Quantum interference device for controlled two-qubit operations

The qubit state is represented by a coherent superposition of its orthonormal basis states (|0〉 and |1〉). The probability distribution of a qubit is a discrete probability distribution of the qubits probability amplitudes. Setting a custom probability amplitudes allows a qubit to evolve to any desired state. In this paper a controlled n-root of X gate is simulated on a real quantum processor using IBMs Quantum Experience platform. A custom quantum gate could be constructed where the only inputs are the control and target qubits and the desired probability distribution for the target qubit.

Optical quantum computing (QC) increasingly uses integrated optics based experiments which permit circuit compactness and phase stability. However, despite the rapid adaptations of integrated waveguide devices for quantum photonics, initial gate demonstrations operate in post-selection, thus not allowing scaling of a quantum circuit beyond the depth of a single gate. Recently, a number of quantum circuits have been demonstrated using the femtosecond laser direct write (FLDW) technique. This technique induces refractive index change in glass substrates which can form three-dimensional waveguide devices. Here we demonstrate a potentially scalable waveguide gate for QC, a controlled-phase gate or Knill gate, produced using the FLDW technique. This gate produces a phase shift on a target qubit conditional on the state of a control qubit, as shown in Fig. 1(a). It requires four photons for operation, two of which act as the target and control path-encoded qubits and two ancillas which herald the successful operation of the circuit.

Quantum gates are fundamental in Quantum computing for their role in manipulating elementary information carriers referred to as quantum bits. In this paper, a theoretical scheme for realizing a quantum Hadamard and a quantum controlled-NOT logic gates operations in the anti-Jaynes-Cummings interaction process is provided. Standard Hadamard operation for a specified initial atomic state is achieved by setting a specific sum frequency and photon number in the normalized anti-Jaynes-Cummings qubit state transition operation with the interaction component of the anti-Jaynes-Cummings Hamiltonian generating the state transitions. The quantum controlled-NOT logic gate is realized when a single atomic qubit defined in a two-dimensional Hilbert space is the control qubit and two non-degenerate and orthogonal polarized cavities defined in a two-dimensional Hilbert space make the target qubit. With precise choice of interaction time in the anti-Jaynes-Cummings qubit state transition operations defined in the anti-Jaynes-Cummings sub-space spanned by normalized but non-orthogonal basic qubit state vectors, ideal unit probabilities of success in the quantum controlled-NOT operations is determined.

We present some deterministic schemes to construct universal quantum gates, that is, controlled- NOT, three-qubit Toffoli, and Fredkin gates, between flying photon qubits and stationary electron-spin qubits assisted by quantum dots inside double-sided optical microcavities. The control qubit of our gates is encoded on the polarization of the moving single photon and the target qubits are encoded on the confined electron spins in quantum dots inside optical microcavities. Our schemes for these universal quantum gates on a hybrid system have some advantages. First, all the gates are accomplished with the success probability of 100% in principle. Second, our schemes require no additional qubits. Third, the control qubits of the gates are easily manipulated and the target qubits are perfect for storage and processing. Fourth, the gates do not require that the transmission for the uncoupled cavity is balanceable to the reflectance for the coupled cavity, in order to get a high fidelity. Fifth, the devices for the three universal gates work in both the weak coupling and the strong coupling regimes, and they are feasible in experiment.

We present a study of quantum computing by engineering nonlocal quantum universal gates. The universal quantum logic gate is based on the interaction of a two-level atom with two modes of the electromagnetic field in a high Q superconducting cavity. The two-level atom acts as a control qubit and the two-mode electromagnetic field serves as a target qubit. Presently available QED experiments make it possible to realize the theoretical suggestion in the laboratory. We check the feasibility of our proposal by calculating the success probability.

Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here, we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented by utilizing non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.

One of the most promising and powerful candidates for future computing is the notion of universal quantum computer. A vital advance towards this direction is the development of quantum simulators and their possible implementation either as standalone quantum systems or as compatible software for classical computers with pros and cons. On the other hand, memristive computing has been proposed recently as a tentative unconventional computing scheme promoting the idea of information storage and processing in the same nanoelectronic device. In this paper we present a memristive quantum computing simulator by coupling quantum simulation principles with memristor aspects and enabling us to tackle the existing difficulties on qubit representation in conventional computing systems. For doing so, we utilize the memristances of identical memristors to represent in 3D the qubit state while its corresponding evolution is defined by the memristors input voltages. In particular, we introduce an appropriate correspondence among the aforementioned memristor voltages and the general qubit state rotation, i.e., the one-qubit quantum gates, and as such we reproduce the rotations imposed by the action of quantum gates in the 3D memristance space. Moreover, we also define the action of the CNOT two-qubit gate and simulate entanglement between two qubits paving the way towards the establishment of a universal set for quantum computing. Our results show that, memristor circuits can simulate effectively quantum computations.

We present a scalable uniform technique for construction of highly conditional C$^n$-NOT quantum gates of trapped ion qubits, such as the Toffoli gate, without using ancilla states and circuits of an exorbitant number of concatenated one- and two-qubit gates. Apart from the initial dressing of the internal qubit states with vibrational phonons and the final restoration of the phonon ground state, our technique requires the application of just a single composite pulse on the target qubit and is applicable both in and outside the Lamb-Dicke regime. We design special narrowband composite pulses, which suppress all transitions but the conditional transition of the target qubit; moreover, these composite pulses significantly improve the spatial addressing selectivity.

Large-scale generation of quantum entanglement between individually controllable qubits is at the core of quantum computing, communications, and sensing. Modular architectures of remotely-connected quantum technologies have been proposed for a variety of physical qubits, with demonstrations reported in atomic and all-photonic systems. However, an open challenge in these architectures lies in constructing high-speed and high-fidelity reconfigurable photonic networks for optically-heralded entanglement among target qubits. Here we introduce a programmable photonic integrated circuit (PIC), realized in a piezo-actuated silicon nitride (SiN)-in-oxide CMOS-compatible process, that implements an N × N Mach–Zehnder mesh (MZM) capable of high-speed execution of linear optical transformations. The visible-spectrum photonic integrated mesh is programmed to generate optical connectivity on up to N = 8 inputs for a range of optically-heralded entanglement protocols. In particular, we experimentally demonstrated optical connections between 16 independent pairwise mode couplings through the MZM, with optical transformation fidelities averaging 0.991 ± 0.0063. The PIC’s reconfigurable optical connectivity suffices for the production of 8-qubit resource states as building blocks of larger topological cluster states for quantum computing. Our programmable PIC platform enables the fast and scalable optical switching technology necessary for network-based quantum information processors.

The main obstacles to the realization of high-fidelity quantum gates are the\ncontrol errors arising from inaccurate manipulation of a quantum system and the\ndecoherence caused by the interaction between the quantum system and its\nenvironment. Nonadiabatic holonomic quantum computation allows for high-speed\nimplementation of whole-geometric quantum gates, making quantum computation\nrobust against control errors. Dynamical decoupling provides an effective\nmethod to protect quantum gates against environment-induced decoherence,\nregardless of collective decoherence or independent decoherence. In this paper,\nwe put forward a protocol of nonadiabatic holonomic quantum computation\nprotected by dynamical decoupling . Due to the combination of nonadiabatic\nholonomic quantum computation and dynamical decoupling, our protocol not only\npossesses the intrinsic robustness against control errors but also protects\nquantum gates against environment-induced decoherence.\n

We analyze the operation of a novel sensor based on atom interferometry, which can achieve supra-classical sensitivity by exploiting quantum correlations in mixed states of many qubits. The interferometer is based on quantum gates which use coherently-controlled Rydberg interactions between a single atom (which acts as a control qubit) and an atomic ensemble (which provides register qubits). In principle, our scheme can achieve precision scaling with the size of the ensemble - which can extend to large numbers of atoms - while using only single-qubit operations on the control and bulk operations on the ensemble. We investigate realistic implementation of the interferometer, and our main aim is to develop a new approach to quantum metrology that can achieve quantum-enhanced measurement precision by exploiting coherent operations on large impure quantum states. We propose an experiment to demonstrate the enhanced sensitivity of the protocol, and to investigate a transition from classical to supra-classical sensitivity which occurs when using highly-mixed probe states.

Multiple‐qubit logic gates, as an essential part of quantum logic gates, have wide practical application in quantum computation. Here, a scheme to directly construct a multiple‐qubit logic gate , in which k control atoms apply an universal operation U on each of m target qubits in the Rydberg atom system is proposed. The scheme, based on Rydberg blockade and geometric quantum operations as well as optimized control theory, can greatly reduce the qubit number and the operation steps, improving the speed and robustness of the gating compared to the conventional multiple‐qubit gates consisting of single‐ and two‐qubit gates. Taking the C2U2 gate as an example, the performance of the proposal is numerically evaluated in terms of the fidelity of the quantum gate as well as the robustness against the static systematic errors and spontaneous emission. This work may provide a significative reference for constructing universal multiple‐qubit logic gates in future Rydberg atom experiments.

In a recent remarkable experiment [Sci. Adv. 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In particular, it is shown that this Fredkin gate can be realized using a single-step operation and more importantly, each target qudit can be in an arbitrary state with arbitrary degrees of freedom. Furthermore, we show that this experimental scheme has many potential applications in quantum computation and quantum information processing such as generating arbitrary entangled states (discrete-variable states or continuous-variable states) of the two memories, measuring the fidelity and the entanglement between the two memories. With state-of-the-art circuit QED technology, the numerical simulation is performed to demonstrate that two-memory NOON states, entangled coherent states, and entangled cat states can be efficiently synthesized.

Using nuclear magnetic resonance techniques with a solution of cytosine molecules, we show an implementation of certain quantum logic gates (including NOT gate, square-root of NOT gate and controlled-NOT gate), which have central importance in quantum computing. In addition, experimental results show that nuclear magnetic resonance spectroscopy can efficiently measure the result of quantum computing without attendant wave-function collapse.

Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations. However, as seen with small-scale demonstrations of quantum computers using other types of qubit, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch-Josza algorithm and the Grover search algorithm-canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85-89 per cent and concurrences of 73-82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.