Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric pi-phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity-about six times better than in a previous experiment demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture that would enable scaling to large numbers of ion-qubits.

Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate*

Adiabatic evolution along the instantaneous eigenstate of a time-dependent Hamiltonian is used for robust and high fidelity state transfer in atomic and molecular physics. Shortcuts to adiabaticity (STA) are systematic approaches to accomplish the same final state transfer in a faster manner. This article presents an introduction to STA and reviews different theoretical approaches and applications of STA to a range of scientific and engineering tasks in quantum physics and beyond.

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Shortcuts to adiabaticity: Concepts, methods, and applications

Dressing-Up Diamond Defects The spin states of nitrogen vacancy defects in diamond are being explored as information carriers and memories in quantum information systems. Their long lifetimes, fast manipulation rates, and the ability to couple them to adjacent electronic and nuclear spins provide the necessary properties for implementation in solid-state quantum networks. To date, however, the readout of the spin state via photoluminescence, either directly or indirectly, results in the destruction of the spin state. Buckley et al. (p. 1212, published online 14 October; see the Perspective by Milburn) have formed a light-matter hybrid state in which the spin interacts with laser light to form a polariton state. This hybrid state can be optically probed to produce a nondestructive measurement and manipulation technique for the spin state of the nitrogen-vacancy center. Optical pulses were used to nondestructively probe and manipulate the spin state of nitrogen vacancy defects in diamond. The exceptional spin coherence of nitrogen-vacancy centers in diamond motivates their function in emerging quantum technologies. Traditionally, the spin state of individual centers is measured optically and destructively. We demonstrate dispersive, single-spin coupling to light for both nondestructive spin measurement, through the Faraday effect, and coherent spin manipulation, through the optical Stark effect. These interactions can enable the coherent exchange of quantum information between single nitrogen-vacancy spins and light, facilitating coherent measurement, control, and entanglement that is scalable over large distances.

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Observation of spin-light coherence for single spin measurement and control in diamond

Nonadiabatic holonomic quantum computation (NHQC) has been developed to shorten the construction times of geometric quantum gates. 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 nonadiabatic geometric gates can be constructed in an extensible way, called NHQC+, for maintaining both flexibility and robustness against certain types of noises. Consequently, this approach makes it possible to incorporate most of the existing optimal control methods, such as dynamical decoupling, composite pulses, and a shortcut to adiabaticity, into the construction of single-looped geometric gates. Furthermore, this extensible approach of geometric quantum computation can be applied to various physical platforms such as superconducting qubits and nitrogen-vacancy centers. Specifically, we performed numerical simulation to show how the noise robustness in recent experimental implementations [Phys. Rev. Lett. 119, 140503 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.140503; Nat. Photonics 11, 309 (2017)NPAHBY1749-488510.1038/nphoton.2017.40] can be significantly improved by our NHQC+.approach. These results cover a large class of new techniques combing the noise robustness of both geometric phase and optimal control theory.

Plug-and-Play Approach to Nonadiabatic Geometric Quantum Gates.

Preface. 1 Introduction and survey. 1.1 Information, computers and quantum mechanics. 1.1.1 Digital information. 1.1.2 Moore's law. 1.1.3 Emergence of quantum behavior. 1.1.4 Energy dissipation in computers. 1.2 Quantum computer basics. 1.2.1 Quantum information. 1.2.2 Quantum communication. 1.2.3 Basics of quantum information processing. 1.2.4 Decoherence. 1.2.5 Implementation. 1.3 History of quantum information processing. 1.3.1 Initial ideas. 1.3.2 Quantum algorithms. 1.3.3 Implementations. 2 Physics of computation. 2.1 Physical laws and information processing. 2.1.1 Hardware representation. 2.1.2 Quantum vs. classical information processing. 2.2 Limitations on computer performance. 2.2.1 Switching energy. 2.2.2 Entropy generation and Maxwell's demon. 2.2.3 Reversible logic. 2.2.4 Reversible gates for universal computers. 2.2.5 Processing speed. 2.2.6 Storage density. 2.3 The ultimate laptop. 2.3.1 Processing speed. 2.3.2 Maximum storage density. 3 Elements of classical computer science. 3.1 Bits of history. 3.2 Boolean algebra and logic gates. 3.2.1 Bits and gates. 3.2.2 2 bit logic gates. 3.2.3 Minimum set of irreversible gates. 3.2.4 Minimum set of reversible gates. 3.2.5 The CNOT gate. 3.2.6 The Toffoli gate. 3.2.7 The Fredkin gate. 3.3 Universal computers. 3.3.1 The Turing machine. 3.3.2 The Church Turing hypothesis. 3.4 Complexity and algorithms. 3.4.1 Complexity classes. 3.4.2 Hard and impossible problems. 4 Quantum mechanics. 4.1 General structure. 4.1.1 Spectral lines and stationary states. 4.1.2 Vectors in Hilbert space. 4.1.3 Operators in Hilbert space. 4.1.4 Dynamics and the Hamiltonian operator. 4.1.5 Measurements. 4.2 Quantum states. 4.2.1 The two dimensional Hilbert space: qubits, spins, and photons. 4.2.2 Hamiltonian and evolution. 4.2.3 Two or more qubits. 4.2.4 Density operator. 4.2.5 Entanglement and mixing. 4.2.6 Quantification of entanglement. 4.2.7 Bloch sphere. 4.2.8 EPR correlations. 4.2.9 Bell's theorem. 4.2.10 Violation of Bell's inequality. 4.2.11 The no cloning theorem. 4.3 Measurement revisited. 4.3.1 Quantum mechanical projection postulate. 4.3.2 The Copenhagen interpretation. 4.3.3 Von Neumann's model. 5 Quantum bits and quantum gates. 5.1 Single qubit gates. 5.1.1 Introduction. 5.1.2 Rotations around coordinate axes. 5.1.3 General rotations. 5.1.4 Composite rotations. 5.2 Two qubit gates. 5.2.1 Controlled gates. 5.2.2 Composite gates. 5.3 Universal sets of gates. 5.3.1 Choice of set. 5.3.2 Unitary operations. 5.3.3 Two qubit operations. 5.3.4 Approximating single qubit gates. 6 Feynman's contribution. 6.1 Simulating physics with computers. 6.1.1 Discrete system representations. 6.1.2 Probabilistic simulations. 6.2 Quantum mechanical computers. 6.2.1 Simple gates. 6.2.2 Adder circuits. 6.2.3 Qubit raising and lowering operators. 6.2.4 Adder Hamiltonian. 7 Errors and decoherence. 7.1 Motivation. 7.1.1 Sources of error. 7.1.2 A counterstrategy. 7.2 Decoherence. 7.2.1 Phenomenology. 7.2.2 Semiclassical description. 7.2.3 Quantum mechanical model. 7.2.4 Entanglement and mixing. 7.3 Error correction. 7.3.1 Basics. 7.3.2 Classical error correction. 7.3.3 Quantum error correction. 7.3.4 Single spin flip error. 7.3.5 Continuous phase errors. 7.3.6 General single qubit errors. 7.3.7 The quantum Zeno effect. 7.3.8 Stabilizer codes. 7.3.9 Fault tolerant computing. 7.4 Avoiding errors. 7.4.1 Basics. 7.4.2 Decoherence free subspaces. 7.4.3 NMR in Liquids. 7.4.4 Scaling considerations. 8 Tasks for quantum computers. 8.1 Quantum versus classical algorithms. 8.1.1 Why Quantum? 8.1.2 Classes of quantum algorithms. 8.2 The Deutsch algorithm: Looking at both sides of a coin at the same time. 8.2.1 Functions and their properties. 8.2.2 Example: one qubit functions. 8.2.3 Evaluation. 8.2.4 Many qubits. 8.2.5 Extensions and generalizations. 8.3 The Shor algorithm: It's prime time. 8.3.1 Some number theory. 8.3.2 Factoring strategy. 8.3.3 The core of Shor's algorithm. 8.3.4 The quantum Fourier transform. 8.3.5 Gates for the QFT. 8.4 The Grover algorithm: Looking for a needle in a haystack. 8.4.1 Oracle functions. 8.4.2 The search algorithm. 8.4.3 Geometrical analysis. 8.4.4 Quantum counting. 8.4.5 Phase estimation. 8.5 Quantum simulations. 8.5.1 Potential and limitations. 8.5.2 Motivation. 8.5.3 Simulated evolution. 8.5.4 Implementations. 9 How to build a quantum computer. 9.1 Components. 9.1.1 The network model. 9.1.2 Some existing and proposed implementations. 9.2 Requirements for quantum information processing hardware. 9.2.1 Qubits. 9.2.2 Initialization. 9.2.3 Decoherence time. 9.2.4 Quantum gates. 9.2.5 Readout. 9.3 Converting quantum to classical information. 9.3.1 Principle and strategies. 9.3.2 Example: Deutsch Jozsa algorithm. 9.3.3 Effect of correlations. 9.3.4 Repeated measurements. 9.4 Alternatives to the network model. 9.4.1 Linear optics and measurements. 9.4.2 Quantum cellular automata. 9.4.3 One way quantum computer. 10 Liquid state NMR quantum computer. 10.1 Basics of NMR. 10.1.1 System and interactions. 10.1.2 Radio frequency field. 10.1.3 Rotating frame. 10.1.4 Equation of motion. 10.1.5 Evolution. 10.1.6 NMR signals. 10.1.7 Refocusing. 10.2 NMR as a molecular quantum computer. 10.2.1 Spins as qubits. 10.2.2 Coupled spin systems. 10.2.3 Pseudo / effective pure states. 10.2.4 Single qubit gates. 10.2.5 Two qubit gates. 10.2.6 Readout. 10.2.7 Readout in multi spin systems. 10.2.8 Quantum state tomography. 10.2.9 DiVincenzo's criteria. 10.3 NMR Implementation of Shor's algorithm. 10.3.1 Qubit implementation. 10.3.2 Initialization. 10.3.3 Computation. 10.3.4 Readout. 10.3.5 Decoherence. 11 Ion trap quantum computers. 11.1 Trapping ions. 11.1.1 Ions, traps and light. 11.1.2 Linear traps. 11.2 Interaction with light. 11.2.1 Optical transitions. 11.2.2 Motional effects. 11.2.3 Basics of laser cooling. 11.3 Quantum information processing with trapped ions. 11.3.1 Qubits. 11.3.2 Single qubit gates. 11.3.3 Two qubit gates. 11.3.4 Readout. 11.4 Experimental implementations. 11.4.1 Systems. 11.4.2 Some results. 11.4.3 Problems. 12 Solid state quantum computers. 12.1 Solid state NMR/EPR. 12.1.1 Scaling behavior of NMR quantum information processors. 12.1.2 31P in silicon. 12.1.3 Other proposals. 12.1.4 Single spin readout. 12.2 Superconducting systems. 12.2.1 Charge qubits. 12.2.2 Flux qubits. 12.2.3 Gate operations. 12.2.4 Readout. 12.3 Semiconductor qubits. 12.3.1 Materials. 12.3.2 Excitons in quantum dots. 12.3.3 Electron spin qubits. 13 Quantum communication. 13.1 Quantum only tasks. 13.1.1 Quantum teleportation. 13.1.2 (Super ) Dense coding. 13.1.3 Quantum key distribution. 13.2 Information theory. 13.2.1 A few bits of classical information theory. 13.2.2 A few bits of quantum information theory. Appendix. A. Two spins 1/2: Singlet and triplet states. B. Symbols and abbreviations. Bibliography. Index.

Quantum Computing: A Short Course from Theory to Experiment

By using transitionless quantum driving algorithm (TQDA), we present an efficient scheme for the shortcuts to the holonomic quantum computation (HQC). It works in decoherence-free subspace (DFS) and the adiabatic process can be speeded up in the shortest possible time. More interestingly, we give a physical implementation for our shortcuts to HQC with nitrogen-vacancy centers in diamonds dispersively coupled to a whispering-gallery mode microsphere cavity. It can be efficiently realized by controlling appropriately the frequencies of the external laser pulses. Also, our scheme has good scalability with more qubits. Different from previous works, we first use TQDA to realize a universal HQC in DFS, including not only two noncommuting accelerated single-qubit holonomic gates but also a accelerated two-qubit holonomic controlled-phase gate, which provides the necessary shortcuts for the complete set of gates required for universal quantum computation. Moreover, our experimentally realizable shortcuts require only two-body interactions, not four-body ones, and they work in the dispersive regime, which relax greatly the difficulty of their physical implementation in experiment. Our numerical calculations show that the present scheme is robust against decoherence with current experimental parameters.

https://iopscience.iop.org/article/10.1088/1367-2630/18/2/023001/pdf

Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm

Three-level quantum systems, which possess some unique characteristics beyond two-level ones, such as electromagnetically induced transparency, coherent trapping, and Raman scatting, play important roles in solid-state quantum information processing. Here, we introduce an approach to implement the physically feasible three-level transitionless quantum driving with multiple Schr\"odinger dynamics (MSDs). It can be used to control accurately population transfer and entanglement generation for three-level quantum systems in a nonadiabatic way. Moreover, we propose an experimentally realizable hybrid architecture, based on two nitrogen-vacancy-center ensembles coupled to a transmission line resonator, to realize our transitionless scheme which requires fewer physical resources and simple procedures, and it is more robust against environmental noises and control parameter variations than conventional adiabatic passage techniques. All these features inspire the further application of MSDs on robust quantum information processing in experiment.

Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics

We present a proposal to realize the quantum Zeno effect (QZE) and quantum Zeno-like effect (QZLE) in a proximal 13C nuclear spin by controlling a proximal electron spin of a nitrogen vacancy (NV) center. The measurement is performed by applying a microwave pulse to induce the transition between different electronic spin states. Under the practical experimental conditions, our calculations show that there exist both QZE and QZLE in a 13C nuclear spin in the vicinity of an NV center.

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Jing Qiu

Papers

Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm

Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics

Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm

Quantum Zeno and Zeno-like effects in nitrogen vacancy centers

Erratum: Physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics [Phys. Rev. A 93, 052324 (2016)]