controlled-NOT Research Articles

Transverse Mode-Encoded Quantum Gate on a Silicon Photonic Chip.

As an important degree of freedom (d.o.f.) in photonic integrated circuits, the orthogonal transverse mode provides a promising and flexible way to increase communication capability, for both classical and quantum information processing. To construct large-scale on-chip multimode multi-d.o.f.s quantum systems, a transverse mode-encoded controlled-NOT (CNOT) gate is necessary. Here, with the help of our new transverse mode-dependent directional coupler and attenuator, we demonstrate the first multimode implementation of a 2-qubit quantum gate. The ability of the gate is demonstrated by entangling two separated transverse mode qubits with an average fidelity of 0.89±0.02 and the achievement of 10 standard deviations of violations in the quantum nonlocality verification. In addition, a fidelity of 0.82±0.01 is obtained from quantum process tomography used to completely characterize the CNOT gate. Our work paves the way for universal transverse mode-encoded quantum operations and large-scale multimode multi-d.o.f.s quantum systems.

Universal hardware-efficient topological measurement-based quantum computation via color-code-based cluster states

Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources. Raussendorf's three-dimensional cluster states (RTCSs) based on the surface codes are mainly considered for topological MBQC. In such schemes, however, the fault-tolerant implementation of the logical Hadamard, phase ($Z^{1/2}$), and $T$ ($Z^{1/4}$) gates which are essential for building up arbitrary logical gates has not been achieved to date without using state distillation, while the controlled-NOT (CNOT) gate does not require it, to best of our knowledge. State distillation generally consumes many ancillary logical qubits, thus it is a severe obstacle against practical quantum computing. To solve this problem, we suggest an MBQC scheme via a family of cluster states called color-code-based cluster states (CCCSs) based on the two-dimensional color codes instead of the surface codes. We define logical qubits, construct elementary logical gates, and describe error correction schemes. We show that all the logical Clifford gates including the CNOT, Hadamard, and phase gates can be implemented fault-tolerantly without state distillation, although the fault-tolerant $T$ gate still requires it. We further prove that the minimal number of physical qubits per logical qubit in a CCCS is at most approximately 1.8 times smaller than the case of an RTCS. We lastly show that the error threshold of MBQC via CCCSs for logical-$Z$ errors is 2.7-2.8%, which is comparable to the value for RTCSs, assuming a simple error model where physical qubits have $X$-measurement or $Z$ errors independently with the same probability.

Timing Constraints Imposed by Classical Digital Control Systems on Photonic Implementations of Measurement-Based Quantum Computing

Most of the architectural research on photonic implementations of measurement-based quantum computing (MBQC) has focused on the quantum resources involved in the problem with the implicit assumption that these will provide the main constraints on system scaling. However, the `flying-qubit' architecture of photonic MBQC requires specific timing constraints that need to be met by the classical control system. This classical control includes, for example: the amplification of the signals from single-photon detectors to voltage levels compatible with digital systems; the implementation of a control system which converts measurement outcomes into basis settings for measuring subsequent cluster qubits, in accordance with the quantum algorithm being implemented; and the digital-to-analog converter (DAC) and amplifier systems required to set these measurement bases using a fast phase modulator. In this paper, we analyze the digital system needed to implement arbitrary one-qubit rotations and controlled-NOT (CNOT) gates in discrete-variable photonic MBQC, in the presence of an ideal cluster state generator, with the main aim of understanding the timing constraints imposed by the digital logic on the analog system and quantum hardware. We use static timing analysis of a Xilinx FPGA (7 series) to provide a practical upper bound on the speed at which the adaptive measurement processing can be performed, in turn constraining the photonic clock rate of the system. Our work points to the importance of co-designing the classical control system in tandem with the quantum system in order to meet the challenging specifications of a photonic quantum computer.

The Optimization and Application of 3-Bit Hermitian Gates and Multiple Control Toffoli Gates

The well-known 3-bit Hermitian gate (a Toffoli gate) has been implemented using Clifford + T circuits. Compared with the Peres gate, its implementation circuit requires more controlled-NOT (CNOT) gates. However, the Peres gate is not Hermitian. This paper reports four 3-bit Hermitian gates named LI gates. Whose realized circuits have the same T-count, T-depth, and CNOT-count as the Peres gate. Furthermore, two decomposition methods of a multiple control Toffoli (MCT) gate are proposed for different primary optimization goals. Then, we design the equality, less-than, and full comparators with the minimum circuit width using proposed Hermitian gates and optimized MCT gates. A fault-tolerant circuit is required for robust quantum computing. Clifford+T circuits are accepted solutions for fault-tolerant implementation. Considering T-count, T-depth, CNOT-count, and circuit width as the primary optimization goals, we design the optimized Clifford + T circuits of three comparators using LI gates and optimized MCT gates. Comparison and analysis show that the proposed comparators have better overall performances for T-count, T-depth, CNOT-count, and circuit width than the best-known comparators without quantum measurements.

Controlled-NOT operation of SiN-photonic circuit using photon pairs from silicon-photonic circuit

We demonstrate controlled-NOT (CNOT) operation of a silicon nitride photonic integrated circuit using path-entangled photon pairs from a silicon-photonic integrated circuit as logical inputs. The CNOT gate is constructed by combining several silicon-nitride Mach–Zehnder interferometers for a linear-optical quantum gate. We package each of the two photonic circuits with electrical wire bonding and optical fiber bonding for stable measurement. The logical-basis fidelity of CNOT operation is measured better than 81% for the fully packaged photonic circuits.

Constructing a Facile Biocomputing Platform Based on Smart Supramolecular Hydrogel Film Electrodes with Immobilized Enzymes and Gold Nanoclusters.

Herein, fluorescent gold nanoclusters (AuNCs) and horseradish peroxidase (HRP) were simultaneously embedded into self-assembled dipeptide supramolecular films of N-fluorenylmethoxycarbonyl diphenylalanine (Fmoc-FF) on the surface of ITO electrodes (Fmoc-FF/AuNCs/HRP) by using a simple single-step process. In the films, both the fluorescence property of AuNCs and the bioelectrocatalytic property of HRP were well maintained and could be reversibly regulated by pH-sensitive structural changes in the Fmoc-FF hydrogel films. Cu(II)/EDTA in the solution could lead to the aggregation/disaggregation of AuNCs and further quenching/dequenching the fluorescence signal from the films. Meanwhile, the blue complexes formed by Cu(II) and EDTA could produce a UV-vis signal in the solution. In addition, the coordinated Cu(II) in the films enhanced the electrocatalytic capacity toward the reduction of H2O2 and could switch the current signal. A biomolecular logic circuit was built based on the smart film electrode system by using pH, the concentrations of EDTA, Cu(II) and H2O2 as inputs, while the fluorescence intensity (FL), current (I) and UV-vis extinction (E) of the solution as outputs. Various logic devices were fabricated using the uniform platform, consisting of an encoder/decoder, demultiplexer, dual-transfer gate, keypad lock, digital comparator, half adder, and controlled NOT (CNOT) gate. Specifically, an electronic three-value logic gate, gullibility (ANY) gate, was first mimicked in this biocomputing system. This work not only demonstrated the construction of a new type of multivalued logic gate by using a dipeptide micromolecular matrix but also provided a new approach for designing sophisticated biologic functions, establishing smart multianalyte biosensing or fabricating biology information processing through the use of a simple film system.

A Quantum Approach Towards the Adaptive Prediction of Cloud Workloads

This work presents a novel Evolutionary Quantum Neural Network (EQNN) based workload prediction model for Cloud datacenter. It exploits the computational efficiency of quantum computing by encoding workload information into qubits and propagating this information through the network to estimate the workload or resource demands with enhanced accuracy proactively. The rotation and reverse rotation effects of the Controlled-NOT (C-NOT) gate serve activation function at the hidden and output layers to adjust the qubit weights. In addition, a Self Balanced Adaptive Differential Evolution (SB-ADE) algorithm is developed to optimize qubit network weights. The accuracy of the EQNN prediction model is extensively evaluated and compared with seven state-of-the-art methods using eight real world benchmark datasets of three different categories. Experimental results reveal that the use of the quantum approach to evolutionary neural network substantially improves the prediction accuracy up to 91.6% over the existing approaches.

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.

Heralded Nondestructive Quantum Entangling Gate with Single-Photon Sources

Heralded entangling quantum gates are an essential element for the implementation of large-scale optical quantum computation. Yet, the experimental demonstration of genuine heralded entangling gates with free-flying output photons in linear optical system, was hindered by the intrinsically probabilistic source and double-pair emission in parametric down-conversion. Here, by using an on-demand single-photon source based on a semiconductor quantum dot embedded in a micropillar cavity, we demonstrate a heralded controlled-NOT (CNOT) operation between two single photons for the first time. To characterize the performance of the CNOT gate, we estimate its average quantum gate fidelity of (87.8±1.2)%. As an application, we generated event-ready Bell states with a fidelity of (83.4±2.4)%. Our results are an important step towards the development of photon-photon quantum logic gates.

Supercompact Photonic Quantum Logic Gate on a Silicon Chip.

To build universal quantum computers, an essential step is to realize the so-called controlled-NOT (CNOT) gate. Quantum photonic integrated circuits are well recognized as an attractive technology offering great promise for achieving large-scale quantum information processing, due to the potential for high fidelity, high efficiency, and compact footprints. Here, we demonstrate a supercompact integrated quantum CNOT gate on silicon by using the concept of symmetry breaking of a six-channel waveguide superlattice. The present path-encoded quantum CNOT gate is implemented with a footprint of 4.8×4.45 μm^{2} (∼3λ×3λ) as well as a high-process fidelity of ∼0.925 and a low excess loss of <0.2 dB. The footprint is shrunk significantly by ∼10 000 times compared to those previous results based on dielectric waveguides. This offers the possibility of realizing practical large-scale quantum information processes and paving the way to the applications across fundamental science and quantum technologies.

Fast and robust implementation of quantum gates by transitionless quantum driving

As a basic operation in quantum computers, quantum logic gates and particularly controlled NOT (CNOT) gates are important in quantum information processing. In this paper, we propose a one-step scheme to generate a CNOT gate via transitionless quantum driving. In this scheme, an effective Hamiltonian is obtained based on quantum Zeno dynamics to drive the system to evolve into the target state when the parameters are reasonably set. The results of explicit numerical simulations indicate that the proposed scheme is robust against instability related to variation in experimental parameters and decoherence. The scheme can also be extended to generate a Toffoli gate, which is useful for large-scale quantum computers. Moreover, the generation process involves only a single step, greatly simplifying its implementation.

High-Fidelity Hybrid Universal Quantum Controlled Gates on Photons and Quantum-Dot Spins

Both photons and semiconductor quantum-dot (QD) spins are promising candidates for quantum information science and technology. It is of critical significance to realize high-fidelity quantum controlled gates on photon-spin hybrid systems. In this paper, based on the novel balance condition for the interaction between a single input photon and a singly charged QD embedded in an optical single-sided microcavity, we present three schemes for implementing three universal quantum controlled gates, i.e., the two-qubit controlled-NOT (CNOT) gate, the three-qubit Toffoli gate, and the three-qubit Fredkin gate, on composite hybrid quantum systems consisting of flying photons and QD-confined electron spins. By exploiting the balance condition, the noise caused by the unbalanced reflectance of the coupled and uncoupled QD-cavity systems can be efficiently suppressed, so that the fidelity of each quantum gate operation can be raised to unity in principle. The balance condition can be met without the strict requirement of strong coupling, making the high-fidelity quantum gates easier to be demonstrated in experiments. These features can improve the fidelity and feasibility of these schemes, which can be applied to large-scaled quantum computing and quantum information networks.

Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations

Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled cluster ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all subterms for each excitation operator, a single-term representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit. With these strategies, VQE calculations on a noiseless quantum simulator achieve energies within a few meVs of those obtained with the full UCCSD ansatz for $\mathrm{H}_4$ square, $\mathrm{H}_4$ chain and $\mathrm{H}_6$ hexagon molecules; while the number of controlled-NOT (CNOT) gates, a measure of the quantum-circuit depth, is reduced by a factor of as large as 35. Furthermore, we introduced an efficient "score" parameter to rank the excitation operators, so that the operators causing larger energy reduction can be applied first. Using $\mathrm{H}_4$ square and $\mathrm{H}_4$ chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational ansatz.

Generation of all-to-all connections in a two-dimensional qubit array with two-body interactions

All-to-all connections are required in general quantum annealing machines to solve various combinatorial optimization problems. The Lechner, Hauke, and Zoller method, which is used to realize the all-to-all connections, requires many-body interactions in locally connected qubits. Because most of the qubit interactions are two-body interactions, Lechner also proposed the construction of each four-body interaction by six controlled-NOT (CNOT) gates between two qubits. However, it is difficult to construct many CNOT gates. Herein, we show more concrete sequences to produce four-body and three-body interactions based on a two-dimensional solid-state qubit system. We show that the number of operations needed to construct the many-body interactions can be reduced using appropriate pulse sequences. These findings will help reduce quantum computation costs for solving combinatorial problems.

Feasible time-bin entanglement purification based on sum-frequency generation.

High quality time-bin entanglement is widely exploited to achieve the purposes of fundamental tests of physics and the implementation of quantum communication protocols both in free space and optical fiber propagation. However, the imperfect approaches of generating time-bin entangled state will degrade its quality and limit its practical application. Entanglement purification is to distill high quality entangled states from low quality entangled states. In this paper, we present the first entanglement purification protocol (EPP) for time-bin entanglement. We first explain this EPP for two-photon time-bin entangled state and then extend it to the system of multi-photon time-bin entangled state. We also design a possible realization of this EPP with practical spontaneous parametric down conversion (SPDC) source. Differ from the conventional EPPs, this EPP does not require the sophisticated controlled-not (CNOT) gate or similar operations, and it uses the feasible sum-frequency generation (SFG) to perform the purification. Moreover, the double-pair noise emitted from the SPDC source can be eliminated automatically which is the other advantage of this EPP. If we combine with the faithful entanglement swapping, this EPP may have potential to be a part of full quantum repeaters.

Efficient Boolean Methods for Preparing Uniform Quantum States

As each quantum algorithm requires a specific initial quantum state, quantum state preparation is an important task in quantum computing. The preparation of quantum states is performed by a quantum circuit consisting of controlled-NOT (CNOT) and single-qubit gates. Known algorithms to prepare arbitrary $n$ -qubit quantum states create quantum circuits in $O(2^n)$ runtime and use $O(2^n)$ CNOTs, which are more expensive than single-qubit gates in NISQ architectures. To reduce runtime and the number of CNOTs, we simplify the problem by considering an important family of quantum states, which are uniform quantum states (UQSs). We map UQSs to Boolean functions and propose a UQS preparation (UQSP) method. Preparing UQSs using Boolean functions allows us to utilize different representations of Boolean functions. We utilize decision diagrams to reduce runtime and enable preparation for a larger number of qubits where the state-of-the-art methods are not applicable. To further reduce the number of CNOTs, we utilize variable reordering and functional dependencies among the variables. Our state preparation method requires an exponential number of CNOTs in the worst case but it reduces CNOTs significantly for practical benchmarks. Moreover, our method generates an exact representation of quantum states without using free-qubits. We compare our algorithm with QisKit. The comparison shows that our UQSP method is capable to reduce the average number of CNOTs by 75.31% for the practical benchmarks. The runtime is almost reduced by a factor of 2.

Femtosecond Laser Direct Writing of Integrated Photonic Quantum Chips for Generating Path-Encoded Bell States.

Integrated photonic quantum chip provides a promising platform to perform quantum computation, quantum simulation, quantum metrology and quantum communication. Femtosecond laser direct writing (FLDW) is a potential technique to fabricate various integrated photonic quantum chips in glass. Several quantum logic gates fabricated by FLDW have been reported, such as polarization and path encoded quantum controlled-NOT (CNOT) gates. By combining several single qubit gates and two qubit gates, the quantum circuit can realize different functions, such as generating quantum entangled states and performing quantum computation algorithms. Here we demonstrate the FLDW of integrated photonic quantum chips composed of one Hadamard gate and one CNOT gate for generating all four path-encoded Bell states. The experimental results show that the average fidelity of the reconstructed truth table reaches as high as 98.8 0.3%. Our work is of great importance to be widely applied in many quantum circuits, therefore this technique would offer great potential to fabricate more complex circuits to realize more advanced functions.

Controlled-not gate with orbital angular momentum in a rare-earth-ion-doped solid

We experimentally demonstrate a controlled-not (CNOT) gate with vortex beams carrying orbital angular momentum (OAM) via light storage in a solid driven by electromagnetically induced transparency (EIT). We use vortex beams with different topological charges to perform EIT storage in the double lambda atomic system, the stored information is transferred into a new information channel. The topological charge of the generated signal field is determined by those of the applied fields. The OAM conservation is satisfied in this EIT storage of the double lambda system. By imposing different OAMs into the control and probe fields, we obtain a CNOT gate using EIT storage. This demonstration can be useful for better understanding and developing the OAM applications in the interactions between the OAM and the mediums.

Deterministic quantum cyclic controlled teleportation of arbitrary multi-qubit states using multi-qubit partially entangled channel

In this paper, we present a deterministic four-party quantum cyclic controlled teleportation (QCYCT) scheme, by using a multi-qubit partially entangled state as the quantum channel. In this scheme, Alice can teleport an arbitrary [Formula: see text]-qubit state to Bob, Bob can teleport an arbitrary [Formula: see text]-qubit state to Charlie and Charlie can teleport an arbitrary [Formula: see text]-qubit state to Alice under the control of the supervisor David. We utilize rotation gate, Hadamard gates and controlled-NOT (CNOT) gates to construct the multi-qubit partially entangled channel. Only Bell-state measurements, single-qubit von-Neumann measurement and proper unitary operations are required in this scheme, which can be realized in practice easily based on the present quantum experiment technologies. The direction of cyclic controlled teleportation of arbitrary multi-qubit states can also be changed by altering the quantum channel. Analysis demonstrates that the success probability of the proposed scheme can still reach 100% although the quantum channel is non-maximally entangled. Furthermore, the proposed four-party scheme can be generalized into the case involving [Formula: see text] correspondents, which is more suitable for quantum communication networks. We also calculate the intrinsic efficiency and discuss the security of the proposed scheme. Compared with the existing QCYCT schemes which realized cyclic controlled teleportation of arbitrary single-qubit states, specific two-qubit and three-qubit states, the proposed scheme is of general significance.

Optimal synthesis of the Fredkin gate in a multilevel system

The optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. By harnessing higher-dimensional Hilbert spaces, we reduce the cost of a three-qubit Fredkin gate from 8 CNOTs to 5 nearest-neighbor CNOTs. We also present a construction of an n-control-qubit Fredkin gate with 2n + 3 CNOTs and 2n single-qudit operations. Finally, we design deterministic and non-deterministic three-qubit Fredkin gates in photonic architectures. The cost of a non-deterministic three-qubit Fredkin gate is further reduced to 4 nearest-neighbor CNOTs, and the success of such a gate is heralded by a single-photon detector. Our insights bridge the gap between the theoretical lower bound and the current best result for the n-qubit quantum computation.