We analyze in detail the proposal for a two-qubit gate for travelling single-photon qubits recently presented by C. Ottaviani \emph{et al}. [Phys. Rev. A \textbf{73}, 010301(R) (2006)]. The scheme is based on an ensemble of five-level atoms coupled to two quantum and two classical light fields. The two quantum fields undergo cross-phase modulation induced by electromagnetically induced transparency. The performance of this two-qubit quantum phase gate for travelling single-photon qubits is thoroughly examined in the steady-state and transient regimes, by means of a full quantum treatment of the system dynamics. In the steady-state regime, we find a general trade-off between the size of the conditional phase shift and the fidelity of the gate operation. However, this trade-off can be bypassed in the transient regime, where a satisfactory gate operation is found to be possible, significantly reducing the gate operation time.
Quantum Phase Estimation is one of the most useful quantum computing algorithms for quantum chemistry and as such, significant effort has been devoted to designing efficient implementations. In this article, we introduce TFermion, a library designed to estimate the T-gate cost of such algorithms, for an arbitrary molecule. As examples of usage, we estimate the T-gate cost of a few simple molecules and compare the same Taylorization algorithms using Gaussian and plane-wave basis.
The accurate implementation of quantum gates is essential for the realisation of quantum algorithms and digital quantum simulations. This accuracy may be increased on noisy hardware through the variational optimisation of gates, however the experimental realisation of such a protocol is impeded by the large effort required to estimate the fidelity of an implemented gate. With a hierarchy of approximations we find a faithful approximation to the quantum process fidelity that can be estimated experimentally with reduced effort. Its practical use is demonstrated with the optimisation of a three-q…
We propose a scheme for linear optical quantum Fredkin gate based on the combination of recently experimentally demonstrated linear optical partial SWAP gate and controlled-Z gates. Both heralded gate and simplified postselected gate operating in the coincidence basis are designed. The suggested setups have a simple structure and require stabilization of only a single Mach-Zehnder interferometer. A proof-of-principle experimental demonstration of the postselected Fredkin gate appears to be feasible and within the reach of current technology.
Universal quantum gates lie at the heart of designing quantum computer. We construct two compact quantum circuits to implement post-selected controlled-phase-flip (CPF) gate and Toffoli gate with linear optics assisted by one and two single photons, respectively. The current existing maximum success probability of 1/4 for linear optical CPF gate is achieved by resorting to an ancillary single photon rather than an entangled photon pair or two single photons. Remarkably, our Toffoli gate is accomplished with current maximum success probability of 1/30 without using additional entangled photon p…
We show that a universal set of gates for quantum computation with optics can be quantum teleported through the use of EPR entangled states, homodyne detection, and linear optics and squeezing operations conditioned on measurement outcomes. This scheme may be used for fault-tolerant quantum computation in any optical scheme (qubit or continuous variable). The teleportation of nondeterministic nonlinear gates employed in linear optics quantum computation is discussed.
We study the class of two qubit gates which can be achieved using only linear optical elements (beam splitters and phase shifters) and post-selection. We are able to exactly characterize this set, and find that it is impossible to implement most two qubit gates in this way. The proof also gives rise to an algorithm for calculating the optimal success probability of those gates which are achievable.
We propose a deterministic SWAP gate for spatially encoded qubits. The gate is constructed from waveguide crossings, Mach Zender Interferometers and phase shifters providing the gate reconfigurability. Through manipulating the phase of the phase shifters, we can apply either the SWAP or identity gates. As an essential element of nearest neighbor qubit networks, the SWAP gate has a simple structure and presents minimal overhead, making it viable for universal quantum computation.
Recently it was realized that linear optics and photo-detectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation (eLOQC) was to design a simple non-deterministic gate, which upon post-selection based on a measurement result implements a non-linear phase shift on one mode. Here a computational strategy is given for finding non-deterministic gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained.
We consider the realization of quantum Fredkin gate with only linear optics and single photons. First we construct a heralded Fredkin gate using four heralded controlled-not (CNOT) gates. Then we simplify this method to a post-selected one utilizing only two CNOT gates. We also give a possible realization of this method which is feasible with current experimental technology. Another post-selected scheme requires time entanglement of the input photons but needs no ancillary photons.
We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realisations, using partially-polarising beamsplitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-Z gate in both continuous-wave and pulsed regimes of operation, fully characterising it in each case using quantum process tomography. We also demonstrate a fully-resolving, nondeterministic optical Bell-state analyser based on this controlled-Z gate. This new architecture is ideally suited to guided optics implementations of …
We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities. Such probabilistic gates can be used for scalable quantum computation.
Aiming the construction of quantum computers and quantum communication systems based on optical devices, in this work we present possible implementations of quantum and classical CNOTs gates, as well an optical setup for generation and distribution of bipartite entangled states, using linear optical devices and photon number quantum non-demolition measurement.
We describe the construction of a conditional quantum control-not (CNOT) gate from linear optical elements following the program of Knill, Laflamme and Milburn [Nature {\bf 409}, 46 (2001)]. We show that the basic operation of this gate can be tested using current technology. We then simplify the scheme significantly.
We present a linear-optical scheme for a controlled-phase gate with tunable phase shift programmed by a qubit state. In contrast to all previous tunable controlled-phase gates, the phase shift is not hard-coded into the optical setup, but can be tuned to any value from 0 to pi by the state of a so-called program qubit. Our setup is feasible with current level of technology using only linear-optical components. We provide an experimental feasibility study to assess the gate's implementability. We also discuss options for increasing the success probability up to 1/12 which approaches the success…
We describe the operation and tolerances of a non-deterministic, coincidence basis, quantum CNOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration.
We describe a simple scheme for implementing the non-linear sign gate of Knill, Laflamme and Milburn (Nature, {\bf 409}, 46-52, Jan. 4 (2001)) which forms the basis of an experiment underway at the University of Vienna.
We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling square root of SWAP, can be obtained by changing a classical control parameter -- namely the path difference in the interferometer. Reconstruction of output states, full process tomography and evaluation of entanglement of formation prove very good performance of the gates.
We have modelled the Zeno effect Control-Sign gate of Franson et al (PRA 70, 062302, 2004) and shown that high two-photon to one-photon absorption ratios, $κ$, are needed for high fidelity free standing operation. Hence we instead employ this gate for cluster state fusion, where the requirement for $κ$ is less restrictive. With the help of partially offline one-photon and two-photon distillations, we can achieve a fusion gate with unity fidelity but non-unit probability of success. We conclude that for $κ> 2200$, the Zeno fusion gate will out perform the equivalent linear optics gate.
We report the first experimental demonstration of an optical controlled-NOT gate constructed entirely in fibre. We operate the gate using two heralded optical fibre single photon sources and find an average logical fidelity of 90% and an average process fidelity of 0.83<F<0.91. On the basis of a simple model we are able to conclude that imperfections are primarily due to the photon sources, meaning that the gate itself works with very high fidelity.
Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a scalable universal quantum computer using only linear-optics elements and conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}]. However, the practical realization of the quantum logic gate for the scheme is still technically difficult. A major difficulty is the requirement for sub-wavelength level stabilization of the interlocking interferometers. Following our recent experimental work[Phys. Rev. Lett.{\bf 92}, 017902 (2004)\cite{Sanaka2}], we describe a more feasible scheme to implement the gate that g…
We present an implementation of quantum logic gates via internal state dependent displacements of ions in a linear Paul trap caused by optical dipole forces. Based on a general quantum analysis of the system dynamics we consider specific implementations with alkaline earth ions. For experimentally realistic parameters gate infidelities as low as $10^{-4}$ can be obtained.
We present and experimentally demonstrate a novel optical nondestructive controlled-NOT gate without using entangled ancilla. With much fewer measurements compared with quantum process tomography, we get a good estimation of the gate fidelity. The result shows a great improvement compared with previous experiments. Moreover, we also show that quantum parallelism is achieved in our gate and the performance of the gate can not be reproduced by local operations and classical communications.
We propose a scheme for conditional implementation of a quantum phase gate by using distant atoms trapped in different optical cavities. Instead of direct interaction between atoms, the present scheme makes use of quantum interference of polarized photons decaying from the optical cavities to conditionally create the desired quantum phase gate between two distant atoms. The proposed scheme only needs linear optical elements and a two-fold coincidence detection, and are insensitive to the quantum noise. The scheme can be directly used to prepare any quantum state of many distant atoms.
We report on the first experimental realization of optimal linear-optical controlled phase gates for arbitrary phases. The realized scheme is entirely flexible in that the phase shift can be tuned to any given value. All such controlled phase gates are optimal in the sense that they operate at the maximum possible success probabilities that are achievable within the framework of any postselected linear-optical implementation. The quantum gate is implemented using bulk optical elements and polarization encoding of qubit states. We have experimentally explored the remarkable observation that the…
Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] showed that linear optics techniques could be used to implement a nonlinear sign gate. They also showed that two of their nonlinear sign gates could be combined to implement a controlled-phase gate, which has a number of practical applications. Here we describe an alternative implementation of a controlled-phase gate that only requires the use of a single nonlinear sign gate. This gives a much higher average probability of success when the required ancilla photons are generated using heralding techniques. This implementation of a controlled-…
We design linear optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto state of a single photon in two modes (e.g. spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In parti…
We consider one possible implementation of Hadamard gate for optical and ion trap holonomic quantum computers. The expression for its fidelity determining the gate stability with respect to the errors in the single-mode squeezing parameter control is analytically derived. We demonstrate by means of this expression the cancellation of the squeezing control errors up to the fourth order on their magnitude.
Large optical nonlinearities occurring in a coherently prepared atomic system are shown to produce phase shifts of order $π$. Such an effect may be observed in ultracold rubidium atoms where it could be feasibly exploited toward the realization of a polarization phase gate.
We propose a geometric phase gate of two ion qubits that are encoded in two levels linked by an optical dipole-forbidden transition. Compared to hyperfine geometric phase gates mediated by electric dipole transitions, the gate has many interesting properties, such as very low spontaneous emission rates, applicability to magnetic field insensitive states, and use of a co-propagating laser beam geometry. We estimate that current technology allows for infidelities of around 10$^{-4}$.
We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the two intracavity modes. The scheme is realizable for sufficiently strong single-photon optomechanical coupling in the resolved sideband regime, and is robust against cavity losses.
We analyse the design and optimisation of quantum logic circuits suitable for the experimental demonstration of a three-qubit quantum computation prototype based on optically-controlled, solid-state quantum logic gates. In these gates, the interaction between two qubits carried by the electron-spin of donors is mediated by the optical excitation of a control particle placed in their proximity. First, we use a geometrical approach for analysing the entangling characteristics of these quantum gates. Then, using a genetic programming algorithm, we develop circuits for the refined Deutsch-Jozsa al…
Linear optics quantum logic gates are the best tool to generate multi-photon entanglement. Simplifying a recent approach [Phys. Rev. A 65, 062324; Phys. Rev. A 66, 024308] we were able to implement the conditional phase gate with only one second order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analysing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multi photon quantum infor…
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 show that it is possible to reduce the number of two-qubit gates needed for the construction of an arbitrary controlled-unitary transformation by up to two times using a tunable controlled-phase gate. On the platform of linear optics, where two-qubit gates can only be achieved probabilistically, our method significantly reduces the amount of components and increases success probability of a two-qubit gate. The experimental implementation of our technique presented in this paper for a controlled single-qubit unitary gate demonstrates that only one tunable controlled-phase gate is needed inst…
In principle the Zeno effect controlled-sign gate of Franson et al's (PRA 70, 062302, 2004) is a deterministic two-qubit optical gate. However, when realistic values of photon loss are considered its fidelity is significantly reduced. Here we consider the use of measurement based quantum processing techniques to enhance the operation of the Zeno gate. With the help of quantum teleportation, we show that it is possible to achieve a Zeno CNOT gate (GC-Zeno gate) that gives (near) unit fidelity and moderate probability of success of 0.76 with a one-photon to two-photon transmission ratio $κ=10^4$…
A two qubit quantum gate, namely the C-Phase, has been realized by exploiting the longitudinal momentum (i.e. the optical path) degree of freedom of a single photon. The experimental setup used to engineer this quantum gate represents an advanced version of the high stability closed-loop interferometric setup adopted to generate and characterize 2-photon 4-qubit Phased Dicke states. Some experimental results, dealing with the characterization of multipartite entanglement of the Phased Dicke states are also discussed in detail.
Assisted with linear optical manipulation, single photon, entangled photon pairs, photon measurement, and classical communication, a scheme for two-spin qubits phase gate and teleportation of a CNOT gate between two electron spins from acting on local qubits to acting on remote qubits using quantum dots in optical microcavities is proposed. The scheme is based on spin selective photon reflection from the cavity and is achieved in a deterministic way by the sequential detection of photons and the single-qubit rotations of a single electron spin in a self-assembled GaAs/InAs quantum dot. The fea…
The concept of directionally unbiased optical multiports is introduced, in which photons may reflect back out the input direction. A linear-optical implementation is described, and the simplest three-port version studied. Symmetry arguments demonstrate potential for unusual quantum information processing applications. The devices impose group structures on two-photon entangled Bell states and act as universal Bell-state processors to implement probabilistic quantum gates acting on state symmetries. These multiports allow optical scattering experiments to be carried out on arbitrary undirected …
We propose a novel scheme for high fidelity photonic controlled phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. The gate operation is obtained by first storing a photonic pulse in the ensemble and then scattering a second pulse from the cavity, resulting in a phase change depending on whether the first pulse contained a single photon. We show that the combination of Rydberg blockade and optical cavities effectively enhances the optical non-linearity created by the strong Rydberg interaction and thereby reduces the requirements for photonic quantum gates. The re…
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…
One of the main advantages of an optical approach to quantum computing is the fact that optical fibers can be used to connect the logic and memory devices to form useful circuits, in analogy with the wires of a conventional computer. Here we describe an experimental demonstration of a simple quantum circuit of that kind in which two probabilistic exclusive-OR (XOR) logic gates were combined to calculate the parity of three input qubits.
We present some compact quantum circuits for a deterministic quantum computing on electron-spin qubits assisted by quantum dots inside single-side optical microcavities, including the CNOT, Toffoli, and Fredkin gates. They are constructed by exploiting the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a single-side optical microcavity as a result of cavity quantum electrodynamics. Our universal quantum gates have some advantages. First, all the gates are accomplished with a success probability of 100% in principle. Second, our schemes require no addit…
Linear optical quantum Fredkin gate can be applied to quantum computing and quantum multi-user communication network. In the existing linear optical scheme, two single photon detectors (SPDs) are used to heralding the success of the quantum Fredkin gate while they have no photon count. But analysis results show that for non-perfect SPD the lower the detector efficiency, the higher the heralded success rate by this scheme. We propose an improved linear optical quantum Fredkin gate by designing a new heralding scheme with an auxiliary qubit and only one SPD, in which the higher the detection eff…
We investigate the effect of variations in beam splitter transmissions and path length differences in the nonlinear sign gate that is used for linear optical quantum computing. We identify two implementations of the gate, and show that the sensitivity to variations in their components differs significantly between them. Therefore, circuits that require a precision implementation may benefit from additional circuit analysis of component variations to identify the most practical implementation. We suggest possible routes to efficient circuit analysis in terms of quantum parameter estimation.
Quantum logic gates are fundamental building blocks of quantum computers. Their integration into quantum networks requires strong qubit coupling to network channels, as can be realized with neutral atoms and optical photons in cavity quantum electrodynamics. Here we demonstrate that the long-range interaction mediated by a flying photon performs a gate between two stationary atoms inside an optical cavity from which the photon is reflected. This single step executes the gate in $2\,\mathrm{μs}$. We show an entangling operation between the two atoms by generating a Bell state with 76(2)% fideli…
We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase modulation induced by electro-magnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for travelling single-photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation.
By using the abstract linear-optical network derived in [S. Scheel and N. Lütkenhaus, New J. Phys. \textbf{6}, 51 (2004)] we show that for the lowest possible ancilla photon numbers the probability of success of realizing a (single-shot) generalized nonlinear sign shift gate on an ($N+1$)-dimensional signal state scales as $1/N^2$. We limit ourselves to single-shot gates without conditional feed-forward. We derive our results by using determinants of Vandermonde-type over a polynomial basis which is closely related to the well-known Jacobi polynomials.
A scheme is proposed to generate an entangled state between two (Lambda-type) four-level atoms that interact effectively by means of a detuned optical cavity and a laser beam that acts perpendicularly to the cavity axis. It is shown how the degree of entanglement for two atoms passing through the cavity can be controlled by manipulating their velocity and the (initial) distance between the atoms. In addition, three realistic schemes are suggested to implement the two-qubit gates within the framework of the suggested atom-cavity-laser setup, namely, the i-swap gate, controlled-Z gate and the co…
Optical qubits uniquely combine information transfer in optical fibers with a good processing capability and are therefore attractive tools for quantum technologies. A large challenge, however, is to overcome the low efficiency of two-qubit logic gates. The experimentally achieved efficiency in an optical controlled NOT (CNOT) gate reached approximately 11% in 2003 and has seen no increase since. Here we report on a new platform that was designed to surpass this long-standing record. The new scheme avoids inherently probabilistic protocols and, instead, combines aspects of two established quan…
We introduce the method of using an annealing genetic algorithm to the numerically complex problem of looking for quantum logic gates which simultaneously have highest fidelity and highest success probability. We first use the linear optical quantum nonlinear sign (NS) gate as an example to illustrate the efficiency of this method. We show that by appropriately choosing the annealing parameters, we can reach the theoretical maximum success probability (1/4 for NS) for each attempt. We then examine the controlled-z (CZ) gate as the first new problem to be solved. We show results that agree with…
Up to now, all the works about constructing quantum logic gates, an essential part in quantum computing, are focused on operating on one degree of freedom (DOF) of quantum systems. Here, we investigate the possibility to achieve a scalable photonic quantum computing based on two DOFs of quantum systems and construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating on both spatial-mode and polarization DOFs of a photon pair simultaneously, by using the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a one-side optical microcavity as a res…
We propose and analyze heralded quantum gates between qubits in optical cavities. They employ an auxiliary qubit to report if a successful gate occurred. In this manner, the errors, which would have corrupted a deterministic gate, are converted into a non-unity probability of success: once successful the gate has a much higher fidelity than a similar deterministic gate. Specifically, we describe that a heralded , near-deterministic controlled phase gate (CZ-gate) with the conditional error arbitrarily close to zero and the success probability that approaches unity as the cooperativity of the s…
With the slow but constant progress in the coherent control of quantum systems, it is now possible to create large quantum superpositions. There has therefore been an increased interest in quantifying any claims of macroscopicity. We attempt here to motivate three criteria which we believe should enter in the assessment of macroscopic quantumness: The number of quantum fluctuation photons, the purity of the states, and the ease with which the branches making up the state can be distinguished.
We propose a new measure of non-classicality of quantum gates which is particularly suitable for probabilistic devices. This measure enables to compare, e.g., deterministic devices which prepare entangled states with low amount of entanglement with probabilistic devices which generate highly entangled states but which fail sometimes. We provide examples demonstrating advantages of this new measure over the so far employed entangling power.
We model an optical implementation of a CSIGN gate that makes use of the Quantum Zeno effect [1,2] in the presence of photon loss. The raw operation of the gate is severely affected by this type of loss. However, we show that by using the same photon loss codes that have been proposed for linear optical quantum computation (LOQC), the performance is greatly enhanced and such gates can outperform LOQC equivalents. The technique can be applied to other types of nonlinearities, making the implementation of nonlinear optical gates much more attractive.
