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A scheme is investigated to realize non-adiabatic geometric quantum computation by directly varying the external parameters of quantum circuit. More intriguingly, we illustrate in detail how to control the parameters of the system to remove the dynamical phase. The scheme depends completely on manipulating both the circuit parameters and the magnetic field parameters, which does not require any rotation operation as done in the conventional geometric gates or the unconventional geometric gates.

Quantum steganography is a technology which can hide information effectively for achieving copyright protection. In this paper, a quantum steganography scheme using quantum wavelet transform and the novel enhanced quantum representation for quantum image is proposed, and this scheme can embed the secret text of size $2^{n-2}\times 2^{n-2}$ into a $2^n\times 2^n$ gray-scale carrier image. In the scrambling operation, the text is scrambled by the scrambling circuit including bit-reverse, quantum equal and CNOT gate to improve its security. Before embedding, the carrier image is first transformed by 1-level quantum Haar wavelet transform, and then its low-frequency part is divided into blocks. The simulation results suggest that the proposed scheme has good performance in visual quality and robustness. Finally, through the analysis of circuit complexity, the scheme has low complexity O(n).

The majority of work in reversible logic circuits has been limited to combinational logic. Researchers are now beginning to suggest designs for sequential circuits. In this paper we propose a new method to design and optimize feedback reversible logic circuits and a specific group of quantum logic circuits based on the reversible state transition table and genetic algorithms (GA). To show the efficiency of the proposed method, some reversible sequential elements such as D and T flip-flops (FFs), with and without clock and reset, and edge triggered FFs are designed. We have also extended our method to multiple loop feedback circuits. The proposed circuits are highly optimized using a GA synthesis tool that allows don't care values. Some of the designs in this paper are presented in other papers; however, the comparisons show that the quantum cost and number of garbage inputs/outputs are reduced efficiently by our method.

A quantum circuit is generalized to a nonunitary one whose constituents are nonunitary gates operated by quantum measurement. It is shown that a specific type of one-qubit nonunitary gates, the controlled-NOT gate, and all one-qubit unitary gates constitute a universal set of gates for the nonunitary quantum circuit, without the necessity of introducing ancilla qubits. A reversing measurement scheme is used to improve the probability of successful nonunitary gate operation. A quantum NAND gate and Abrams–Lloyd's nonlinear gate are analyzed as examples. Our nonunitary circuit can be used to reduce the qubit overhead needed to ensure fault-tolerant quantum computation.

General n-qubit controlled unitary gates are frequently used in quantum information processing tasks. Barenco, Bennett, Cleve, Di Vincenzo, Margolus and Shor [Phys. Rev. A52 (1995) 3457] have given the general construction methods, and explicit results for up-to-four-qubits controlled unitary gates. We extended their calculation and gave two analytic expressions for the construction of general n-qubit controlled unitary gates in terms of one-qubit and two-qubit CNOT gates. There are two expressions – one is exponential in the qubit number which is efficient for up to ten qubits, and the other is polynomial in the qubit number, which is efficient for more than ten qubits.

Utilizing W state, which is much more robust than GHZ state, we propose a protocol for three-party controlled quantum secure direct communication (QSDC). The feature of this protocol is that the sender encodes the secret message directly on a sequence of particle states and faithfully transmits them to an arbitrary one of two receivers without revealing any information to a potential eavesdropper. On the other hand, we construct the efficient quantum circuit to implement the QSDC by means of primitive operations in quantum computation.

We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate the relation between the generalized controlled phase construction of a quantum gate entangler and graph state for two-qubit and three-qubit states.

An efficient and economical scheme is proposed for the perfect quantum teleportation of n-qubit non-maximally entangled state of generalized Bell-type. A Bell state is used as the quantum channel in the proposed scheme. It is also shown that the controlled teleportation of this n-qubit state can be achieved by using a GHZ state or a GHZ-like state as quantum channel. The proposed schemes are economical because for the perfect and controlled teleportation of n-qubit non-maximally entangled state of generalized Bell-type, we only need a Bell state and a tripartite entangled state respectively. It is also established that there exists a family of 12 orthogonal tripartite GHZ-like states which can be used as quantum channel for controlled teleportation. The proposed protocols are critically compared with the existing protocols.

Due to the great difficulty in scalability, quantum computers are limited in the number of qubits during the early stages of the quantum computing regime. In addition to the required qubits for storing the corresponding eigenvector, suppose we have additional k qubits available. Given such a constraint k, we propose an approach for the phase estimation for an eigenphase of exactly n-bit precision. This approach adopts the standard recursive circuit for quantum Fourier transform (QFT) in [R. Cleve and J. Watrous, Fast parallel circuits for quantum fourier transform, Proc. 41st Annual Symp. on Foundations of Computer Science (2000), pp. 526–536.] and adopts classical bits to implement such a task. Our algorithm has the complexity of O(n log k), instead of O(n²) in the conventional QFT, in terms of the total invocation of rotation gates. We also design a scheme to implement the factorization algorithm by using k available qubits via either the continued fractions approach or the simultaneous Diophantine approximation.

In this paper, we provide a genetic programming (GP) based method for generating quantum circuits preparing maximally multipartite entangled states (MMES). The presented method is faster that known realizations thanks to the applied fitness function and several modifications to the GP schema. Moreover, we enrich the described method by the unique possibility to define an arbitrary structure of a system. We use the developed method to find new quantum circuits, which are simpler from known results. We also analyze the efficiency of generating entanglement in the spin chain system and in the system of complete connections.

Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in von Neumann entropy to quantify the amount of the bipartite entanglement. In this paper, we map the Schmidt basis and the associated coefficients to quantum circuits to generate random quantum states. We also show that it is possible to adjust the entanglement between subsystems by changing the quantum gates corresponding to the Schmidt coefficients. In this manner, random quantum states with predefined bipartite entanglement amounts can be generated using random Schmidt basis. This provides a technique for generating equivalent quantum states for given weighted graph states, which are very useful in the study of entanglement, quantum computing, and quantum error correction.

In this paper, we propose a scheme for deterministic joint remote state preparation (JRSP). Two spatially separated senders intend to help a receiver remotely prepare an arbitrary single-qubit state. Four-particle partially entangled state is constructed to serve as the quantum channel. By determining right unitary operations for the senders and appropriate recovery operations for the receiver, the target state can be reestablished with unit success probability, irrespective of the channel parameter.

Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system, e.g. a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels, and particularly the channel decomposition problem in terms of convex sum of extreme channels. We provide various quantum circuit representations of extreme and generalized extreme channels, which can be employed in an optimization to approximately decompose an arbitrary channel. Numerical simulations of low-dimensional channels are performed to demonstrate our channel decomposition scheme.

In this paper, a quantum color image watermarking scheme is proposed through twice-scrambling of Arnold transformations and steganography of least significant bit (LSB). Both carrier image and watermark images are represented by the novel quantum representation of color digital images model (NCQI). The image sizes for carrier and watermark are assumed to be $2^n\times 2^n$ and $2^{n-1}\times 2^{n-1}$, respectively. At first, the watermark is scrambled into a disordered form through image preprocessing technique of exchanging the image pixel position and altering the color information based on Arnold transforms, simultaneously. Then, the scrambled watermark with $2^{n-1}\times 2^{n-1}$ image size and 24-qubit grayscale is further expanded to an image with size $2^n\times 2^n$ and 6-qubit grayscale using the nearest-neighbor interpolation method. Finally, the scrambled and expanded watermark is embedded into the carrier by steganography of LSB scheme, and a key image with $2^n\times 2^n$ size and 3-qubit information is generated at the meantime, which only can use the key image to retrieve the original watermark. The extraction of watermark is the reverse process of embedding, which is achieved by applying a sequence of operations in the reverse order. Simulation-based experimental results involving different carrier and watermark images (i.e. conventional or non-quantum) are simulated based on the classical computer’s MATLAB 2014b software, which illustrates that the present method has a good performance in terms of three items: visual quality, robustness and steganography capacity.

Recently, a novel Multi-layer Quantum Secret Sharing (MQSS) scheme based on GHZ state and generalized Bell measurement is presented in [X.-J. Wang, L.-X. An, X.-T. Yu and Z.-C. Zhang, Phys. Lett. A381(38) (2017) 3282.]. The novelty of the MQSS scheme is that a quantum secret can be shared by up to $3^n$ parties at the $n$th layer. In this paper, we show that the MQSS scheme can be significantly simplified and improved. The improved MQSS scheme is much easier to implement in practice and more efficient. In our improved scheme, the parties of the $n$th layer need not put their particles together to carry out the generalized Bell measurement, which is needed to share the secret to the next layer in the original scheme. Instead, each party only has to carry out local operations.

Based on the novel enhanced quantum representation for quantum image (NEQR), a new blind quantum steganography scheme is proposed. In this scheme, an improved quantum representation of text utilizing American Standard Code for Information Interchange (ASCII) is provided that uses two qubit sequences to store the same quantum text message. The general embedding process of the scheme is as follows: First, the cover image of size $2^n\times 2^n$ will be divided into eight blocks of size $2^{n-2}\times 2^{n-1}$ and the secret quantum text of size $2^{n-2}\times 2^{n-1}$ is scrambled by Gray code transform method. Then, the disorder quantum text is embedded into the eight blocks of cover image employing the Gray code as a judgment condition. Meanwhile, the corresponding quantum circuits are drawn. Through the analysis of all quantum circuits, it can be concluded that the scheme has a lower complexity that is $\mathrm{\text{O}}(n)$. And the performance of the proposed scheme is analyzed in terms of simulation results of three items: visual quality, capacity and robustness.

The efficient quantum circuits of arithmetic operations are important to perform quantum algorithms. To implement efficient matrix operations, we first modify the generalized model of the novel enhanced quantum representation of digital images (GNEQR) to store unsigned and signed integer matrices. Next, we design the circuits of the circuits of quantum addition, quantum modulo addition, quantum subtraction, and quantum modulo subtraction, these operations all keeping two operands unchanged. Then, we propose the circuits of quantum matrix addition, quantum matrix modulo addition, quantum matrix subtraction, and quantum matrix modulo subtraction for the first time. Furthermore, we present a simulation method to verify the correctness of the proposed arithmetic operations of matrix. The results of simulation experiment show that the propose arithmetic operations of matrix are efficient and correct.

We investigate the counterparts of random walks in universal quantum computing and their implementation using standard quantum circuits. Quantum walks have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1D graph, namely a circle, and show how to implement a discrete-time quantum walk in quantum circuits built with universal CNOT and single qubit gates. We review elementary quantum gates and circuit decomposition techniques and propose a generalized version of all CNOT-based circuits of the quantum walk. We simulated these circuits on five different qubits IBM-Q quantum devices. This quantum computer has nonperfect gates based on superconducting qubits, and, therefore, we analyzed the impact of the CNOT errors and CNOT-depth on the fidelity of the circuit.

A common assumption in an open quantum system is that the noise induced by the environment, due to the interaction between a quantum system and its environment, is responsible for the disappearance of quantum properties. Interestingly, Barreiro et al. [Nature470 (2011) 486] show, experimentally, using an open-system quantum ion traps simulator, an environment state can be engineered and controlled to pump an arbitrary quantum system toward a maximally entangled state and thus can be considered a resource for quantum information processing. Here, we demonstrate this idea to pump an arbitrary maximally mixed state into Greenberger–Horne–Zeilinger (GHZ) state by simulating our quantum circuit using one of the IBM Q processors. Barreiro et al. [Nature470 (2011) 486] offer the circuits for the execution of the GHZ pumping. Nevertheless, those are collected gates that are suitable to the trapped-ions platform, so their circuits implementation on the IBM Q devices would result in large depth circuits and thus requires many gates. Consequently, we suggest a different circuit structure that follows a similar goal, but has been considered the features of the IBM Q platform. Moreover, we run the simulation of our circuit using the QASM simulator and free-web-based interface, IBM Quantum Experience, with and without error mitigation, to investigate the effect of the noise on the preparation of the initial mixed states of the qubits in addition to the population of the target state of the system.

In the NISQ era, quantum computers have insufficient qubits to support quantum error correction, which can only perform shallow quantum algorithms under noisy conditions. Aiming to improve the fidelity of quantum circuits, it is necessary to reduce the circuit depth as much as possible to mitigate the coherent noise. To address the issue, we propose PaF, a Pattern matching-based quantum circuit rewriting algorithm Framework to optimize quantum circuits. The algorithm framework finds all sub-circuits satisfied in the input quantum circuit according to the given external pattern description, then replaces them with better circuit implementations. To extend the capabilities of PaF, a general pattern description format is proposed to make rewriting patterns in existing work become machine-readable. In order to evaluate the effectiveness of PaF, we employ the BIGD benchmarks in QUEKO benchmark suite to test the performance and the result shows that PaF provides a maximal speedup of $8\times$ by using few patterns.