controlled-NOT Gate Operation Research Articles

Theoretical concept of error-rejecting entanglement purification of quantum-dots electronic spins in single-sided optical microcavity

We use the quantum-dots (QD) coupled with single-sided microcavities system to construct the error-rejecting controlled not (CNOT) gate of electronic spins system in QD; We have designed an error-rejecting entanglement purification protocol (EPP) of electronic spins system in QD by using the error-rejecting CNOT gate and unitary operation. It can extract the high entanglement from the mixed entanglement states of the electronic spins with low entangled states. This EPP can eliminate the operation errors caused by the nonideal interaction between photons and QD coupled with optical microcavities system, and improve the fidelity of the EPP through iteration. Our scheme is more practical in future long-distance quantum communications, especially providing significant benefits for solving decoherence problems in quantum networks and quantum repeaters.

Simplified quantum teleportation for a distinctive six-qubit target state via a six-qubit entangled state

Based on a six-qubit entangled state, a quantum information processing scheme for teleporting a distinctive six-qubit state is presented. In the scheme, only Bell-state measurements and two-qubit controlled-NOT gate operations as well as some single-qubit transformed operations are needed. Compared with a rival scheme put forwarded by Tan et al [Int. J. Theor. Phys. 55, 155 (2016)], the present scheme is more simpler and easier to execute because it does not require to make the six-qubit entangled state measurement. Besides, it is deterministic and feasible in terms of the current experimental technologies.

Non‐Markovian Cost Function for Quantum Error Mitigation

AbstractIn near‐term quantum computers like noisy intermediate‐scale quantum (NISQ) devices, reducing the impact of errors and decoherence is critical for practical implementation. Existing studies have primarily focused on Markovian noise sources; however, understanding the relationship between quantum error mitigation (QEM) and non‐Markovian noise sources is essential, as these effects are practically unavoidable in most solid‐state devices used for quantum computing. Here, a non‐Markovian model of quantum state evolution and a QEM cost function of controlled‐NOT (CNOT) gate operation are presented for NISQ devices interacting with an environment characterized by simple harmonic oscillators as a noise source. Using the projection operator formalism and both advanced and retarded propagators in time, the reduced‐density operator is derived for output quantum states in a time‐convolutionless form by solving the quantum Liouville equation. Output quantum state fluctuations are analyzed for identity and CNOT gate operations in two‐qubit operations across various input states and compare these results with experimental data from ion‐trap and superconducting quantum computing systems to estimate the key parameters of the QEM cost functions. These findings demonstrate that the QEM cost function increases as the coupling strength between the quantum system and its environment intensifies. This study highlights the significance of non‐Markovian models for understanding quantum state evolution and the practical implications of the QEM cost function in assessing experimental results from NISQ devices.

Quantum teleportation of a two-qubit arbitrary entangled state with four-qubit cluster state

Based on the four-qubit cluster state as quantum channel, we put forward a novel scheme for teleporting a two-qubit arbitrary entangled state. The necessary quantum operations for accomplishing the task are two controlled-not gate operations, one controlled-phase gate operation, four single-qubit measurements and two single-qubit transformed operations. They are easily achievable with current experimental techniques. Besides, the present scheme is deterministic because its probability of success is 100% .

Quantum Gate Operations on a Spectrally Addressable Photogenerated Molecular Electron Spin-Qubit Pair

Sub-nanosecond photodriven electron transfer from a molecular donor to an acceptor can be used to generate a radical pair (RP) having two entangled electron spins in a well-defined pure initial singlet quantum state to serve as a spin-qubit pair (SQP). Achieving good spin-qubit addressability is challenging because many organic radical ions have large hyperfine couplings (HFCs) in addition to significant g-anisotropy, which results in significant spectral overlap. Moreover, using radicals with g-factors that deviate significantly from that of the free electron results in difficulty generating microwave pulses with sufficiently large bandwidths to manipulate the two spins either simultaneously or selectively as is necessary to implement the controlled-NOT (CNOT) quantum gate essential for quantum algorithms. Here, we address these issues by using a covalently linked donor-acceptor(1)-acceptor(2) (D-A1-A2) molecule with significantly reduced HFCs that uses fully deuterated peri-xanthenoxanthene (PXX) as D, naphthalenemonoimide (NMI) as A1, and a C60 derivative as A2. Selective photoexcitation of PXX within PXX-d9-NMI-C60 results in sub-nanosecond, two-step electron transfer to generate the long-lived PXX•+-d9-NMI-C60•- SQP. Alignment of PXX•+-d9-NMI-C60•- in the nematic liquid crystal 4-cyano-4'-(n-pentyl)biphenyl (5CB) at cryogenic temperatures results in well-resolved, narrow resonances for each electron spin. We demonstrate both single-qubit gate and two-qubit CNOT gate operations using both selective and nonselective Gaussian-shaped microwave pulses and broadband spectral detection of the spin states following the gate operations.

Dynamical Behavior of Two Interacting Double Quantum Dots in 2D Materials for Feasibility of Controlled-NOT Operation.

Two interacting double quantum dots (DQDs) can be suitable candidates for operation in the applications of quantum information processing and computation. In this work, DQDs are modeled by the heterostructure of two-dimensional (2D) MoS2 having 1T-phase embedded in 2H-phase with the aim to investigate the feasibility of controlled-NOT (CNOT) gate operation with the Coulomb interaction. The Hamiltonian of the system is constructed by two models, namely the 2D electronic potential model and the matrix model whose matrix elements are computed from the approximated two-level systems interaction. The dynamics of states are carried out by the Crank–Nicolson method in the potential model and by the fourth order Runge–Kutta method in the matrix model. Model parameters are analyzed to optimize the CNOT operation feasibility and fidelity, and investigate the behaviors of DQDs in different regimes. Results from both models are in excellent agreement, indicating that the constructed matrix model can be used to simulate dynamical behaviors of two interacting DQDs with lower computational resources. For CNOT operation, the two DQD systems with the Coulomb interaction are feasible, though optimization of engineering parameters is needed to achieve optimal fidelity.

Scheme for implementing nonlocal high-fidelity quantum controlled-not gates on quantum-dot-confined electron spins using optical microcavities and photonic hyperentanglement

Quantum information networks can transmit quantum states and perform quantum operations between different quantum network nodes, which are essential for various applications of quantum information technology in the future. In this paper, a potentially practical scheme for implementing nonlocal quantum controlled-not (CNOT) gate operations on quantum-dot-confined electron spins between two quantum network nodes is presented. The scheme can realize parallel teleportation of two nonlocal quantum CNOT gates simultaneously by employing hyperentangled photon pairs to establish quantum channel, which can effectively improve the channel capacity and operational speed. The core of the scheme are two kinds of photon-spin hybrid quantum CNOT gate working in a failure-heralded and fidelity-robust fashion. With the heralded mechanism, the nonlocal CNOT gates can be implementated with unity fidelities in principle, even if the particularly ideal conditions commonly used in other schemes are not satisfied strictly. Our analysis and calculations indicate that the scheme can be demonstrated efficiently (with efficiency exceeding 99%) with current or near-future technologies. Moreover, the utilized photon-spin hybrid quantum gates can be regarded as universal modules for many other quantum information processing (QIP) tasks. Therefore, the scheme is potential for constructing elementary quantum networks, and realizing nolocal QIP with high channel capacities, high fidelities, and high efficiencies.

(Invited, Digital Presentation) Exciton Controlled-NOT Gate Realized By Carbon Nanotube Coupled Quantum Dots

Among various methods for constructing the quantum bits (qubits) required to perform the quantum computing, there is the concept to use the exciton in nano-structured material such as semiconductor quantum dot (QD), colloidal nanocrystal, or molecule. When the presence/absence of exciton is associated with two-level system of |1>/|0>, the Rabi oscillation of exciton serves as a basis for one-qubit operation. In order to realize the controlled-NOT (CNOT) gate which is essential for the quantum computing, one needs four-level system consisting of two qubits (i.e., |0>|0>, |1>|0>, |0>|1>, and |1>|1>). The construction of exciton CNOT gate is theoretically possible, however, the experimental demonstration has not been conducted. The optical processes of carbon nanotubes are governed by excitons. We attempted to realize the exciton CNOT gate by using the coupled QDs formed in a carbon nanotube.We fabricated two QDs by terminating both ends of a single-walled carbon nanotube (SWNT) with the collagen model peptides via peptide bonds. The scanning tunneling microscopy and spectroscopy measurements revealed that two QDs of ~ 3.1 nm and ~ 3.9 nm in widths, respectively, were formed in that SWNT with the inter-dot spacing of ~ 5.4 nm. It was confirmed by observing the Rabi oscillations that each QD acted as the exciton two-level system. When the excitons were produced in both QDs, additional exciton emission lines appeared, which may be originating from the coupled state of excitons across two QDs. We define the exciton four-level system as follows; |0>|0> when both QDs are empty, |1>|0>/|0>|1> when exciton is present in either of two QDs, and |1>|1> when excitons coupled across two QDs are generated. |1>|0>, |0>|1>, or |1>|1> could be prepared by irradiating the corresponding π pulse determined from the Rabi oscillation.The CNOT gate consists of a control qubit and a target qubit, and the logic of the target qubit is flipped only if the control qubit is in logic |1>. When we regard two QDs in our sample as a pair of control qubit and target qubit, the conditional flip of the target qubit corresponds to the π pulse-induced transition between |1>|1> and |1>|0> or between |1>|1> and |0>|1> depending on which QD we choose for the target qubit. The exciton CNOT gate operations were executed by irradiating that π pulse onto the states prepared as inputs. The input/output relations were measured in both ZZ and XX bases, which allowed us to estimate the quantum process fidelity. Our exciton CNOT gate actualized the expected operations whichever QD we used as the target qubit. By executing the CNOT gate operations three times, logic exchange is made between |1>|0> and |0>|1>, which is called the SWAP gate. It was also ascertained that the exchange of the exciton population took place between two QDs when conducting the SWAP operation by applying our CNOT gate.

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.

Quantum Process Tomography of a Controlled-Phase Gate for Time-Bin Qubits

Time-bin qubits, where information is encoded in a single photon at different times, have been widely used in optical fiber and waveguide based quantum communications. With the recent developments in distributed quantum computation, it is logical to ask whether time-bin encoded qubits may be useful in that context. We have recently realized a time-bin qubit controlled-phase (C-Phase) gate using a 2 X 2 optical switch based on a lithium niobate waveguide, with which we demonstrated the generation of an entangled state. However, the experiment was performed with only a pair of input states, and thus the functionality of the C-Phase gate was not fully verified. In this research, we used quantum process tomography to establish a process fidelity of 97.1%. Furthermore, we demonstrated the controlled-NOT gate operation with a process fidelity greater than 94%. This study confirms that typical two-qubit logic gates used in quantum computational circuits can be implemented with time-bin qubits, and thus it is a significant step forward for realization of distributed quantum computation based on time-bin qubits.

Quantum computing with exciton-polariton condensates

Exciton-polariton condensates have attractive features for quantum computation, e.g., room temperature operation, high dynamical speed, ease of probe, and existing fabrication techniques. Here, we present a complete theoretical scheme of quantum computing with exciton-polariton condensates formed in semiconductor micropillars. Quantum fluctuations on top of the condensates are shown to realize qubits, which are externally controllable by applied laser pulses. Quantum tunneling and nonlinear interactions between the condensates allow SWAP, square-root-SWAP and controlled-NOT gate operations between the qubits.

CNOT gate operation on a photogenerated molecular electron spin-qubit pair.

Implementation of the two-qubit controlled-NOT (CNOT) gate is necessary to develop a complete set of universal gates for quantum computing. Here, we demonstrate that a photogenerated radical (spin qubit) pair within a covalent donor-chromophore-acceptor molecule can be used to successfully execute a CNOT gate with high fidelity. The donor is tetrathiafulvalene (TTF), the chromophore is 8-aminonaphthalene-1,8-dicarboximide (ANI), and the acceptor is pyromellitimide (PI). Selective photoexcitation of ANI with a 416 nm laser pulse results in subnanosecond formation of the TTF•+-ANI-PI•- radical (spin qubit) pair at 85 K having a 1.8 µs phase memory time. This is sufficiently long to execute a CNOT gate using a sequence of five microwave pulses followed by a sequence of two pulses that read out all the elements of the density matrix. Comparing these data to a simulation of the data that assumes ideal conditions results in a fidelity of 0.97 for the execution of the CNOT gate. These results show that photogenerated molecular spin qubit pairs can be used to execute this essential quantum gate at modest temperatures, which affords the possibility that chemical synthesis can be used to develop structures to execute more complex quantum logic operations using electron spins.

Implementation of a Two-Qubit C-NOT Quantum Gate in a System of Two Double Quantum Dots, a Microcavity, and a Laser

We study the possibility of implementing a two-qubit controlled-NOT gate operation in a structure consisting of two semiconductor double quantum dots placed in a high-Q optical microcavity and governed by a resonant laser field. The effect of relaxation processes on the dynamics of the two-electron system is discussed. The dissipation rates allowing quantum error correction algorithms to be used are determined. The existing additional excitation channel (laser pulse) is shown to weaken the effect of the nonideality of the cavity on the evolution of the states. Optimal electron coupling coefficients in the quantum dots with control fields are fitted, in which the controlled qubit is switched with the highest probability and the gate implementation takes several hundreds of picoseconds.

Spatial interference between pairs of disjoint optical paths with a single chaotic source.

We demonstrate a novel second-order spatial interference effect between two indistinguishable pairs of disjoint optical paths from a single chaotic source. Beside providing a deeper understanding of the physics of multi-photon interference and coherence, the effect enables retrieving information on both the spatial structure and the relative position of two distant double-pinhole masks, in the absence of first order coherence. We also demonstrate the exploitation of the phenomenon for simulating quantum logic gates, including a controlled-NOT gate operation.

Experimental controlled-NOT gate simulation with thermal light.

We report a recent experimental simulation of a controlled-NOT gate operation based on polarization correlation measurements of thermal fields in photon-number fluctuations. The interference between pairs of correlated paths at the very heart of these experiments has the potential for the simulation of correlations between a larger number of qubits.

Two-step measurement of the concurrence for hyperentangled state

We describe an efficient way of measuring the concurrence for the hyperentanglement. In this protocol, the hyperentangled state is encoded in both the polarization and the momentum degrees of freedom. We show that measurement of the concurrences of both polarization and momentum entanglements can be conversed into the measurement of the total probability of picking up the odd-parity state and can be measured directly. This protocol requires the weak cross-Kerr nonlinearity to construct the quantum nondemolition measurement and does not require the sophisticated controlled-not gate operation. It is feasible in future experimental technology.

Quantum Controlled-Not Gate Operation and Complete Bell-State Analysis Using Hybrid Quantum Circuits

Here we propose a hybrid quantum circuit for achieving the quantum controlled-not (CNOT) gate operation on a photon-spin hybrid state. The hybrid quantum circuit consists of a nitrogen-vacancy (N-V) center and microtoroidal resonator coupling system, and a single photon waveguide. We implement the complete Bell state analysis using the proposed circuit. This proposed hybrid quantum circuit could enable a high fidelity of qubit manipulation and allows the feasible with the current experimental technologies.

A controlled-NOT gate in a chain of qubits embedded in a spin field-effect transistor and its process tomography

We have investigated the realizability of the controlled-NOT (CNOT) gate and characterized the gate operation by quantum process tomography for a chain of qubits, realized by electrons confined in self-assembled quantum dots embedded in the spin field-effect transistor. We have shown that the CNOT gate operation and its process tomography are performable by using the spin exchange interaction and several local qubit rotations within the coherence time of qubits. Moreover it is shown that when the fluctuation of operation time and the imperfection of polarization of channel electrons are considered as sources of decay of fidelity, the process fidelity of CNOT decreases at most 5% by the fluctuation of the operation time and its values of 0.49 and 0.72 are obtained for polarizations of the channel spin 0.6 and 0.8, respectively.

Controlled quantum perfect teleportation of multiple arbitrary multi-qubit states

We present an efficient controlled quantum perfect teleportation scheme. In our scheme, multiple senders can teleport multiple arbitrary unknown multi-qubit states to a single receiver via a previously shared entanglement state with the help of one or more controllers. Furthermore, our scheme has a very good performance in the measurement and operation complexity, since it only needs to perform Bell state and single-particle measurements and to apply Controlled-Not gate and other single-particle unitary operations. In addition, compared with traditional schemes, our scheme needs less qubits as the quantum resources and exchanges less classical information, and thus obtains higher communication efficiency.

Universal quantum computing in linear nearest neighbor architectures

We introduce a scheme for realizing universal quantum computing in a linear nearest neighbor architecture with fixed couplings. We first show how to realize a controlled-NOT gate operation between two adjacent qubits without having to isolate the two qubits from qubits adjacent to them. The gate operation is implemented by applying two consecutive pulses of equal duration, but varying amplitudes, on the target qubit. Since only a single control parameter is required in implementing our scheme, it is very efficient. We next show how our scheme can be used to realize single qubit rotations and two-qubit controlled-unitary operations. As most proposals for solid state implementations of a quantum computer use a one-dimensional line of qubits, the schemes presented here will be extremely useful.