We present the first demonstration of a CNOT gate using neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8 μ\rm m. We measure CNOT fidelities of F=0.73 and 0.72 using two different gate protocols, and show by measurement of parity oscillations that the gate can be used to generate two-atom states with fidelity at the threshold for entanglement. We anticipate that the long range nature of the Rydberg interaction will be attractive for future extensions of this work to multi-qubit systems.
We report the experimental demonstration of a controlled-NOT (CNOT) quantum logic gate between motional and internal state qubits of a single ion where, as opposed to previously demonstrated gates, the conditional dynamics depends on the extent of the ion's wave-packet. Advantages of this CNOT gate over one demonstrated previously are its immunity from Stark shifts due to off-resonant couplings and the fact that an auxiliary internal level is not required. We characterize the gate logic through measurements of the post-gate ion state populations for both logic basis and superposition input sta…
We demonstrate a quadratic phase gate for one-way quantum computation in the continuous-variable regime. This canonical gate, together with phase-space displacements and Fourier rotations, completes the set of universal gates for realizing any single-mode Gaussian transformation such as arbitrary squeezing. As opposed to previous implementations of measurement-based squeezers, the current gate is fully controlled by the local oscillator phase of the homodyne detector. Verifying this controllability, we give an experimental demonstration of the principles of one-way quantum computation over con…
We introduce a fully tuneable entangling gate for continuous-variable one-way quantum computation. We present a proof-of-principle demonstration by propagating two independent optical inputs through a three-mode linear cluster state and applying the gate in various regimes. The genuine quantum nature of the gate is confirmed by verifying the entanglement strength in the output state. Our protocol can be readily incorporated into efficient multi-mode interaction operations in the context of large-scale one-way quantum computation, as our tuning process is the generalisation of cluster state sha…
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.
Local implementation of non-local quantum gates is necessary in a distributed quantum computer. Here, we demonstrate the non-local implementation of controlled-unitary quantum gates proposed by Eisert et al. (Phys Rev A 62:052317, 2000) using the five-qubit IBM quantum computer. We verify the fidelity and accuracy of the implementation through the techniques of quantum state and process tomographies.
We present the first quantum controlled-NOT (CNOT) gate realized using a fiber-based indistinguishable photon-pair source in the 1.55 $μ$m telecommunications band. Using this free-space CNOT gate, all four Bell states are produced and fully characterized by performing quantum state tomography, demonstrating the gate's unambiguous entangling capability and high fidelity. Telecom-band operation makes this CNOT gate particularly suitable for quantum information processing tasks that are at the interface of quantum communication and linear optical quantum computing.
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light fields. We experimentally demonstrate a QND sum gate, employing the scheme by R. Filip, P. Marek, and U.L. Andersen [\pra {\bf 71}, 042308 (2005)], solely based on offline squeezed states, homodyne measurements, and feedforward. The results are verified by simultaneously satisfying t…
Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum information processing. However, the photons, one of the best candidates for qubits, suffer from the lack of strong nonlinear coupling required for quantum logic operations. Here we show how this drawback can be overcome by reporting a proof-of-principle experimental demonstration of a non-destructive controlled-NOT (CNOT) gate for two independent photons using only linear optical elements in conjunction with single-photon sources and conditional dynamics. Moreover, we have exploited the CNOT gate to di…
We experimentally demonstrate a programmable quantum gate that applies a sign flip operation to data qubit in an arbitrary basis fully specified by the quantum state of a two-qubit program register. Our linear-optical implementation is inspired by teleportation-based schemes for quantum computing and relies on multiphoton interference and coincidence detection. We confirm the programmability of the gate and its high-fidelity performance by carrying out full quantum process tomography of the resulting operation on data qubit for several different programs.
We discuss and experimentally demonstrate a probabilistic Hadamard gate for coherent state qubits. The scheme is based on linear optical components, non-classical resources and the joint projective action of a photon counter and a homodyne detector. We experimentally characterize the gate for the coherent states of the computational basis by full tomographic reconstruction of the transformed output states. Based on the parameters of the experiment we simulate the fidelity for all coherent state qubits on the Bloch sphere.
We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals (Phys. Rev. A {\bf 66}, 024308 (2001), Phys. Rev. A {\bf 65}, 012314 (2002)) have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittances and reflectances. The performance of the device is evaluated using a recently proposed method (Phys. Rev. Lett. {\bf 94}, 160504 (2005)), by which the quantum process fidelity and the entanglement capability can be…
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 …
To employ a quantum device, the performance of the quantum gates in the device needs to be evaluated first. Since the dimensionality of a quantum gate grows exponentially with the number of qubits, evaluating the performance of a quantum gate is a challenging task. Recently, a scheme called quantum gate verification (QGV) has been proposed, which can verifies quantum gates with near-optimal efficiency. In this paper, we implement a proof-of-principle optical experiment to demonstrate this QGV scheme. We show that for a single-qubit quantum gate, only $\sim300$ samples are needed to confirm the…
Quantum gates are essential for the realization of quantum computer and have been implemented in various types of two-level systems. However, high-dimensional quantum gates are rarely investigated both theoretically and experimentally even that high-dimensional quantum systems exhibit remarkable advantages over two-level systems for some quantum information and quantum computing tasks. Here we experimentally demonstrate the four-dimensional X gate and its unique higher orders with the average conversion efficiency 93\%. All these gates are based on orbital-angular-momentum degree of freedom of…
Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing…
In state-of-the-art quantum computing platforms, including superconducting qubits and trapped ions, imperfections in the 2-qubit entangling gates are the dominant contributions of error to system-wide performance. Recently, a novel 2-qubit parametric gate was proposed and demonstrated with superconducting transmon qubits. This gate is activated through RF modulation of the transmon frequency and can be operated at an amplitude where the performance is first-order insensitive to flux-noise. In this work we experimentally validate the existence of this AC sweet spot and demonstrate its dependenc…
Optimizing the physical realization of quantum gates is important to build a quantum computer. The controlled-SWAP gate, also named Fredkin gate, can be widely applicable in various quantum information processing schemes. In the present research, we propose and experimentally implement quantum Fredkin gate in a single-photon hybrid-degrees-of-freedom system. Polarization is used as the control qubit, and SWAP operation is achieved in a four-dimensional Hilbert space spanned by photonic orbital angular momentum. The effective conversion rate $\mathcal{P}$ of the quantum Fredkin gate in our expe…
The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit condi…
We experimentally demonstrate a controlled-phase gate for continuous variables in a fully measurement-based fashion. In our scheme, the two independent input states of the gate, encoded in two optical modes, are teleported into a four-mode Gaussian cluster state. As a result, one of the entanglement links present in the initial cluster state appears in the two unmeasured output modes as the corresponding entangling gate acting on the input states. The genuine quantum character of this gate becomes manifest and is verified through the presence of entanglement at the output for a product two-mod…
We demonstrate an optical gate that increases the size of polarization-based W states by accessing only one of the qubits. Using this gate, we have generated three-photon and four-photon W states with fidelities $0.836\pm 0.042 $ and $0.784\pm 0.028$, respectively. We also confirmed existence of pairwise entanglement in every pair of the qubits including the one that was left untouched by the gate. The gate is applicable to any size of W states and hence is a universal tool for expanding entanglement.
A neutral-atom system serves as a promising platform for realizing gate-based quantum computing because of its capability to trap and control several atomic qubits in different geometries and the ability to perform strong, long-range interactions between qubits; however, the two-qubit entangling gate fidelity lags behind competing platforms such as superconducting systems and trapped ions. The aim of our work is to design a fast, robust, high-fidelity controlled-Z (CZ) gate, based on the Rydberg-blockade mechanism, for neutral atoms. We propose a gate procedure that relies on simultaneous and …
We propose several schemes for implementing a fast two-qubit quantum gate for neutral atoms with the gate operation time much faster than the time scales associated with the external motion of the atoms in the trapping potential. In our example, the large interaction energy required to perform fast gate operations is provided by the dipole-dipole interaction of atoms excited to low-lying Rydberg states in constant electric fields. A detailed analysis of imperfections of the gate operation is given.
The resonator-induced phase (RIP) gate is a multi-qubit entangling gate that allows a high degree of flexibility in qubit frequencies, making it attractive for quantum operations in large-scale architectures. We experimentally realize the RIP gate with four superconducting qubits in a three-dimensional (3D) circuit-quantum electrodynamics architecture, demonstrating high-fidelity controlled-Z (CZ) gates between all possible pairs of qubits from two different 4-qubit devices in pair subspaces. These qubits are arranged within a wide range of frequency detunings, up to as large as 1.8 GHz. We fu…
We propose and experimentally demonstrate an approximate universal-NOT (U-NOT) operation that is robust against operational errors. In our proposal, the U-NOT operation is composed of stochastic unitary operations represented by the vertices of regular polyhedrons. The operation is designed to be robust against random operational errors by increasing the number of unitary operations (i.e., reference axes). Remarkably, no increase in the total number of measurements nor additional resources are required to perform the U-NOT operation. Our method can be applied in general to reduce operational e…
One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on a…
Holonomies, arising from non-Abelian geometric transformations of quantum states in Hilbert space, offer a promising way for quantum computation. These holonomies are not commutable and thus can be used for the realization of a universal set of quantum logic gates, where the global geometric feature may result in some noise-resilient advantages. Here we report the first on-chip realization of a non-Abelian geometric controlled-Not gate in a superconducting circuit, which is a building block for constructing a holonomic quantum computer. The conditional dynamics is achieved in an all-to-all con…
We propose a scheme to achieve quantum computation with neutral atoms whose interactions are catalyzed by single photons. Conditional quantum gates, including an $N$-atom Toffoli gate and nonlocal gates on remote atoms, are obtained through cavity-assisted photon scattering in a manner that is robust to random variation in the atom-photon coupling rate and which does not require localization in the Lamb-Dicke regime. The dominant noise in our scheme is automatically detected for each gate operation, leading to signalled errors which do not preclude efficient quantum computation even if the err…
We demonstrate quantum control techniques for a single trapped ion in a cryogenic, surface-electrode trap. A narrow optical transition of Sr+ along with the ground and first excited motional states of the harmonic trapping potential form a two-qubit system. The optical qubit transition is susceptible to magnetic field fluctuations, which we stabilize with a simple and compact method using superconducting rings. Decoherence of the motional qubit is suppressed by the cryogenic environment. AC Stark shift correction is accomplished by controlling the laser phase in the pulse sequencer, eliminatin…
We demonstrate high fidelity single-qubit gate operation in a trapped single neutral atom. The atom is trapped in the recently invented magic-intensity optical dipole trap (MI-ODT) with more stable magnetic field. The MI-ODT efficiently mitigates the detrimental effects of light shifts thus sufficiently improves the performance of single qubit-gates. The gates are driven with microwave, and the fidelity of gate operation is characterized by using the randomized benchmarking method. We obtain an average error per Clifford gate of $3.0(7)\times10^{-5}$ which is much below the error threshold ($1…
We examine three possible implementations of non-deterministic linear optical cnot gates with a view to an in-principle demonstration in the near future. To this end we consider demonstrating the gates using currently available sources such as spontaneous parametric down conversion and coherent states, and current detectors only able to distinguish between zero or many photons. The demonstration is possible in the co-incidence basis and the errors introduced by the non-optimal input states and detectors are analysed.
Compared with the idea of universal quantum computation, a direct synthesis of a multiqubit logic gate can greatly improve the efficiency of quantum information processing tasks. Here we propose an efficient scheme to implement a three-qubit controlled-not (Toffoli) gate of neutral atoms based on unconventional Rydberg pumping. By adjusting the strengths of Rabi frequencies of driving fields, the Toffoli gate can be achieved within one step, which is also insensitive to the fluctuation of the Rydberg-Rydberg interaction. Considering different atom alignments, we can obtain a high-fidelity Toff…
High-fidelity non-adiabatic dark state gates for neutral atoms
Zentrum für Optische Quantentechnologien, Universität Hamburg（汉堡大学光学量子技术中心）；The Hamburg Centre for Ultrafast Imaging, Universität Hamburg（汉堡超快成像中心，汉堡大学）；UTC Quantum Center, University of Tennessee, Chattanooga（田纳西大学查塔努加分校UTC量子中心）
To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in p…
We theoretically study specific schemes for performing a fundamental two-qubit quantum gate via controlled atomic collisions by switching microscopic potentials. In particular we calculate the fidelity of a gate operation for a configuration where a potential barrier between two atoms is instantaneously removed and restored after a certain time. Possible implementations could be based on microtraps created by magnetic and electric fields, or potentials induced by laser light.
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}(θ)$], from which alone a circuit can be constructed so that any feasible quantum computing is attainable. As far as we know, however, $\mathbb{D}(θ)$ has not been demonstrated. Here we design an easily realizable $\mathbb{D}(θ)$ by usin…
Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and …
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…
Linear optics is a promising candidate to enable the construction of quantum computers. A number of quantum protocols gates based on linear optics have been demonstrated. However, it is well-known that these gates are non-deterministic and that higher order nonlinearity is necessary for deterministic operations. We found the quantum leader election protocol (QLE) can be operated deterministically only with linear optics, and we have demonstrated the nearly deterministic operation which overcomes classical limit.
Although the quality of quantum bits (qubits) and quantum gates has been steadily improving, the available quantity of qubits has increased quite slowly. To address this important issue in quantum computing, we have demonstrated arbitrary single qubit gates based on targeted phase shifts, an approach that can be applied to atom, ion or other atom-like systems. These gates are highly insensitive to addressing beam imperfections and have little crosstalk, allowing for a dramatic scaling up of qubit number. We have performed gates in series on 48 individually targeted sites in a 40% full $5\times…
The long-range interaction between Rydberg-excited atoms endows a medium with large optical nonlinearity. Here, we demonstrate an optical switch to operate on a single photon from an entangled photon pair under a Rydberg electromagnetically induced transparency configuration. With the presence of the Rydberg blockade effect, we switch on a gate field to make the atomic medium nontransparent thereby absorbing the single photon emitted from another atomic ensemble via the spontaneous four-wave mixing process. In contrast to the case without a gate field, more than 50% of the photons sent to the …
Neutral atom platform has become an attractive choice to study the science of quantum information and quantum simulation, where intense efforts have been devoted to the entangling processes between individual atoms. For the development of this area, two-qubit controlled-PHASE gate via Rydberg blockade is one of the most essential elements. Recent theoretical studies have suggested the advantages of introducing non-trivial waveform modulation into the gate protocol, which is anticipated to improve its performance towards the next stage. We report our recent experimental results in realizing a t…
We demonstrate a trapped-ion entangling-gate scheme proposed by Bermudez et al. [Phys. Rev. A 85, 040302 (2012)]. Simultaneous excitation of a strong carrier and a single-sideband transition enables deterministic creation of entangled states. The method works for magnetic field-insensitive states, is robust against thermal excitations, includes dynamical decoupling from qubit dephasing errors, and provides simplifications in experimental implementation compared to some other entangling gates with trapped ions. We achieve a Bell state fidelity of 0.974(4) and identify the main sources of error.
We present a detailed, realistic analysis of the implementation of a proposal for a quantum phase gate based on atomic vibrational states, specializing it to neutral rubidium atoms on atom chips. We show how to create a double--well potential with static currents on the atom chips, using for all relevant parameters values that are achieved with present technology. The potential barrier between the two wells can be modified by varying the currents in order to realize a quantum phase gate for qubit states encoded in the atomic external degree of freedom. The gate performance is analyzed through …
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design which, in general, increases the complexity of the implementation. Here, we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In…
The Zeno effect occurs in quantum systems when a very strong measurement is applied, which can alter the dynamics in non-trivial ways. Despite being dissipative, the dynamics stay coherent within any degenerate subspaces of the measurement. Here we show that such a measurement can turn a single-qubit operation into a two- or multi-qubit entangling gate, even in a non-interacting system. We demonstrate this gate between two effectively non-interacting transmon qubits. Our Zeno gate works by imparting a geometric phase on the system, conditioned on it lying within a particular non-local subspace…
The fidelity of the gate operation and the coherence time of neutral atoms trapped in an optical dipole trap are figures of merit for the applications. The motion of the trapped atom is one of the key factors which influence the gate fidelity and coherence time. The motion has been considered as a classical oscillator in analyzing the influence. Here we treat the motion of the atom as a quantum oscillator. The population on the vibrational states of the atom are considered in analyzing the gate fidelity and decoherence. We show that the fidelity of a coherent rotation gate is dramatically limi…
Expanding the Neutral Atom Gate Set: Native iSWAP and Exchange Gates from Dipolar Rydberg Interactions
Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Parity Quantum Computing GmbH（Parity量子计算有限公司）；Parity Quantum Computing Germany GmbH（Parity量子计算德国有限公司）；Parity Quantum Computing France SAS（Parity量子计算法国股份有限公司）
Möbius-Guided Diagonal-Gate Compilation with Native Multiqubit Controlled-Phase Gates on Neutral-Atom Processors
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Department of Computer Science and Engineering, The Chinese University of Hong Kong（香港中文大学计算机科学与工程系）；State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）
