Gates For Quantum Computation Research Articles

Facilitation of controllable excitation in Rydberg atomic ensembles

Strongly-interacting Rydberg atomic ensembles have shown intense collective excitation effects due to the inclusion of single Rydberg excitation shared by multiple atoms in the ensemble. In this paper we investigate a counter-intuitive Rydberg excitation facilitation with a strongly-interacting atomic ensemble in the strong probe-field regime, which is enabled by the role of a control atom nearby. Differing from the case of a single ensemble, we show that, the control atom's excitation adds to a second two-photon transition onto the doubly-excited Rydberg state, arising an excitation facilitation for the ensemble atoms. Our numerical studies depending on the method of quantum Monte Carlo wave function, exhibit the observation constraints of this excitation facilitation effect under practical experimental conditions. The results obtained can provide a flexible control for the excitation of Rydberg atomic ensembles and participate further uses in developing mesoscopic Rydberg gates for multiqubit quantum computation.

Implementation of a Frenkel exciton-based controlled phase shifter

Frenkel excitons are of interest for ultrafast switching applications due to the femtosecond timescale at which coherent exciton transfer between chromophores takes place. The Frenkel Hamiltonian, which governs the dynamics of Frenkel excitons, belongs to a class of Hamiltonians that enable universal quantum computation. It is thus of interest to determine how a complete set of exciton-based gates for quantum computing could be constructed as aggregates of chromophores. We demonstrate that a controlled phase shifter can be constructed as a pair of exciton transmission lines that employ two types of chromophores and that are cross coupled by a two-exciton interaction. This element facilitates the construction of controlled basis-change gates, thereby enabling the implementation of a complete set of exciton-based gates for universal quantum computation.

Effect of Gaussian and Bessel laser beams on linear and nonlinear optical properties of vertically coupled cylindrical quantum dots

Vertically coupled quantum dots are one of the most interesting and promising structures, which find application in a wide range of fields. Particularly, they are noteworthy candidates as a source of single photon and entangled photon pair sources, as qubits and quantum gates in quantum computation, etc. Various external perturbations can act as an instrument for the manipulation of the properties of these structures and an intense laser field is a great example of this. In this work, vertically coupled cylindrical quantum dots made of InAs in a GaAs matrix with a modified Pöschl–Teller potential have been considered under intense laser fields with two laser beam profiles: Gaussian and Bessel. The energy levels and wave functions have been obtained for this structure. Linear and third-order nonlinear absorption coefficients, refractive index changes and second and third harmonic generation susceptibilities have been investigated at different temperatures and for different values of the laser parameters.

Quantum Control of Hole Spin Qubits in Double Quantum Dots

Hole spin qubits in semiconductor quantum dots (QDs) are promising candidates for quantum information processing due to their weak hyperfine coupling to nuclear spins, and to the strong spin-orbit coupling which allows for rapid operation time. We propose a coherent control on two heavy-hole spin qubits in a double QD by a fast adiabatic driving protocol, which helps to achieve higher fidelities than other experimentally commonly used protocols as linear ramping, $\pi$-pulses or Landau-Zener passages. Using fast quasiadiabatic driving via spin-orbit coupling, it is possible to reduce charge noise significantly for qubit manipulation and achieve high robustness for the qubit initialization. We also implement one and two-qubit gates, in particular, NOT, CNOT, and SWAP-like gates, of hole spins in a double QD achieving fidelities above $99\%$, exhibiting the capability of hole spins to implement universal gates for quantum computing.

Universal quantum computation via quantum controlled classical operations

A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results in universal quantum computing. Motivated by the latter, we pose the following question: can one perform universal quantum computation by supplementing a set of classical gates with a quantum control, and a set of quantum gates operating solely on the latter? In this work we provide an affirmative answer to this question by considering a computational model that consists of 2n target bits together with a set of classical gates controlled by log (2n + 1) ancillary qubits. We show that this model is equivalent to a quantum computer operating on n qubits. Furthermore, we show that even a primitive computer that is capable of implementing only SWAP gates, can be lifted to universal quantum computing, if aided with an appropriate quantum control of logarithmic size. Our results thus exemplify the information processing power brought forth by the quantum control system.

The Self-Learning Gate for Quantum Computing

Self-learning is one of the most important scientific methods that helps develop sciences, as it derives from the desire and interests of the individual. However, self-learning loses importance if it does not follow the scientific methodology for building and organizing information. The case becomes harder if the science is new and few scientific sources are available. Quantum computing is one of the new sciences in computer science and needs the support of specialists to develop it. Quantum computing overlaps with many sciences such as physics, chemistry, and mathematics, so any student in one of the previous disciplines may lose the correct self-learning path to find themselves learning the details of another discipline that does not achieve their goals. This article motivates students and those interested in computer science to begin studying the science of quantum computing and choose the same specialization that suits their interests. The article also provides a roadmap for self-learning steps to protect the learner from losing the correct learning path. I have categorized the stages of learning quantum computing into four steps through which all the essential basics can be learned, provided the goals mentioned in each stage which should be achieved. The learning strategy proposed in this article corresponds with individuals’ self-learning rules. Through my personal experience, the proposed learning strategy has proven its effectiveness in building information in an enjoyable scientific way.

Skyrmion Qubits: A New Class of Quantum Logic Elements Based on Nanoscale Magnetization.

We introduce a new class of primitive building blocks for realizing quantum logic elements based on nanoscale magnetization textures called skyrmions. In a skyrmion qubit, information is stored in the quantum degree of helicity, and the logical states can be adjusted by electric and magnetic fields, offering a rich operation regime with high anharmonicity. By exploring a large parameter space, we propose two skyrmion qubit variants depending on their quantized state. We discuss appropriate microwave pulses required to generate single-qubit gates for quantum computing, and skyrmion multiqubit schemes for a scalable architecture with tailored couplings. Scalability, controllability by microwave fields, operation time scales, and readout by nonvolatile techniques converge to make the skyrmion qubit highly attractive as a logical element of a quantum processor.

Deterministic CNOT gate and complete Bell-state analyzer on quantum-dot-confined electron spins based on faithful quantum nondemolition parity detection

The quantum controlled-NOT (CNOT) gate is a prototypical two-qubit quantum logic gate that provides the basic controlled logic for a set of gates for universal quantum computation. It has been shown that parity checking devices can be used to construct CNOT gates, and the fidelity of a CNOT operation is highly constrained by the fidelity of parity detection with this strategy. In this paper, a scheme to implement a CNOT operation on two stationary electron spins confined in quantum dots (QDs) inside double-sided optical microcavities is presented, based on the faithful parity detection achieved by a heralded and robust two-electron-spin quantum nondemolition (QND) parity detector. The QND parity detector is considerably different from previous implementations and experimentally more realizable, and works in the heralded and repeat-until-success fashion with robust fidelity, which enables our CNOT gate to be implemented deterministically with unity fidelity. Moreover, based on the features of the QND parity detector, a complete Bell-state analysis on two QD-confined electron spins can be realized without wrong judgment or any destruction of the analyzed entangled state. The efficiency of parity detection is also discussed by considering currently achievable system parameters.

Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings

Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long one-dimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit couplings. Here, we devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor such localized modes by tuning the local potential of individual ions with programmable optical tweezers. Localized modes of small subsets of qubits form the basis to perform entangling gates on these subsets in parallel. We demonstrate the inherent scalability of this approach by presenting analytical and numerical results for long 1D ion chains and even for infinite chains of uniformly spaced ions. Furthermore, we show that combining our methods with optimal coherent control techniques allows to realize maximally dense universal parallelized quantum circuits.

On the robustness of the hybrid qubit computational gates through simulated randomized benchmarking protocols

One of the main challenges in building a quantum processor is to characterize the environmental noise. Noise characterization can be achieved by exploiting different techniques, such as randomization where several sequences of random quantum gates are applied to the qubit under test to derive statistical characteristics about the affecting noises. A scalable and robust algorithm able to benchmark the full set of Clifford gates using randomization techniques is called randomized benchmarking. In this study, we simulated randomized benchmarking protocols in a semiconducting all-electrical three-electron double-quantum dot qubit, i.e. hybrid qubit, under different error models, that include quasi-static Gaussian and the more realistic 1/f noise model, for the input controls. The average error of specific quantum computational gates is extracted through interleaved randomized benchmarking obtained including Clifford gates between the gate of interest. It provides an estimate of the fidelity as well as theoretical bounds for the average error of the gate under test.

Holistic and Compositional Logics Based on the Bertini Gate

The theory of logical gates in quantum computation has inspired the development of new forms of quantum logic where the meaning of a formula is identified with a density operator and the logical connectives are interpreted as operations defined in terms of quantum gates. We show some relations between the Bertini gate and many valued connectives by probability values. On this basis, one can deal with quantum circuits as expressions in an algebraic environment such as product many valued algebra for combinational circuits. As can be expected, we show that the compositional logic characterized by the qubit semantics is stronger than the compositional Łukasiewicz quantum computational logic by a counterexample. But, in the holistic case, we conjecture that they can characterize the same logic.

High-fidelity heralded quantum squeezing gate based on entanglement.

Squeezing operation is critical in Gaussian quantum information. A high-fidelity heralded squeezing gate was recently realized using a noiseless linear amplifier with moderate ancillary squeezing. Here we analyze the heralded scheme based on squeezing [J. Zhao, Nat. Photonics, 14, 306 (2020)] and find that its fidelity depends heavily on the purity of auxiliary squeezing, and even the fidelity with a 6 dB pure squeezed state is better than with a 15 dB thermal squeezed state. On this basis, we construct a new heralded squeezing gate based on teleportation, which can overcome the shortcomings of the heralded scheme based on squeezing and is immune to the purity of input squeezing. It can better use the current best available squeezing (15 dB) to realize a perfect squeezing gate for fault-tolerant continuous-variable quantum computation. This scheme is promising to realize other single-mode Gaussian operations and non-classical state squeezing operations.

Massless Majorna bispinors and two-qubit entangled states

This is a pedagogical paper, where bispinors solutions to the four-dimensional massless Dirac equation are considered in relativistic quantum mechanics and in quantum computation, taking advantage of the common mathematical description of four-dimensional spaces. First, Weyl and massless Majorana bispinors are shown to be unitary equivalent, closing a gap in the literature regarding their equivalence. A discrepancy in the number of linearly independent solutions reported in the literature is also addressed. Then, it is shown that Weyl bispinors are algebraically equivalent to two-qubit direct product states, and that the massless Majorana bispinors are algebraically equivalent to maximally entangled sates (Bell states), with the transformations relating the two bispinors types acting as entangling gates in quantum computation. Different types of entangling gates are presented, highlighting a set that fulfills the required properties for Majorana zero mode operators in topological quantum computation. Based on this set, a general topological quantum computation model with four Majorana operators is presented, which exhibits all the required technical and physical properties to obtain entanglement of two logical qubits from tpological operations.

Controlled phase gate and Grover’s search algorithm on two distant NV-centers assisted by an NAMR

We propose a scheme to construct a controlled phase gate on two distant nitrogen-vacancy centers (NV-centers) assisted by a quantized nanomechanical cantilevel resonator (NAMR). Unlike the previous work to complete the gate in the dispersive regime to let NV-centers detune with the NAMR largely, our gate is completed by using resonant operations between NV-centers and the NAMR, and single-qubit operations on the NV-center, which let the gate to be achieved within a short time with a high fidelity. To study the performance of the gate for universal quantum computation, we simulate a two-qubit Grover’s search algorithm on the NV-centers with a fidelity of $$98.46\%$$.

Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System.

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

Fuzzy representation of finite-valued quantum gates

The theory of logical gates in quantum computation has inspired the development of new forms of quantum logic based on the following semantic idea: the meaning of a formula is identified with a quantum information quantity, represented by a density operator. At the same time, the logical connectives are interpreted as operations defined in terms of quantum gates. In this framework, some possible relations between fuzzy representations based on continuous t-norms for quantum gates and the probabilistic behavior of quantum computational finite-valued connectives are investigated. In particular, a fuzzy-type representation for quantum many-valued extensions of the gates introduced by Toffoli, Fredkin and Peres is described.

Quantum origami: Transversal gates for quantum computation and measurement of topological order

In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and fusion rules of emergent anyonic excitations and thus serve as a diagnostic of topological order. Moreover, modular transformations of higher genus surfaces, e.g. a torus with multiple handles, can enhance the computational power of a topological state, in many cases providing a universal fault-tolerant set of gates for quantum computation. However, due to the intrusive nature of modular transformations, which abstractly involve global operations and manifold surgery, physical implementations of them in local systems have remained elusive. Here, we show that by folding manifolds, modular transformations can be applied in a single shot by independent local unitaries, providing a novel class of transversal logic gates for fault-tolerant quantum computation. Specifically, we demonstrate that multi-layer topological states with appropriate boundary conditions and twist defects allow modular transformations to be effectively implemented by a finite sequence of local SWAP gates between the layers. We further provide methods to directly measure the modular matrices, and thus the fractional statistics of anyonic excitations, providing a novel way to directly measure topological order.

CNOT gate operation on a photogenerated molecular electron spin-qubit pair.

Implementation of the two-qubit controlled-NOT (CNOT) gate is necessary to develop a complete set of universal gates for quantum computing. Here, we demonstrate that a photogenerated radical (spin qubit) pair within a covalent donor-chromophore-acceptor molecule can be used to successfully execute a CNOT gate with high fidelity. The donor is tetrathiafulvalene (TTF), the chromophore is 8-aminonaphthalene-1,8-dicarboximide (ANI), and the acceptor is pyromellitimide (PI). Selective photoexcitation of ANI with a 416 nm laser pulse results in subnanosecond formation of the TTF•+-ANI-PI•- radical (spin qubit) pair at 85 K having a 1.8 µs phase memory time. This is sufficiently long to execute a CNOT gate using a sequence of five microwave pulses followed by a sequence of two pulses that read out all the elements of the density matrix. Comparing these data to a simulation of the data that assumes ideal conditions results in a fidelity of 0.97 for the execution of the CNOT gate. These results show that photogenerated molecular spin qubit pairs can be used to execute this essential quantum gate at modest temperatures, which affords the possibility that chemical synthesis can be used to develop structures to execute more complex quantum logic operations using electron spins.

Interaction between helical phase and Kerr nonlinear phase in vortex four- and six-wave mixing

We analyze the properties of vortex probe transmission signal (PTS), four-wave mixing (FWM) and six-wave mixing (SWM) via photonic band gap in an atomic ensemble with different topological charge (). We demonstrate the transfer of orbital angular momentum (OAM) from probe to SWM in experiment. We show that the shapes of vortex SWM and FWM spots intensity have been manipulated by the interaction, which can be modulated by the detuning and topological charge of related fields, between helical phase and nonlinear phase. Due to the stronger interaction, the shape of vortex FWM and SWM with m = 2, m = 3 are strongly destroyed compared to m = 1. Such results could have potential applications in logical gates for quantum computation.

Two-qubit pure state tomography by five product orthonormal bases**Project supported partially by the National Key Research and Development Program of China (Grant No. 2016YFB1000902), the National Natural Science Foundation of China (Grant No. 61472412), and the Program for Creative Research Group of the National Natural Science Foundation of China (Grant No. 61621003).

In this paper, we focus on two-qubit pure state tomography. For an arbitrary unknown two-qubit pure state, separable or entangled, it has been found that the measurement probabilities of 16 projections onto the tensor products of Pauli eigenstates are enough to uniquely determine the state. Moreover, these corresponding product states are arranged into five orthonormal bases. We design five quantum circuits, which are decomposed into the common gates in universal quantum computation, to simulate the five projective measurements onto these bases. At the end of each circuit, we measure each qubit with the projective measurement {|0⟩⟨0|,|1⟩⟨1|}. Then, we consider the open problem whether three orthonormal bases are enough to distinguish all two-qubit pure states. A necessary condition is given. Suppose that there are three orthonormal bases . Denote the unitary transition matrices from to as U1 and U2. All 32 elements of matrices U1 and U2 should not be zero. If not, these three bases cannot distinguish all two-qubit pure states.