In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.
In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.
In this research, a quantum system consists of three qubits is considered; it has eight states (|000˃, |001˃, |010˃, |011˃, |100˃, |101˃, |110˃ and |111˃).Each of these states is passed through a quantum circuit made of a sequence of quantum gates.The circuit applies X-gate on the first qubit from the left, then using CNOT-gate on the first and second qubits and using the Hadamard-gate on the first qubit.Finally, Hadamard-gate is applied on the third qubit.When the state |000˃ is passed as input through the proposed quantum circuit then the output includes four entanglement states; for the other input states the output will be another non-repeatable entanglement states.So, for using all states in quantum circuit the result will be eight equations each one consists of four entanglement states; which called ML-Quadripartite.
Estimating the overlap between two states is an important task with several applications in quantum information. However, the typical swap test circuit can only measure a sole pair of quantum states at a time. In this study we designed a recursive quantum circuit to measure overlaps of multiple quantum states ∣ϕ1...ϕn⟩ concurrently with O(nlogn) controlled-swap (CSWAP) gates and O(logn) ancillary qubits. This circuit enables us to get all pairwise overlaps among input quantum states ∣⟨ϕi∣ϕj⟩∣2. Compared with existing schemes for measuring the overlap of multiple quantum states, our scheme provides higher precision and less consumption of ancillary qubits. In addition, we performed simulation experiments on IBM quantum cloud platform to verify the superiority of the scheme.
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that preserve them. Such states are obtained by stabilizer circuits (consisting of CNOT, Hadamard and Phase only) and can be represented compactly on conventional computers using Omega(n^2) bits, where n is the number of qubits. Although techniques for the efficient simulation of stabilizer circuits have been studied extensively, techniques for efficient manipulation of stabilizer states are not currently available. To this end, we design new algorithms for: (i) obtaining canonical generators for stabilizer states, (ii) obtaining canonical stabilizer circuits, and (iii) computing the inner product between stabilizer states. Our inner-product algorithm takes O(n^3) time in general, but observes quadratic behavior for many practical instances relevant to QECC (e.g., GHZ states). We prove that each n-qubit stabilizer state has exactly 4(2^n - 1) nearest-neighbor stabilizer states, and verify this claim experimentally using our algorithms. We design techniques for representing arbitrary quantum states using stabilizer frames and generalize our algorithms to compute the inner product between two such frames.
A quantum gate is the quantum analog of the classical logic gate of digital computers. It is a basic structural unit of a quantum circuit which operates on a small number of qubits to deliver a predefined output. A quantum circuit is a graphical representation of the sequence of the quantum gates used and the measurements performed in a quantum computation. Various quantum logic gates, namely, the Hadamard, T phase, NOT, Pauli-X, controlled NOT (CNOT), controlled-Z, SWAP and controlled phase gates as well as higher-level Toffoli and Fredkin gates are described. Conventions of reading quantum circuit diagrams are explained. Operation of a quantum full adder consisting of registers and gates is discussed, elaborating the role of the NOT gate, the sum calculation with CNOTgates and the carry C-out calculation with Toffoli gates. A primary tool used for performing arithmetic operations on a quantum computer is the quantum Fourier transform (QFT). The QFT adder and multiplier circuits are presented.
Quantum gates are building blocks of quantum circuits and they are used to carry out corresponding operations on quantum bits or qubits. The distinguishing feature of multi-qubit quantum control-gates is that they act on target qubits according to the state of control qubit(s). In this sense, there exist 2- and 3-qubit quantum gates such as Controlled-NOT, Toffoli (Controlled-Controlled-NOT), Controlled-Hadamard, Controlled-Swap and so on. In order to make complex quantum circuits easier and control more qubits, it is necessary to work out mathematical models of new control gates acting on more than three qubits depending on the state of control qubit. Therefore, in this work, mathematical model of multi-qubit universal control gate is worked out and some control gates are formulated in accordance with the proposed model, moreover the tests of these novel control gates are carried out using online open resource or virtual laboratory that is called “Quirk”. Existing 2- and 3-qubit control gates can also be derived using this model. Matrix representations of Controlled-NOT-NOT, Controlled-Hadamard-Hadamard, Controlled-NOT-NOT-Hadamard, Controlled-Hadamard-Swap and Controlled-Hadamard-SWAP-NOT gates are derived using the proposed mathematical model. These quantum gates are unitary and reversible gates. Using the proposed model and novel quantum gates will help to reduce complexity of quantum circuits and develop new cryptographic algorithms.
We studied the outputs that a quantum circuit consisting of four qubits can produce by using quantum gates, which operate on the states of the qubit as a state vector that can be expressed through unitary matrices. We made the change by exploiting the superposition property of the Hadamard gate, and with its presence in the quantum circuit, we used CNOT gates, which produced entangled states . The study explained the output of a quantum circuit consisting of four qubits and gave a methodology for changing this output by installing one input type for the quantum circuit (we used the input ). It showed the importance of measurement in the quantum circuit and its effect on the and the . Starting from, produce all 16 states of the four qubits, which can be expressed as the computational basis state of a vector state using only an x-gate.