Hadamard Gate Research Articles

Transformation of coherent state in Hadamard gate via multi-photon catalysis

Based on two-mode continuous Hadamard gate (TCHG) and multi-photon catalysis, this paper presents a scheme to generate non-classical quantum states via coherent state. When considering the m-photon input and m-photon detection in a-mode, the output state is obtained for the input coherent in b-mode. An interesting finding is that as the amplitude of the output coherent state increases, both the detection efficiency and the fidelity of the output quantum state gradually approach zero. Thus, only certain low-intensity quantum light field states can pass through Hadamard gate. In addition, the quantum statistical distribution and squeezing properties of the output quantum states are also analyzed in detail. Our results show that TCHG is a powerful tool for generating non-classical quantum states under multi-photon catalysis.

Preparation of the Hadamard and CNOT gates to realize the maximum entangled states

This paper studies the preparation of quantum gates that enable the realization of maximum entangled states, i.e., Bell states. A series of unitary time-evolution operators are derived to realize the Bell states through the Hadamard and CNOT gates. These operators are decomposed based on the Cartan decomposition method and steered by control laws designed based on the Lyapunov control theorem. The numerical simulations show that by adjusting proper control parameters in the designed Lyapunov-based control laws, the Hadamard and CNOT gates can be faster and better prepared through the decomposed operators, and more stable and accelerated Bell states can be achieved.

Realization of the Hadamard gate based on superposition of the composite solitons

In this article, we propose the implementation of quantum Hadamard gate through the superposition of composite solitons. Single qubit of the quantum state is defined by the components of the composite soliton which are the exact solution of the Manakov system. Through a rotation operation with an appropriate rotation angle, the Hadamard operation is realized on the single qubit, leading to the superposition state in which the measurement probability of individual qubits is half. Subsequently, repeating the similar Hadamard operation on the superposition state leads to the restoration of the original states of the qubit, as expected. Additionally, the measure of quantum fidelity of the qubit is expressed through the density operator matrix using Uhlmann-Jozsa fidelity. The versatility in the application of composite solitons to accomplish the quantum Hadamard operation through diverse physical systems is also demonstrated through suitable examples.

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.

Nematic bits and universal logic gates.

Liquid crystals (LCs) can host robust topological defect structures that essentially determine their optical and elastic properties. Although recent experimental progress enables precise control over nematic LC defects, their practical potential for information storage and processing has yet to be explored. Here, we introduce the concept of nematic bits (nbits) by exploiting a quaternionic mapping from LC defects to the Poincaré-Bloch sphere. Through theory and simulations, we demonstrate how single-nbit operations can be implemented using electric fields, to construct LC analogs of Pauli, Hadamard, and other elementary logic gates. Using nematoelastic interactions, we show how four-nbit configurations can realize universal classical NOR and NAND gates. Last, we demonstrate the implementation of generalized logical functions that take values on the Poincaré-Bloch sphere. These results open a route toward the implementation of classical digital and nonclassical continuous computation strategies in topological soft matter systems.

Quantum and braided ZX calculus* *Work done on sabbatical at Cambridge Quantum Computing.

We apply quantum group methods to quantum computing, starting with the notion of interacting Frobenius Hopf algebras for ZX calculus with noncommutative algebra and noncocommutative coalgebra. We introduce the notion of *-structures in ZX calculus at this algebraic level and construct examples based on the quantum group u q (sl 2) at a root of unity. We provide an abstract formulation of the Hadamard gate related to Hopf algebra self-duality. We then solve the problem of extending the notion of interacting Hopf algebras and ZX calculus to take place in a braided tensor category. In the ribbon case, the Hadamard gate coming from braided self-duality obeys a modular identity. We give the example of b q (sl 2), the self-dual braided version of u q (sl 2).

一种新颖的基于类GHZ态的两方半量子密钥分配协议

In this paper, we propose a novel two-party semiquantum key distribution (SQKD) protocol by only employing one kind of GHZ-like state. The proposed SQKD protocol can create a private key shared between one quantum party with unlimited quantum abilities and one classical party with limited quantum abilities without the existence of a third party. The proposed SQKD protocol doesn't need the Hadamard gate or quantum entanglement swapping. Detailed security analysis turns out that the proposed SQKD protocol can resist various famous attacks from an outside eavesdropper, such as the Trojan horse attacks, the entangle-measure attack, the double CNOT attacks, the measure-resend attack and the intercept-resend attack.

Silicon photonics 2 × 2 trench coupler design and foundry fabrication.

A 2×2 photonic coupler is realized at the intersection of two 480nm×220nm silicon on insulator waveguides. The designed 2×2 coupler is simulated in both High Frequency Simulator System (HFSS) and Lumerical and shows an equal split of an input signal into transmitted and reflected signals for a 45 deg, ∼100nmSiO2 filled trench. The principle of operation of the coupler is frustrated total internal reflection. Thus, this behavior is reasonably flat across wavelength, which is confirmed by Lumerical simulations and by experiment. Also, it has been shown that this coupler has a flat behavior across trench thickness for the chosen geometry and material system, which makes it insensitive to fabrication variation and resolution. We are interested to make this coupler a part of silicon photonic foundry process development kits. Therefore, fabrication is done at the AIM Photonics Foundry to study the performance in the context of the foundry's design rules and process flow of the foundry. Good agreement between theory and experiment is reported herein. A 2×2 trench coupler is, when operated in the single photon or quantum regime, an integrated photonic realization of a Hadamard gate.

Hybrid Hadamard and controlled-Hadamard based quantum random number generators in IBM QX

Designing novel circuits and models for generating truly random numbers is of great importance. Recent attention has been focused on the idea of using real quantum computers to generate random numbers. In order to generate purely random bits and numbers, one method relies on the natural superposition of quantum gates. Here, we design a Quantum Random Number Generator (QRNG) exploiting combinations of Hadamard and controlled-Hadamard gates in IBM Quantum Experience (QX). In order to verify that the generated bit sequences were truly random, the proposed circuit’s outputs were subjected to the National Institute of Standards and Technology (NIST) test suite. In comparison to previous works, we found that not only had the total number of passed tests increased, but the P-values had also improved in many cases. For example, in the simulation style of the IBM QX, the number of passed tests is 14 out of 15 standard NIST tests. For the experimental mood of the IBM 16Q Melbourne, the number of passed tests is six without using any extractions. Furthermore, one more test is passed by adding Barrier operations to the circuits, and the P-values have increased. As a result, we found that the proposed method had more passed tests than previous works. The average of P-values for the six passed tests in former research for the mood of using a combination of extractors is about However, the best result we can get with our circuits is around 0.60 (the average of P-values for 14 passed tests), which is an improvement of 0.17 compared to former works . Because of this, our circuits are getting ever closer to being a true QRNG.

Computationally Efficient Quantum Expectation with Extended Bell Measurements

Evaluating an expectation value of an arbitrary observable A∈C2n×2n through naïve Pauli measurements requires a large number of terms to be evaluated. We approach this issue using a method based on Bell measurement, which we refer to as the extended Bell measurement method. This analytical method quickly assembles the 4n matrix elements into at most 2n+1 groups for simultaneous measurements in O(nd) time, where d is the number of non-zero elements of A. The number of groups is particularly small when A is a band matrix. When the bandwidth of A is k=O(nc), the number of groups for simultaneous measurement reduces to O(nc+1). In addition, when non-zero elements densely fill the band, the variance is O((nc+1/2n)tr(A2)), which is small compared with the variances of existing methods. The proposed method requires a few additional gates for each measurement, namely one Hadamard gate, one phase gate and at most n−1 CNOT gates. Experimental results on an IBM-Q system show the computational efficiency and scalability of the proposed scheme, compared with existing state-of-the-art approaches. Code is available at https://github.com/ToyotaCRDL/extended-bell-measurements.

Universal topological quantum computation with strongly correlated Majorana edge modes

Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In reference Hu and Kane (2018 Phys. Rev. Lett. 120 066801), it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibonacci anyon τ and a thermal operator anyon ɛ in the tricritical Ising model. The deconfinement of τ and ɛ via the interaction between the fermion modes yields the anyon collisions and gives the braiding of either τ or ɛ. With these braidings, the complete members of a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for one-qubit as well as controlled-NOT (CNOT) gate for two-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit where the CNOT gate turns out to be a probabilistic gate and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor’s integer factorization algorithm.

Optimized realization of Quantum Fourier Transform for domestic DCU accelerator

Abstract Quantum Fourier Transform (QFT) is a key part of quantum algorithms such as Shor algorithm, Grover algorithm, and quantum phase estimation algorithm. The “Songshan” supercomputer system adopts the heterogeneous architecture of domestic CPU+DCU. The simulation implementation of the quantum Fourier transform on the “Songshan” supercomputer can promote the research and optimization of related quantum algorithms. Based on the HIP heterogeneous programming model, this paper first maps the phase shift transformation R gate operation of the QFT transformation to the DCU accelerator, and initially constructs the heterogeneous implementation of QFT on the “Songshan” supercomputer; then, the Hadamard gate transformation operation originally implemented on the host side was implemented on the DCU, which greatly reduces the communication overhead caused by the quantum information data transmission between the CPU and the DCU device; finally, the quantum logic gate is analyzed, and based on the operation of the phase shift transformation R gate on the probability amplitude information in the simulation algorithm, an optimization scheme to improve the activity of the DCU thread is proposed. During the experimental verification process, the realized 28-qubit quantum Fourier transform optimization has achieved 13.440 speedup compared with the serially realized QFT simulation on the CPU. The basic quantum gate optimization method based on DCU acceleration equipment in this paper can provide a reference for the efficient simulation of other quantum algorithms on domestic heterogeneous platforms.

Laser-Controlled Implementation of Controlled-NOT, Hadamard, SWAP, and Pauli Gates as Well as Generation of Bell States in a 3d-4f Molecular Magnet.

Using high-level ab initio many-body theory, we theoretically propose that the Dy and the Ni atoms in the [Dy2Ni2(L)4(NO3)2(DMF)2] real molecular magnet as well as in its core, that is, the [Dy2Ni2O6] system, act as two-level qubit systems. Despite their spatial proximity we can individually control each qubit in this highly correlated real magnetic system through specially designed laser-pulse combinations. This allows us to prepare any desired two-qubit state and to build several classical and quantum logic gates, such as the two-qubit (binary) CNOT gate with three distinct laser pulses. Other quantum logic gates include the single-qubit (unary) quantum X, Y, and Z Pauli gates; the Hadamard gate (which necessitates the coherent quantum superposition of two many-body electronic states); and the SWAP gate (which plays an important role in Shor's algorithm for integer factorization). Finally, by sequentially using the achieved CNOT and Hadamard gates we are able to obtain the maximally entangled Bell states, for example, ()(|00⟩ + |11⟩).

Simulation of Two‐Qubit Gates with a Superconducting Qudit

In article number 2100500, Xinsheng Tan, Yang Yu, and co-workers use a four-level superconducting quantum loop to simulate a two-qubit quantum system. By mapping the energy levels of the two-qubit system to a non-composite system, simulations of several quantum gate operations, including the CNOT gate and the Hadamard gate, are completed in a convenient way. Furthermore, the authors generate entangled states to verify the log2 entropic inequality. The results indicate that the superconducting qudit is indeed a huge quantum platform for quantum information.

An Improved Quantum Private Set Intersection Protocol Based on Hadamard Gates

An Improved Quantum Private Set Intersection Protocol Based on Hadamard Gates

Quantum Identity-Based Encryption from the Learning with Errors Problem

To prevent eavesdropping and tampering, network security protocols take advantage of asymmetric ciphers to establish session-specific shared keys with which further communication is encrypted using symmetric ciphers. Commonly used asymmetric algorithms include public key encryption, key exchange, and identity-based encryption (IBE). However, network security protocols based on classic identity-based encryption schemes do not have perfect forward secrecy. To solve this problem, we construct the first quantum IBE (QIBE) scheme based on the learning with errors (LWE) problem, which is also the first cryptographic scheme that applies the LWE problem to quantum encryption. We prove that our scheme is fully secure under the random oracle model and highlight the following advantages: (1) Network security protocols with our QIBE scheme provide perfect forward secrecy. The ciphertext is transmitted in the form of a quantum state unknown to the adversary and cannot be copied and stored. Thus, in network security protocols based on QIBE construction, the adversary does not have any previous quantum ciphertext to decrypt for obtaining the previous session key, even if the private identity key is threatened. (2) Classic key generation centre (KGC) systems can still be used in the QIBE scheme to generate and distribute private identity keys, reducing the cost when implementing this scheme. The classic KGC systems can be used because the master public and secret keys of our scheme are both in the form of classic bits. Finally, we present quantum circuits to implement this QIBE scheme and analyse its required quantum resources for given numbers of qubits, Hadamard gates, phase gates, T gates, and CNOT (controlled-NOT) gates. One of our main findings is that the quantum resources required by our scheme increase linearly with the number of plaintext bits to be encrypted.

Iterated nth order nonlinear quantum dynamics with mixed initial states

Nonlinear quantum transformations play an important role in quantum state distillation, aiding quantum communication schemes. The simplest of these involve quadratic rational maps for qubits, higher order versions have not been explored in detail. We consider such iterated nonlinear protocols for qubits, involving a generalized CNOT, a measurement, and a single-qubit Hadamard gate processing n inputs in identical quantum states. To characterize the global properties of these protocols, we determine the fixed points and relevant fixed cycles. We show that a repelling mixed fixed point exists for all orders, marking a phase transition related to the disappearance of the fractalness of borders of different basins of attraction.

Quantum true random number generation on IBM’s cloud platform

Random numbers are the lifeline of any cryptographic operation in modern computing. Quantum True Random Number Generator (QTRNG) can yield real random data to replace random-looking periodic sequences. Here, we present the fastest QTRNG on factual Quantum Computational Devices (QCD) locally on our device to save time. To construct a random number generator, the IBM Q Experience called Qiskit is used. The ease of our source Hadamard gate pooled with its verifiably sole randomness is imperative for attaining quantum random number generators at no cost. The inner matrix product of the square of the Hadamard gate is proved to be identified in the quantum lab. Applying the H gate twice on the quantum register cancelled out the H gate pair. It acted as a single Hadamard gate that was practically visualised using the IMB Q experience. The 24-qubit random number is experimented with and investigated in this work. The min-entropy of such generated random numbers is 0.0007244 with the worst-case entropy value of 0.999507. Besides, subsequent verification of genuine randomness was confirmed by steering restart experimentation, & the statistical properties of TRNG were evaluated over autocorrelation study, National Institute of Standards and Technology (NIST) SP 800-90B & 800-22 tests.

Universal quantum computation via quantum controlled classical operations

A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results in universal quantum computing. Motivated by the latter, we pose the following question: can one perform universal quantum computation by supplementing a set of classical gates with a quantum control, and a set of quantum gates operating solely on the latter? In this work we provide an affirmative answer to this question by considering a computational model that consists of 2n target bits together with a set of classical gates controlled by log (2n + 1) ancillary qubits. We show that this model is equivalent to a quantum computer operating on n qubits. Furthermore, we show that even a primitive computer that is capable of implementing only SWAP gates, can be lifted to universal quantum computing, if aided with an appropriate quantum control of logarithmic size. Our results thus exemplify the information processing power brought forth by the quantum control system.

Universal set of quantum gates for the flip-flop qubit in the presence of 1/f noise

Impurities hosted in semiconducting solid matrices represent an extensively studied platform for quantum computing applications. In this scenario, the so-called flip-flop qubit emerges as a convenient choice for scalable implementations in silicon. Flip-flop qubits are realized implanting phosphorous donor in isotopically purified silicon, and encoding the logical states in the donor nuclear spin and in its bound electron. Electrically modulating the hyperfine interaction by applying a vertical electric field causes an Electron Dipole Spin Resonance (EDSR) transition between the states with antiparallel spins {|downarrow Uparrow rangle ,|uparrow Downarrow rangle }, that are chosen as the logical states. When two qubits are considered, the dipole-dipole interaction is exploited to establish long-range coupling between them. A universal set of quantum gates for flip-flop qubits is here proposed and the effect of a realistic 1/f noise on the gate fidelity is investigated for the single qubit R_{z}(-frac{pi }{2}) and Hadamard gate and for the two-qubit sqrt{mathit{iSWAP}} gate.