We present a calculation of the shot noise in a ballistic electron waveguide square root of NOT gate. A general expression for the shot noise in the leads connected to these types of gates is shown. We then parameterize an S-matrix which qualitatively describes the action of a square root of NOT gate previously found through numerical methods for GaAs/Al_xGa_{1-x}As based waveguides systems. Using this S-matrix, the shot noise in a single output lead and across two output leads is calculated. We find that the measurement of the shot noise across two output leads allows for the determination of the fidelity of the gate itself.
By coupling a $Λ$-type quantum emitter to a chiral waveguide, in which the polarization of a photon is locked to its propagation direction, we propose a controllable photon-emitter interface for quantum networks. We show that this chiral system enables the SWAP gate and a hybrid-entangling gate between the emitter and a flying single photon. It also allows deterministic storage and retrieval of single-photon states with high fidelities and efficiencies. In short, this chirally coupled emitter-photon interface can be a critical building block toward a large-scale quantum network.
Quantum computers require technologies that offer both sufficient control over coherent quantum phenomena and minimal spurious interactions with the environment. We show, that photons confined to photonic crystals, and in particular to highly efficient waveguides formed from linear chains of defects doped with atoms can generate strong non-linear interactions which allow to implement both single and two qubit quantum gates. The simplicity of the gate switching mechanism, the experimental feasibility of fabricating two dimensional photonic crystal structures and integrability of this device wit…
We propose a new scheme for solid-state photonic quantum computation in which trapped photons in optical cavities are taken as a quantum bit. Quantum gates can be realized by coupling the cavities with quantum dots through waveguides. The proposed scheme allows programmable and deterministic gate operations and the system can be scaled up to many quantum bits.
A fully optical method to perform any quantum computation with optical waveguide modes is proposed by supplying the prescriptions for a universal set of quantum gates. The proposal for quantum computation is based on implementing a quantum bit with two normal modes of multi-mode waveguides. The proposed universal set of gates has the potential of being more compact and easily realized than other optical implementations, since it is based on planar lightwave circuit technology and can be constructed by using Mach-Zehnder interferometer configurations having semiconductor optical amplifiers with…
This is an exposition of some basic mathematical aspects of quantum logic gates. At first we established some general formulas for the case of arbitrary quantum gate A with unique restriction A^2=I. The explicit form of the generators and roots of matrix A have been found . Then we apply general results to the particular cases of one-qubit and multi-qubit quantum gates. Some interesting properties of square roots of basic Pauli and Hadamard gates are demonstrated.
The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.
Entanglement between atoms and microwave photons in a superconducting coplanar waveguide~(SCW) can enable hybrid quantum devices and interface static and flying qubits. We study a one-step controlled-Z~(C$_{\text{Z}}$) gate between a neutral atom trapped near a SCW and a microwave mode in the SCW, which is an extension of the gate proposed in [J. D. Pritchard, et.al., Phys. Rev. A 89, 010301(R) (2014)]. The gate protocol is simple and requires one laser pulse for exciting a transition between the ground and Rydberg states of the neutral atom.
It has been proved that surface plasmon polariton (SPP) can well conserve and transmit the quantum nature of entangled photons. Therefore, further utilization and manipulation of such quantum nature of SPP in a plasmonic chip will be the next task for scientists in this field. In quantum logic circuits, the controlled-NOT (CNOT) gate is the key building block. Here, we implement the first plasmonic quantum CNOT gate with several-micrometer footprint by utilizing a single polarization-dependent beam-splitter (PDBS) fabricated on the dielectric-loaded SPP waveguide (DLSPPW). The quantum logic fu…
Full control over the spatio-temporal structure of quantum states of light is an important goal in quantum optics, to generate for instance single-mode quantum pulses or to encode information on multiple modes, enhancing channel capacities. Quantum light pulses feature an inherent, rich spectral broadband-mode structure. In recent years, exploring the use of integrated optics as well as source-engineering has led to a deep understanding of the pulse-mode structure of guided quantum states of light. In addition, several groups have started to investigate the manipulation of quantum states by me…
Adiabatic techniques have much potential to realise practical and robust optical waveguide devices. Traditionally photonic elements are limited to coupling schemes that rely on proximity to nearest neighbour elements. We combine adiabatic passage with a continuum based long-range optical bus to break free from such topological restraints and thereby outline a new approach to photonic quantum gate design. We explicitly show designs for adiabatic quantum gates that produce a Hadamard, 50:50 and 1/3:2/3 beam splitter, and non-deterministic CNOT gate based on planar thin, shallow ridge waveguides.…
The first realization of solid state quantum computer was demonstrated recently by using artificial atoms -- transmons in superconducting resonator. Here, we propose a novel architecture of flexible and scalable quantum computer based on a waveguide circuit coupling many quantum nodes of controlled atomic ensembles. For the first time, we found the optimal practically attainable parameters of the atoms and circuit for 100{%} efficiency of quantum memory for multi qubit photon fields and confirmed experimentally the predicted perfect storage. Then we revealed self modes for reversible transfer …
Recent progress in integrated-optics technology has made photonics a promising platform for quantum networks and quantum computation protocols. Integrated optical circuits are characterized by small device footprints and unrivalled intrinsic interferometric stability. Here, we take advantage of femtosecond-laser-written waveguides' ability to process polarization-encoded qubits and present the first implementation of a heralded controlled-NOT gate on chip. We evaluate the gate performance in the computational basis and a superposition basis, showing that the gate can create polarization entang…
We extend the Krylov-subspace based time-dependent numerical simulation technique for a qubit interacting with photons in a waveguide to the multiple qubit case. We analyze photon scattering from two qubits analytically and derive expressions for the bound states in the continuum (BIC). We show how the BIC can be excited. We use the BIC in a recent Pauli-Z gate proposal involving decoherence free subspaces and obtain the gate fidelity as a function of the gate parameters. The techniques presented in the paper are useful for investigating the time evolution of quantum gates and other many-body …
Multiqubit entanglement is extremely important to perform truly secure quantum optical communication and computing operations. However, the efficient generation of long-range entanglement over extended time periods between multiple qubits randomly distributed in a photonic system remains an outstanding challenge. This constraint is mainly due to the detrimental effects of decoherence and dephasing. To alleviate this issue, we present engineered epsilon-near-zero (ENZ) nanostructures that can maximize the coherence of light-matter interactions at room temperature. We investigate a practical ENZ…
We propose a new scheme for quantum computation using flying qubits--propagating photons in a one-dimensional waveguide--interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a three- or four-level system, based on which photon-photon π-phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
We propose a novel hybrid quantum gate between an atom and a microwave photon in a superconducting coplanar waveguide cavity by exploiting the strong resonant microwave coupling between adjacent Rydberg states. Using experimentally achievable parameters gate fidelities $> 0.99$ are possible on sub-$μ$s timescales for waveguide temperatures below 40 mK. This provides a mechanism for generating entanglement between two disparate quantum systems and represents an important step in the creation of a hybrid quantum interface applicable for both quantum simulation and quantum information processing.
Quantum computers form a technological cluster with huge growth in the last few years. Although this technology is of still very limited size: perhaps the reason it is not seen as a technology which may be mass produced or of public use in the near future: it is one of the most promising developments with a potential to change the world. The IBM Quantum Experience Platform makes it possible for every person around the world, without limitation as to geographical location, to get acquainted with the technology of quantum computing. It is a resource for both researchers and enthusiasts entering …
We present a microfabricated surface-electrode ion trap with a pair of integrated waveguides that generate a standing microwave field resonant with the 171Yb+ hyperfine qubit. The waveguides are engineered to position the wave antinode near the center of the trap, resulting in maximum field amplitude and uniformity along the trap axis. By calibrating the relative amplitudes and phases of the waveguide currents, we can control the polarization of the microwave field to reduce off-resonant coupling to undesired Zeeman sublevels. We demonstrate single-qubit pi-rotations as fast as 1 us with less …
This paper presents a novel way to use the algebra of unit quaternions to express arbitrary roots or fractional powers of single-qubit gates, and to use such fractional powers as generators for algebras that combine these fractional input signals, behaving as a kind of nonlinear addition. The method works by connecting several well-known equivalences. The group of all single-qubit gates is $U(2)$, the unitary transformations of $C^2$. Using an appropriate phase multiplier, every element of $U(2)$ can be mapped to a corresponding element of $SU(2)$ with unit determinant, whose quantum mechanica…
The Pauli matrices are a set of three 2x2 complex Hermitian, unitary matrices. In this article, we investigate the relationships between certain roots of the Pauli matrices and how gates implementing those roots are used in quantum circuits. Techniques for simplifying such circuits are given. In particular, we show how those techniques can be used to find a circuit of Clifford+T gates starting from a circuit composed of gates from the well studied NCV library.
Access to the electron spin is at the heart of many protocols for integrated and distributed quantum-information processing [1-4]. For instance, interfacing the spin-state of an electron and a photon can be utilized to perform quantum gates between photons [2,5] or to entangle remote spin states [6-9]. Ultimately, a quantum network of entangled spins constitutes a new paradigm in quantum optics [1]. Towards this goal, an integrated spin-photon interface would be a major leap forward. Here we demonstrate an efficient and optically programmable interface between the spin of an electron in a quan…
We consider the unitary and the anti--unitary operator realizations of two important genuine quantum gates that transform elements of the computational basis of into superpositions: the square root of the identity and the square root of the negation.
The Clifford+$T$ quantum computing gate library for single qubit gates can create all unitary matrices that are generated by the group $\langle H, T\rangle$. The matrix $T$ can be considered the fourth root of Pauli $Z$, since $T^4 = Z$ or also the eighth root of the identity $I$. The Hadamard matrix $H$ can be used to translate between the Pauli matrices, since $(HTH)^4$ gives Pauli $X$. We are generalizing both these roots of the Pauli matrices (or roots of the identity) and translation matrices to investigate the groups they generate: the so-called Pauli root groups. In this work we introdu…
We show that a flying particle, such as an electron or a photon, scattering along a one-dimensional waveguide from a pair of static spin-1/2 centers, such as quantum dots, can implement a CZ gate (universal for quantum computation) between them. This occurs quasi-deterministically in a single scattering event, hence with no need for any post-selection or iteration, {and} without demanding the flying particle to bear any internal spin. We show that an easily matched hard-wall boundary condition along with the elastic nature of the process are key to such performances.
We propose a new solid state implementation of a quantum computer (quputer) using ballistic single electrons as flying qubits in 1D nanowires. We use a single electron pump (SEP) to prepare the initial state and a single electron transistor (SET) to measure the final state. Single qubit gates are implemented using quantum dots as phase shifters and electron waveguide couplers as beam splitters. A Coulomb coupler acts as a 2-qubit gate, using a mutual phase modulation effect. Since the electron phase coherence length in GaAs/AlGaAs heterostructures is of the order of 30$μ$m, several gates (tens…
We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)= - α/cosh(βx), which provides a good fit for potential profiles of existing top-gated graphene structures. We show that there is a threshold value of the characteristic potential strength α/β for which the first mode appears, in striking contrast to the non-relativistic case. A simple relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the…
We propose a scalable version of a KLM CNOT gate based upon integrated waveguide microring resonators (MRR), vs the original KLM-approach using beam splitters (BS). The core element of our CNOT gate is a nonlinear phase-shift gate (NLPSG) using three MRRs, which we examine in detail. We find an expanded parameter space for the NLPSG over that of the conventional version. Whereas in all prior proposals for bulk optical realizations of the NLPSG the optimal operating point is precisely a single zero dimensional manifold within the parameter space of the device, we find conditions for effective t…
Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant but the T gate is very costly to implement. As a result, reducing T-count has become an important optimization goal. Further, quantum circuits with many qubits are difficult to realize, making designs that save qubits and produce no garbage outputs desirable. In this work, we present a T-count optimized quantum square root circuit with only $2 \cdot n +1$ qu…
