Torus. After further reducing the symmetry, the geometric representation of nonlocal gates is seen to be conveniently visualized as a tetrahedron. Each point in this tetrahedron except on the base corresponds to a different equivalent class of nonlocal gates. This geometric representation is one of the cornerstones for the discussion on quantum computation in this dissertation.
We investigate the properties of those two-qubit operations that can generate maximal entanglement. It is an astonishing finding that if we randomly choose a two-qubit operation, the probability that we obtain a perfect entangler is exactly one half. We prove that given a two-body interaction Hamiltonian, it is always possible to explicitly construct a quantum circuit for exact simulation of any arbitrary nonlocal two-qubit gate by turning on the two-body interaction for at most three times, together with at most four local gates. We also provide an analytic approach to construct a universal quantum circuit from any entangling gate supplemented with local gates. Closed form solutions have been derived for each step in this explicit construction procedure. Moreover, the minimum upper bound is found to construct a universal quantum circuit from any Controlled-Unitary gate. A near optimal explicit construction of universal quantum circuits from a given Controlled-Unitary is provided. For the Controlled-NOT and Double-CNOT gate, we then develop simple analytic ways to construct universal quantum circuits with exactly three applications, which is the least possible for these gates. We further discover a new quantum gate (named B gate) that achieves the desired universality with minimal number of gates. Optimal implementation of single-qubit quantum gates is also investigated. Finally, as a real physical application, a constructive way to implement any arbitrary two-qubit operation on a spin electronics system is discussed.
Quantum gates based on geometric phases possess intrinsic noise-resilience features and attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates. As a result, their experimental control inevitably suffers from the cumulative disturbances of systematic errors due to excessive time consumption. Here, we experimentally implement noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit, significantly shortening the gate time. Moreover, we experimentally verify that our universal single-qubit geometric gates are more robust to both the Rabi frequency and the qubit frequency shift-induced error, compared with the conventional dynamical gates, using the randomized benchmarking method. This scheme can also be utilized to construct two-qubit geometric operations while the generation of maximally entangled Bell states is demonstrated. Therefore, our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates in superconducting quantum circuits.