Universal Set Of Quantum Gates Research Articles

Deutsch, Toffoli, and cnot Gates via Rydberg Blockade of Neutral Atoms

Universal quantum gates and quantum error correction~(QEC) lie in the heart of quantum information science. Large-scale quantum computing depends on a universal set of quantum gates, in which some gates may be easily carried out, while others are hard with a certain physical system. There is a unique three-qubit quantum gate called the Deutsch gate~[$\mathbb{D}(\theta)$], from which alone a circuit can be constructed so that any feasible quantum computing is attainable. As far as we know, however, $\mathbb{D}(\theta)$ has not been demonstrated. Here we design an easily realizable $\mathbb{D}(\theta)$ by using Rydberg blockade of neutral atoms, where $\theta$ can be tuned to any value in $[0,\pi]$ by adjusting the strengths of external control fields. Using similar protocols, we further show that both the Toffoli and CNOT gates can be achieved with only three laser pulses. The Toffoli gate, being universal for classical reversible computing, is also useful for QEC that plays an important role in quantum communication and fault-tolerant quantum computation. The possibility and briefness to realize these gates shed new light on the study of quantum information with neutral atoms.

Universal non-adiabatic holonomic quantum computation in decoherence-free subspaces with quantum dots inside a cavity

A scheme for implementing the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with the interactions between a microcavity and quantum dots. A universal set of quantum gates can be constructed on the encoded logical qubits with high fidelities. The current scheme can suppress both local and collective noises, which is very important for achieving universal quantum computation. Discussions about the gate fidelities with the experimental parameters show that our schemes can be implemented in current experimental technology. Therefore, our scenario offers a method for universal and robust solid-state quantum computation.

Realizing universal quantum gates with topological bases in quantum-simulated superconducting chains

One-dimensional time-reversal invariant topological superconducting wires of the symmetry class DIII exhibit exotic physics which can be exploited to realize the set of universal operations in topological quantum computing. However, the verification of DIII-class physics in conventional condensed matter materials is highly nontrivial due to realistic constraints. Here we propose a symmetry-protected hard-core boson simulator of the one-dimensional DIII topological superconductor. By using the developed dispersive dynamic modulation approach, not only the faithful simulation of this new type of spinful superconducting chains is achieved, but also a set of universal quantum gates can be realized with the computational basis formed by the degenerate ground states that are topologically protected against random local perturbations. Physical implementation of our scheme based on a Josephson quantum circuit is presented, where our detailed analysis pinpoints that this scheme is experimentally feasible with the state-of-the-art technology.

Learning robust pulses for generating universal quantum gates.

Constructing a set of universal quantum gates is a fundamental task for quantum computation. The existence of noises, disturbances and fluctuations is unavoidable during the process of implementing quantum gates for most practical quantum systems. This paper employs a sampling-based learning method to find robust control pulses for generating a set of universal quantum gates. Numerical results show that the learned robust control fields are insensitive to disturbances, uncertainties and fluctuations during the process of realizing universal quantum gates.

Deterministic implementations of quantum gates with circuit QEDs via Stark-chirped rapid adiabatic passages

We show that a set of universal quantum gates could be implemented robustly in a circuit QED system by using Stark-chirped rapid adiabatic passage (SCRAP) technique. Under the adiabatic limit we find that the population transfers could be deterministically passaged from one selected quantum states to the others, and thus the desired quantum gates can be implemented. The proposed SCRAP-based gates are insensitive to the details of the operations and thus relax the designs of the applied pulses, operational imperfections, and the decoherence of the system.

Cavity QED implementation of non-adiabatic holonomies for universal quantum gates in decoherence-free subspaces with nitrogen-vacancy centers.

A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-vacancy centers, can be used to construct a universal set of quantum gates on the encoded logical qubits. Therefore, our scheme opens up the possibility of realizing universal holonomic quantum computation with cavity assisted interaction on solid-state spins characterized by long coherence times.

Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond

A negatively charged nitrogen vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.

The expressive power of quantum walks in terms of language acceptance

Discrete time quantum walks are known to be universal for quantum computation. This has been proven by showing that they can simulate a universal quantum gate set. In this paper, we examine computation by quantum walks in terms of language acceptance, and present two ways in which discrete time quantum walks can accept some languages with certainty. These walks can take quantum as well as classical inputs, and we show that when the input is quantum, the walks can also be interpreted as performing the task of quantum state discrimination.

Study of a quantum CNOT logic gate with electron spins of diamond impurities

Quantum computing requires a set of universal quantum gates. The standard set includes single quantum bit (qubit) gates and the controlled-NOT (CNOT) which is the analog of the classical XOR gate. It flips the state of the target qubit conditioned on the state of the control qubit. We investigated the possibility of implementing a CNOT logic gate using magnetically coupled impurity spins of diamond, namely the electron spin-1 carried by the nitrogen-vacancy color center and the electron spin-12 carried by a nearby nitrogen atom in substitutional position (P1 center). It is shown that a 96ns gate time with a high-fidelity can be realized by means of pulsed electron spin resonance spectroscopy.

Quantum computing through electron propagation in edge states of quantum spin Hall systems

We propose to implement quantum computing based on electronic spin qubits by controlling the propagation of the electron wave packets through the helical edge states of quantum spin Hall systems (QSHs). Specfically, two non-commutative single-qubit gates, which rotate a qubit around z and y axes, can be realized by utilizing gate voltages either on a single QSH edge channel or on a quantum point contact structure. The more challenging two-qubit controlled phase gate can be implemented through the on-demand capacitive Coulomb interaction between two adjacent edge channels from two parallel QSHs. As a result, a universal set of quantum gates can be achieved in an all-electrical way. The fidelity and purity of the two-qubit gate are calculated with both time delay and finite width of the wave packets taken into consideration, which can reach high values with the existing high-quality single electron source.

Universal quantum computation with Majorana fermion edge modes through microwave spectroscopy of quasi-one-dimensional cold gases in optical lattices

We describe how microwave spectroscopy of cold fermions in quasi-1D traps can be used to detect, manipulate, and entangle exotic non-local qbits associated with "Majorana" edge modes. We present different approaches to generate the p-wave superfluidity which is responsible for these topological zero-energy edge modes. We find that the edge modes have clear signatures in the microwave spectrum, and that the line shape distinguishes between the degenerate states of a qbit encoded in these edge modes. Moreover, the microwaves rotate the system in its degenerate ground-state manifold. We use these rotations to implement a set of universal quantum gates, allowing the system to be used as a universal quantum computer.

Nonadiabatic processes in Majorana qubit systems

We investigate the non-adiabatic processes occurring during the manipulations of Majorana qubits in 1-D semiconducting wires with proximity induced superconductivity. Majorana qubits are usually protected by the excitation gap. Yet, manipulations performed at a finite pace can introduce both decoherence and renormalization effects. Though exponentially small for slow manipulations, these effects are important as they may constitute the ultimate decoherence mechanism. Moreover, as adiabatic topological manipulations fail to produce a universal set of quantum gates, non-adiabatic manipulations might be necessary to perform quantum computation.

Nonadiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

Geometric manipulation of ensembles of atoms on an atom chip for quantum computation

We propose a feasible scheme to achieve quantum computation based on geometric manipulation of ensembles of atoms and analyze it for neutral rubidium atoms magnetically trapped in planoconcave microcavities on an atom chip. The geometric operations are accomplished by optical excitation of a single atom into a Rydberg state in a constant electric field. Strong dipole-dipole interactions and incident lasers drive the dark state of the atom ensembles to undergo cyclic evolutions that realize a universal set of quantum gates. Such geometric manipulation turns out naturally to protect the qubits from the errors induced by nonuniform laser illumination as well as cavity loss. The gate performance and decoherence processes are assessed by numerical simulation.

Universal Quantum Gate Set Approaching Fault-Tolerant Thresholds with Superconducting Qubits

We use quantum process tomography to characterize a full universal set of all-microwave gates on two superconducting single-frequency single-junction transmon qubits. All extracted gate fidelities, including those for Clifford group generators, single-qubit π/4 and π/8 rotations, and a two-qubit controlled-not, exceed 95% (98%), without (with) subtracting state preparation and measurement errors. Furthermore, we introduce a process map representation in the Pauli basis which is visually efficient and informative. This high-fidelity gate set serves as a critical building block towards scalable architectures of superconducting qubits for error correction schemes and pushes up on the known limits of quantum gate characterization.

Universal quantum computation with ordered spin-chain networks

It is shown that anisotropic spin chains with gapped bulk excitations and magnetically ordered ground states offer a promising platform for quantum computation, which bridges the conventional single-spin-based qubit concept with recently developed topological Majorana-based proposals. We show how to realize the single-qubit Hadamard, phase, and $\ensuremath{\pi}/8$ gates as well as the two-qubit controlled-not (cnot) gate, which together form a fault-tolerant universal set of quantum gates. The gates are implemented by judiciously controlling Ising exchange and magnetic fields along a network of spin chains, with each individual qubit furnished by a spin-chain segment. A subset of single-qubit operations is geometric in nature, relying on control of anisotropy of spin interactions rather than their strength. We contrast topological aspects of the anisotropic spin-chain networks to those of $p$-wave superconducting wires discussed in the literature.

Robust high-fidelity universal set of quantum gates through non-adiabatic rapid passage

We show how a robust high-fidelity universal set of quantum gates can be implemented using a single form of non-adiabatic rapid passage whose parameters are optimized to maximize gate fidelity and reward gate robustness. Each gate in the universal set is found to operate with a fidelity ℱ in the range 0.99988 < ℱ < 0.99999, and to require control parameters with no more than 14 bit (1 part in 104) precision. Such precision is within reach of commercially available arbitrary waveform generators, so that an experimental study of this approach to high-fidelity universal quantum control appears feasible.

The trapped-ion qubit tool box

In this tutorial we review the basic building blocks of Quantum Information Processing with cold trapped atomic ions. We mainly focus on methods to implement single-qubit rotations and two-qubit entangling gates, which form a universal set of quantum gates. Different ion qubit choices and their respective gate implementations are described.

Adiabatic coherent control in the anharmonic ion trap: Proposal for the vibrational two-qubit system

A method for encoding a multiqubit system into the quantized motional states of ion string in an anharmonic linear trap is proposed. Control over this system is achieved by applying oscillatory electric fields (rf) shaped optimally for desired state-to-state transitions. Anharmonicity of the vibrational spectrum of the system plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. The anharmonic trap architecture proposed earlier [Phys. Rev. A 83, 022305 (2011)] is explored here and the optimal control theory is used to derive pulses for a set of universal quantum gates. An accurate choice of pulse parameters allows deriving gates that are both accurate and simple. A practical realization of this approach seems to be within the reach of today's technology.

High Fidelity Quantum Gates via Dynamical Decoupling

Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of magnitude improvement in the fidelities of a universal set of quantum gates, relative to unprotected evolution, is achieved over a broad range of system-environment coupling strengths, using recursively constructed (concatenated) dynamical decoupling pulse sequences.