controlled-NOT Operation Research Articles

A quantum secure multi-party summation protocol with quantum Fourier transform

In this paper, a quantum secure multi-party summation scheme with a third party based on quantum Fourier transform (QFT) is put forward, where the third party cannot be permitted to cooperate with others but is allowed for all kinds of attacks. Under the help of third party, [Formula: see text] users can calculate the addition modulo [Formula: see text] of their private integer strings. The third party generates two-level single qubit and its product state as the initial quantum resource, produces the traveling particles with QFT and the controlled-not (CNOT) operations, and sends the traveling particles out to the first users; then, [Formula: see text] users encode their private integer sequences by performing the phase shifting operations on the travelling particles one after another; and finally, the third party decodes out the summation of the private integer sequences from [Formula: see text] users through CNOT operations and inverse quantum Fourier transform (IQFT). This protocol only adopts two-level single particle state and its product state as initial quantum resource, only needs [Formula: see text]-level single particle measurement and does not need to perform quantum entanglement swapping. Security analysis indicates that this protocol can overcome not only the outside attack but also the participant attack.

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.

A novel quantum dialogue without information leakage based on single photons in both polarization and spatial-mode degrees of freedom

This paper puts forward a novel quantum dialogue (QD) protocol without information leakage based on single photons in both polarization and spatial-mode degrees of freedom. In this protocol, the receiver sends his private message to the sender in the way of quantum secure direct communication; and the receiver decodes out the private message of the sender with the help of auxiliary single photons in two degrees of freedom, double controlled-not (CNOT) operations and an auxiliary classical bit sequence sent from the sender. As a result, no information leakage takes place. Moreover, this protocol is proven to defeat the intercept-resend attack, the measure-resend attack, the entangle-measure attack and the Trojan horse attack from an outside eavesdropper. This protocol only employs single photons in two degrees of freedom as quantum resource and needs single-photon measurements. The qubit efficiency of this protocol is as high as 66.7%.

An identity-verifiable quantum threshold group signature scheme based on three-particle GHZ states

With the advancement of the new generation of information technology in recent years, quantum digital signatures have been widely concerned. Among them, quantum threshold group signatures have become a hot research field due to their advantages such as low cost and strong scalability. Therefore, in this paper, we propose an identity-verifiable quantum threshold group signature scheme based on three-particle GHZ states. The characteristics of the scheme are as follows. The signers can reconstruct the key K for signature’s generation and verification by using the Shamir threshold secret sharing scheme. A quantum signature is generated by performing controlled-not operations, von Neumann measurements, and quantum Fourier transform. When the signature is verified, only classical hash values need to be compared, without comparing quantum states. Identity verification is performed between participants by using hash functions. The efficiency of the scheme is improved by using super-dense coding. Security analysis shows that our scheme is unforgeable and undeniable.

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% .

Hyper-parallel nonlocal CNOT operation assisted by quantum-dot spin in a double-sided optical microcavity

Implementation of controlled-NOT (CNOT) operation between different nodes in a quantum communication network nonlocally plays an important role in distributed quantum computation. We present a protocol for implementation of hyper-parallel nonlocal CNOT operation via hyperentangled photons simultaneously entangled in spatial-mode and polarization degrees of freedom (DOFs) assisted by quantum-dot spin in a double-sided optical microcavity. The agent Alice lets photons traverse the double-sided optical microcavity sequentially and applies single-qubit measurements on the electron and the hyperentangled photon. The agent Bob first performs corresponding unitary operations according to Alice’s measurement results on his hyperentangled photon, and then lets photons traverse the double-sided optical microcavity sequentially and performs the single-qubit measurements on the electron and the hyperentangled photon. The hyper-parallel nonlocal CNOT operation can be implemented simultaneously in spatial-mode and polarization DOFs if Alice performs single-qubit operations in accordance with Bob’s measurement results. The protocol has the advantage of having high channel capacity for long-distance quantum communication by using a hyperentangled state as the quantum channel.

Universal logic with encoded spin qubits in silicon

Quantum computation features known examples of hardware acceleration for certain problems, but is challenging to realize because of its susceptibility to small errors from noise or imperfect control. The principles of fault tolerance may enable computational acceleration with imperfect hardware, but they place strict requirements on the character and correlation of errors1. For many qubit technologies2–21, some challenges to achieving fault tolerance can be traced to correlated errors arising from the need to control qubits by injecting microwave energy matching qubit resonances. Here we demonstrate an alternative approach to quantum computation that uses energy-degenerate encoded qubit states controlled by nearest-neighbour contact interactions that partially swap the spin states of electrons with those of their neighbours. Calibrated sequences of such partial swaps, implemented using only voltage pulses, allow universal quantum control while bypassing microwave-associated correlated error sources1,22–28. We use an array of six 28Si/SiGe quantum dots, built using a platform that is capable of extending in two dimensions following processes used in conventional microelectronics29. We quantify the operational fidelity of universal control of two encoded qubits using interleaved randomized benchmarking30, finding a fidelity of 96.3% ± 0.7% for encoded controlled NOT operations and 99.3% ± 0.5% for encoded SWAP. The quantum coherence offered by enriched silicon5–9,16,18,20,22,27,29,31–37, the all-electrical and low-crosstalk-control of partial swap operations1,22–28 and the configurable insensitivity of our encoding to certain error sources28,33,34,38 all combine to offer a strong pathway towards scalable fault tolerance and computational advantage.

Single-Copy Certification of Two-Qubit Gates Without Entanglement

A quantum state transformation can be generally approximated by single- and two-qubit gates. This, however, does not hold with noisy intermediate-scale quantum technologies due to the errors appearing in the gate operations, where errors of two-qubit gates such as controlled-NOT and SWAP operations are dominated. In this work, we present a cost efficient single-copy certification for a realization of a two-qubit gate in the presence of depolarization noise, where it is aimed to identify if the realization is noise-free, or not. It is shown that entangled resources such as entangled states and a joint measurement are not necessary for the purpose, i.e., a noise-free two-qubit gate is not needed to certify an implementation of a two-qubit gate. A proof-of-principle demonstration is presented with photonic qubits.

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.

Exploring entanglement resource in Si quantum dot systems with operational quasiprobability approach

We characterize the quantum entanglement of the realistic two-qubit signals that are sensitive to charge noises. Our working example is the time response generated from a silicon double quantum dot (DQD) platform, where a single-qubit rotation and a two-qubit controlled-NOT operation are conducted sequentially in time to generate arbitrary entangled states. In order to characterize the entanglement of two-qubit states, we employ the marginal operational quasiprobability (OQ) approach that allows negative values of the probability function if a given state is entangled. While the charge noise, which is omnipresent in semiconductor devices, severely affects logic operations implemented in the DQD platform, causing huge degradation in fidelity of unitary operations as well as resulting two-qubit states, the pattern in the OQ-driven entanglement strength turns out to be quite invariant, indicating that the resource of quantum entanglement is not significantly broken though the physical system is exposed to noise-driven fluctuations in exchange interaction between quantum dots.

Cnot Gates for Fluxonium Qubits via Selective Darkening of Transitions

We analyze the cross-resonance effect for fluxonium circuits and investigate a two-qubit gate scheme based on selective darkening of a transition. In this approach, two microwave pulses at the frequency of the target qubit are applied simultaneously with a proper ratio between their amplitudes to achieve a controlled-NOT operation. We study in detail coherent gate dynamics and calculate gate error. With nonunitary effects accounted for, we demonstrate that gate error below $10^{-4}$ is possible for realistic hardware parameters. This number is facilitated by long coherence times of computational transitions and strong anharmonicity of fluxoniums, which easily prevents excitation to higher excited states during the gate microwave drive.

A lightweight three-user secure quantum summation protocol without a third party based on single-particle states

In this paper, a lightweight three-user secure quantum summation protocol is put forward by using single-particle states, which can accomplish the goal that three users cooperate together to calculate the modulo 2 addition of their private messages without the help of a third party. This protocol only requires single-particle states rather than quantum entangled states as the initial quantum resource and only needs single-particle measurements and Bell basis measurements. This protocol needs none of quantum entanglement swapping, the Pauli operations, the controlled-not (CNOT) operation, the Hadamard gate or a pre-shared private key sequence. Security analysis proves that this protocol is secure against both the outside attacks and the participant attacks. Compared with the existing two-dimensional three-user quantum summation protocols, this protocol more or less takes advantage over them on the aspects of the initial quantum resource, users’ quantum measurement, the usage of quantum entanglement swapping, the usage of Pauli operations, the usage of CNOT operation or the usage of Hadamard gate.

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.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator.

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

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.

Theoretical Realization of a Two Qubit Quantum Controlled-NOT Logic Gate and a Single Qubit Quantum Hadamard Logic Gate in the Anti-Jaynes-Cummings Model

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

Bidirectional Controlled Quantum Teleportation Using Eight-Qubit Quantum Channel in Noisy Environments

In this work, a novel protocol is proposed for bidirectional controlled quantum teleportation (BCQT) in which a quantum channel is used with the eight-qubit entangled state. Using the protocol, two users can teleport an arbitrary entangled state and a pure two-qubit state (QBS) to each other simultaneously under the permission of a third party in the role of controller. This protocol is based on the controlled-not operation, appropriate single-qubit (SIQ) UOs, and SIQ measurements in the Z and X-basis. Also, in this paper, a new criterion of merit named as (predictability of the controller’s qubit (QB) by the eavesdropper) is introduced, and the protocol is improved based on it. Then, the proposed protocol is investigated in two typical noisy channels, the amplitude-damping noise (ADN) and the phase-damping noise (PDN). The analysis of the protocol in the noisy environment shows that it only depends on the amplitude of the initial state and the decoherence noisy rate (DR).

Quantum proxy signature with provable security

A quantum proxy signature scheme makes the proxy signer can generate a quantum signature on behalf of the original signer. Although many quantum proxy signature schemes have been proposed, none of them can be formally proved to be secure. There is not even security model for the quantum proxy signatures. Some quantum proxy signature schemes have been proved to be insecure against forgery attacks. In this paper, first, the formal definition and the corresponding security model for the quantum proxy signatures are proposed. Second, based on the Hadamard operator and the controlled NOT operation, a new quantum proxy signature scheme is proposed. The security of our quantum proxy signature scheme can be formally proved under security model. The security model of the quantum proxy signatures is helpful for analyzing and improving the security of the quantum proxy signature schemes. On the other hand, compared with the other quantum proxy signatures, the new one proposed in this paper is the first that can be formally proved to be secure under security model.

Controlled Cavity-Free, Single-Photon Emission and Bipartite Entanglement of Near-Field-Excited Quantum Emitters.

We report theoretical statistics of 1- and 2-qubit (bipartite) systems, namely, photon antibunching and entanglement, of near-field excited quantum emitters. The sub-diffraction focusing of a plasmonic waveguide is shown to generate enough power over a sufficiently small region (<50 × 50 nm2) to strongly drive quantum emitters. This enables ultrafast (10-14 s) single-photon emission as well as creates entangled states between two emitters when performing a controlled-NOT operation. A comparative analysis of silicon and near-zero index materials demonstrates advantages and uncovers challenges of embedding quantum emitters for single-photon emission and for bipartite entanglement. The use of a movable plasmonic waveguide, in lieu of stationary nanostructures, allows high-speed rasterization between sets of qubits and enables spatially flexible data storage and quantum information processing. Furthermore, the sub-diffraction focusing of the waveguide is shown to achieve cavity-free dynamic entanglement. This greatly reduces fabrication constraints and increases the speed and scalability of nanophotonic quantum devices.