CNOT Research Articles

Spin-Polarized Molecular Triplet States as Qubits: Phosphorus Hyperfine Coupling in the Triplet State of Benzoisophosphinoline.

Advances in quantum information science (QIS) require the development of new molecular materials to serve as microwave addressable qubits that can be read out optically. Laser photoexcitation of organic π-conjugated molecules often results in spin-polarized phosphorescent triplet states that can be readily observed and manipulated using time-resolved electron paramagnetic resonance (EPR) techniques. Photoexcitation of N-mesityl-1,8-naphthalimide (M-NMI) and its phosphorus analogues, 2-mesitylbenzoisophosphinoline (M-BIPD) and 2-mesitylbenzoisophosphinoline oxide (M-BIPDO) results in ultrafast spin-orbit charge-transfer intersystem crossing to form the corresponding phosphorescent triplet states M-3*NMI, M-3*BIPD and M-3*BIPDO. The ultrafast triplet formation dynamics, phosphorescence, and spin-polarized EPR spectra of these triplet states were examined. The most promising qubit candidate, M-3*BIPD, was examined using pulse-EPR to measure its spin relaxation times, and pulse electron-nuclear double resonance spectroscopy to perform a two-qubit CNOT gate using the phosphorus nuclear spin.

Qiskit pulse: programming quantum computers through the cloud with pulses

The quantum circuit model is an abstraction that hides the underlying physical implementation of gates and measurements on a quantum computer. For precise control of real quantum hardware, the ability to execute pulse and readout-level instructions is required. To that end, we introduce Qiskit Pulse, a pulse-level programming paradigm implemented as a module within Qiskit-Terra []. To demonstrate the capabilities of Qiskit Pulse, we calibrate both un-echoed and echoed variants of the cross-resonance entangling gate with a pair of qubits on an IBM Quantum system accessible through the cloud. We perform Hamiltonian characterization of both single and two-pulse variants of the cross-resonance entangling gate with varying amplitudes on a cloud-based IBM Quantum system. We then transform these calibrated sequences into a high-fidelity CNOT gate by applying pre and post local-rotations to the qubits, achieving average gate fidelities of F = 0.981 and F = 0.979 for the un-echoed and echoed respectively. This is comparable to the standard backend CNOT fidelity of FCX = 0.984. Furthermore, to illustrate how users can access their results at different levels of the readout chain, we build a custom discriminator to investigate qubit readout correlations. Qiskit Pulse allows users to explore advanced control schemes such as optimal control theory, dynamical decoupling, and error mitigation that are not available within the circuit model.

Space-efficient quantum multiplication polynomials for binary finite fields with sub-quadratoc Toffoli gate count

Multiplication is an essential step in a lot of calculations. In this paper we look at multiplication of 2 binary polynomials of degree at most n-1, modulo an irreducible polynomial of degree n with 2n input and n output qubits, without ancillary qubits, assuming no errors. With straightforward schoolbook methods this would result in a quadratic number of Toffoli gates and a linear number of CNOT gates. This paper introduces a new algorithm that uses the same space, but by utilizing space-efficient variants of Karatsuba multiplication methods it requires only O(n^{\log_2(3)}) Toffoli gates at the cost of a higher CNOT gate count: theoretically up to O(n^2) but in examples the CNOT gate count looks a lot better.

Controlled bidirectional quantum secure direct communication protocol based on Grover’s algorithm

A novel controlled bidirectional quantum secure direct communication (CBQSDC) protocol based on Grover’s algorithm is proposed in our paper, which is on the basis of investigating the properties of it. To avoid information leakage, the strategy of adding control-not gate is employed in our protocol. The proposed protocol uses Bell state as quantum resource to transmit information in a dual-quantum-channel. Through the proposed measures, we can not only prevent information leakage, but also improve the efficiency of transmission. As can be shown from the security analysis, the Grover’s algorithm has great application prospects in the research of CBQSDC.

Efficient Quantum Gates for Individual Nuclear Spin Qubits by Indirect Control.

Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hardware for implementing quantum information and computing protocols in scalable systems. Nevertheless, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times that are generally longer than the coherence time of the electron. Here, we demonstrate a scheme for circumventing this problem by indirect control: we apply a small number of short pulses only to the electron and let the full system undergo free evolution under the hyperfine coupling between the pulses. Using this scheme, we realize robust quantum gates in an electron-nuclear spin system, including a Hadamard gate on the nuclear spin and a controlled-NOT gate with the nuclear spin as the target qubit. The durations of these gates are shorter than the electron coherence time, and thus additional operations to extend the system coherence time are not needed. Our demonstration serves as a proof of concept for achieving efficient coherent control of electron-nuclear spin systems, such as nitrogen vacancy centers in diamond. Our scheme is still applicable when the nuclear spins are only weakly coupled to the electron.

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.

Quantum Teleportation of Ten-qubit State Based on the Cluster State Quantum Channel

We propose a novel and applicable teleportation protocol for certain class of ten-qubit state by utilizing an eight-qubit entangled state as a quantum channel. In this scheme, the sender applies a four-qubit C-NOT gate and an eight-qubit von-Neumann projective measurement. Based on this channel we explicitly demonstrate how the protocol works by recurring the original quantum state of ten-qubit state at the receiver terminal with considerable efficiency.

Quantum Neural Network with Improved Quantum Learning Algorithm

We present a quantum BP neural network with the universality of single-qubit rotation gate and two-qubit Controlled-NOT gate. Also, we show the process of the BP learning algorithm for the quantum model, and propose an improved BP learning algorithm based on quantum genetic algorithm. The type recognition simulation of the Matlab program shows the efficiencies of the quantum neural network and the improved learning algorithm.

High-fidelity geometric gate for silicon-based spin qubits

High-fidelity manipulation is the key for the physical realization of fault-tolerant quantum computation. Here, we present a protocol to realize universal nonadiabatic geometric gates for silicon-based spin qubits. We find that the advantage of geometric gates over dynamical gates depends crucially on the evolution loop for the construction of the geometric phase. Under appropriate evolution loops, both the geometric single-qubit gates and the CNOT gate can outperform their dynamical counterparts for both systematic and detuning noises. We also perform randomized benchmarking using noise amplitudes consistent with experiments in silicon. For the static noise model, the averaged fidelities of geometric gates are around 99.90\% or above, while for the time-dependent $1/f$-type noise, the fidelities are around 99.98\% when only the detuning noise is present. We also show that the improvement in fidelities of the geometric gates over dynamical ones typically increases with the exponent $\alpha$ of the $1/f$ noise, and the ratio can be as high as 4 when $\alpha\approx 3$. Our results suggest that geometric gates with judiciously chosen evolution loops can be a powerful way to realize high-fidelity quantum gates.

Logical performance of 9 qubit compass codes in ion traps with crosstalk errors

We simulate four quantum error correcting codes under error models inspired by realistic noise sources in near-term ion trap quantum computers: T2 dephasing, gate overrotation, and crosstalk. We use this data to find preferred codes for given error parameters along with logical error biases and a pseudothreshold which compares the physical and logical gate failure rates for a CNOT gate. Using these results we conclude that Bacon–Shor-13 is the most promising near term candidate as long as the impact of crosstalk can be mitigated through other means.

Efficient verification of quantum gates with local operations

Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary transformations that can be applied to both individual quantum gates and gate sets, including quantum circuits. This framework enables efficient verification of many important unitary transformations, including but not limited to all bipartite unitaries, Clifford unitaries, generalized controlled-$Z$ gates, generalized controlled-NOT gates, the controlled-SWAP gate, and permutation transformations. For all these unitaries, the sample complexity increases at most linearly with the system size and is often independent of the system size. Moreover, little overhead is incurred even if one can only prepare Pauli eigenstates and perform local measurements. Our approach is applicable in many scenarios in which randomized benchmarking (RB) does not apply and is thus instrumental to quantum computation and many other applications in quantum information processing.

Feynman gate based design of n-bit reversible inverter and its implementation on quantum-dot cellular automata

This paper proposed the design of n-bit controllable inverter using reversible logic and implementation based on QCA. The proposed inverter is designed by cascading Feynman gates. Conventional technology based implementation cost, i.e., quantum cost is compared with QCA based implementation cost. This comparative study shows the cost effective implementation in QCA. Besides n-bit controllable inverter, the design of 2-bit double controllable inverter is also proposed using Feynman gate and is implemented using QCA. The evaluation of those designs are performed using parameters like the number of QCA cells, majority voters, inverters, areas, clocking zones and circuit cost. The simulation output is evaluated based on theoretical values which established that all the circuits are functioning accurately. The proposed CNOT gate is superior in cell count and device area. The designs have less area-delay cost than conventional design. The stuck-at-fault analysis of those proposed inverters is performed and to achieve 100% fault coverage of proposed circuits, a set of test vector has been proposed. The proposed circuits can be used as a basic component for more powerful low energy dissipated nano-scale reversible adder/subtractor circuit.

Clifford 3-qubit states

Let us denote by [Formula: see text] the Clifford group (the circuit or operations generated by Hadamard, [Formula: see text] phase and the controlled-NOT gates) and by [Formula: see text] the set of qubit states that can be prepared by circuits from the Clifford group. In other words, a state [Formula: see text] if [Formula: see text] where [Formula: see text]. We will refer to states in [Formula: see text] as Clifford states. This paper studies the set of all three-qubit Clifford states. We prove that [Formula: see text] has 8640 states and if we define two states [Formula: see text] and [Formula: see text] in [Formula: see text] to be equivalent if [Formula: see text], with [Formula: see text] a local transformation in [Formula: see text], then the resulting quotient space has five orbits. More exactly, [Formula: see text] where the orbit [Formula: see text] is made up of states with entanglement entropy [Formula: see text]. For example, the first orbit [Formula: see text] contains the state [Formula: see text] and corresponds to the unentangled Clifford states. We say that [Formula: see text] is a real state if all its amplitudes [Formula: see text] are real numbers. We also say that an operator is real if all the entries of its matrix representation with respect to the computational basis are real numbers. In this paper, we also study the set of real Clifford 3 qubits and the way this set splits when we identify two real Clifford states [Formula: see text] and [Formula: see text] to be equivalent if [Formula: see text] where [Formula: see text] is a local real Clifford operator. An interesting aspect that follows from this study of Clifford states is the existence of two real Clifford states [Formula: see text] and [Formula: see text] that can be connected with a Clifford local transformation but they cannot be connected with a real Clifford local transformation. This is, the equation [Formula: see text] for [Formula: see text], does have a solution in the set of local transformations from [Formula: see text] but it does not have a solution among the local transformations from [Formula: see text] that are real. We go a little deeper and show that the equation [Formula: see text] does not have a solution for any local operation (not necessarily Clifford) whose entries are real numbers. Finally, we show how the CNOT gates act on the set of Clifford states and also in the set of real Clifford states.

Error correction schemes for fully correlated quantum channels protecting both quantum and classical information

We study efficient quantum error correction schemes for the fully correlated channel on an n-qubit system with error operators that assume the form \(\sigma _x^{\otimes n}\), \(\sigma _y^{\otimes n}\), \(\sigma _z^{\otimes n}\). Previous schemes are improved to facilitate implementation. In particular, when n is odd and equals \(2k+1\), we describe a quantum error correction scheme using one arbitrary qubit \(\sigma \) to protect the data state \(\rho \) in a 2k-qubit system. The encoding operation \(\sigma \otimes \rho \mapsto \Phi (\sigma \otimes \rho )\) only requires 3k CNOT gates (each with one control bit and one target bit). After the encoded state \(\Phi (\sigma \otimes \rho )\) goes through the channel, we can apply the inverse operation \(\Phi ^{-1}\) to produce \({\tilde{\sigma }} \otimes \rho \) so that a partial trace operation can recover \(\rho \). When n is even and equals \(2k+2\), we describe a hybrid quantum error correction scheme using any one of the two classical bits \(\sigma \in \{|ij{\rangle }{\langle }ij|: i, j \in \{0,1\}\}\) to protect a 2k-qubit state \(\rho \) and two classical bits. The encoding operation \(\sigma \otimes \rho \mapsto \Phi (\sigma \otimes \rho )\) can be done by \(3k+2\) CNOT gates and a single-qubit Hadamard gate. After the encoded state \(\Phi (\sigma \otimes \rho )\) goes through the channel, we can apply the inverse operation \(\Phi ^{-1}\) to produce \(\sigma \otimes \rho \) so that a perfect protection of the two classical bits \(\sigma \) and the 2k-qubit state is achieved. If one uses an arbitrary two-qubit state \(\sigma \), the same scheme will protect 2k-qubit states. The scheme was implemented using MATLAB, Mathematica, Python and the IBM’s quantum computing framework qiskit.

Implementing a multi-target-qubit controlled-not gate with logical qubits outside a decoherence-free subspace and its application in creating quantum entangled states

In general, implementing a multi-logical-qubit gate by manipulating quantum states in a decoherence-free subspace (DFS) becomes more complex and difficult when increasing the number of logical qubits. In this work, we propose an idea to realize quantum gates by manipulating quantum states outside their DFS but having the states of the logical qubits remain in their DFS before and after the gate operation. This proposal has the following features: (i) because the states are manipulated outside the DFS, the multiqubit gate implementation can be simplified when compared to realizing a multiqubit gate via manipulating quantum states within the DFS, which usually requires unitary operations over a large DFS, and (ii) because the states of the logical qubits return to the DFS after the gate operation, the errors caused by decoherence during the gate operation are not accumulated for a long-running calculation, and the states of the logical qubits are immune to decoherence when they are stored. Based on this proposal, we then present a way for realizing a multi-target-qubit controlled-not gate using logical qubits encoded in a decoherence-free subspace against collective dephasing. This gate is realized by employing qutrits (three-level quantum systems) placed in a cavity or coupled to a resonator. This proposal has the following advantages: (i) the states of the logical qubits return to their DFS after the gate operation; (ii) the gate can be implemented with only a few basic operations; (iii) the gate operation time is independent of the number of logical qubits; (iv) this gate can be deterministically implemented because no measurement is needed; (v) the intermediate higher-energy level for all qutrits is not occupied during the entire operation, thus decoherence from this level is greatly suppressed; (vi) this proposal is universal and can be applied to realize the proposed gate using natural atoms or artificial atoms (e.g., quantum dots, nitrogen-vacancy centers, and various superconducting qutrits, etc.) placed in a cavity or coupled to a resonator. As an application, we also show how to apply this gate to create a Greenberger-Horne-Zeilinger (GHZ) entangled state of multiple logical qubits encoded in DFS, and further investigate the experimental feasibility for creating the GHZ state of three logical qubits in the DFS, by using six superconducting transmon qutrits coupled to a one-dimensional coplanar waveguide resonator.

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.

A Quantum Control NOT Gate Based on Four-Wave Mixing in a Cavity for Photonic Qubits with Orbital Angular Momentum

Photonic qubits with angular momentum states interacting in a medium with Kerr-type nonlinearity in a cavity are considered. The use of a quantum logic gate (a controlled NOT gate) in the process of four-wave mixing on such qubits is considered. A theory of the functioning of this gate is constructed using the input/output formalism. The conditions for matching the parameters that must be realized for the effective operation of the gate are obtained.

Quantum double-direction cyclic controlled communication via a thirteen-qubit entangled state

Combining with the idea of quantum multi-cast, in this paper, a novel theoretical scheme is presented to fulfil four-party quantum double-direction cyclic controlled communication by using a thirteen-qubit entangled state as the quantum channel. In the proposed scheme, each observer can transmit two different single-qubit states to the other two observers under the supervision of the controller, respectively and synchronously, which realizes quantum cyclic controlled communication in clockwise and anticlockwise directions simultaneously. The quantum channel is structured by Hadamard (H) gates and controlled-NOT (CNOT) gates. Based on the quantum channel that we construct, we exhibit how the four-party double-direction cyclic controlled communication scheme works in a minute detail. Only specific two-qubit projective measurements, single-qubit von Neumann measurement and suitable unitary operations are needed in the proposed four-party scheme, which can be implemented in physics easily. Furthermore, the presented four-party double-direction controlled communication scheme can be generalized into the situation with $$n>3$$ observers through preparing a $$(4n+1)$$-qubit entangled channel. Analysis demonstrates that the success probability of the proposed scheme can reach $$100\mathrm{{\% }}$$. We also calculate the intrinsic efficiency and investigate the security of the proposed scheme.

Quantum algorithm for the collisionless Boltzmann equation

A novel quantum algorithm implementing a discrete-velocity method for the collisionless Boltzmann equation is introduced. The algorithm is designed for application on a quantum computer with a number of quantum bits feasible in the near future (e.g. 40−50). Following the quantum-circuit model of quantum computation, the present works shows the quantum-circuit implementations for the convection or transport part of the kinetic model, inspired by work on quantum algorithms for the Dirac equation. The present work represents the advection step as a quantum walk process, implemented as a series of multiple-input controlled-NOT gates. A detailed discussion on the background to this new method is presented, including how a rarefied-flow problem can be encoded as the quantum state of a qubit register in a quantum computer. A complexity analysis is presented showing potential benefits of the proposed algorithm. Based on the concept of quantum parallelism, the extension to multiple species is demonstrated to not increase the number of required gate operations. A key aspect of the developed algorithm is the implementation of boundary conditions. This work describes how the specular-reflection boundary conditions can be effectively imposed with a quantum circuit implementation. The developed method is then applied to the supersonic flow around a blunt body as well as the free-molecular flow escaping from a rectangular container. As validation, the flow along the stagnation streamline of the blunt-body flow is compared with exact solutions for a piston-driven flow, showing excellent agreement. Finally, directions for future work are discussed in this work.

Heralded universal quantum computing on electron spins in diamond nitrogen-vacancy centers assisted by low-Q microtoroidal resonators

Heralded universal quantum gates can largely decrease the quantum resource consumed in the integration of a multiqubit quantum circuit. Here, we present a scheme for heralded universal quantum computing, including the construction of the CNOT gate, Fredkin gate, and Toffoli gate on the electron spins in diamond nitrogen-vacancy (NV) centers assisted by low- Q microtoroidal resonators. These quantum gates can achieve unity fidelity, as the infidelity induced by the imperfect input–output process is transferred into photon loss. The clicks on different single-photon detectors can either herald the success of the quantum gates or instruct an immediate recycling procedure, even without reinitializing the NV centers. Besides the heralding, this scheme is also more realistic, observing that the non-monochromatic auxiliary photon and the inhomogeneous NV centers have no adverse impact on fidelity. The high fidelity and efficiency with experimental parameters show that the scheme is feasible with current technology.