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.
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.
Quantum information processing and information exchange in the world of quantum computing demands novel methods, strategies and techniques based on quantum gates. Due to the facts that quantum computing is becoming more powerful and there are impactful scientific developments that would make quantum computers practical, post-quantum cryptography would require novel methods. In this sense, the paper presents a new approach or tool to be used in ciphering and deciphering information using multi-qubit control gates. This technique would be beneficial in terms of transforming information to another form and rebuilding it through asymmetric methods by the help of previously developed multi-qubit quantum gates. The underlying methodology of the technique is based on unitary transformations which may be divided into two parts: ciphering and deciphering parts. Moreover, controlling target qubits in accordance with the control qubit was also benefited within the methodology. In this sense, multi-qubit control gates, derived from mathematical model of universal control gates, play important role. Post-quantum cryptographic methods and strategies would be improved through this kind of methodologies.
In this paper, we study the optimal simulation of three-qubit unitary by using two-qubit gates. First, we give a lower bound on the two-qubit gates cost of simulating a multi-qubit gate. Secondly, we completely characterize the two-qubit gate cost of simulating a three-qubit controlled controlled gate by generalizing our result on the cost of Toffoli gate. The function of controlled controlled gate is simply a three-qubit controlled unitary gate and can be intuitively explained as follows: the gate will output the states of the two control qubit directly, and apply the given one-qubit unitary u on the target qubit only if both the states of the control are ∣1⟩. Previously, it is only known that five two-qubit gates is sufficient for implementing such a gate [Sleator and Weinfurter, Phys. Rev. Lett. 74, 4087 (1995)]. Our result shows that if the determinant of u is 1, four two-qubit gates is achievable optimal. Otherwise, five is optimal. Thirdly, we show that five two-qubit gates are necessary and sufficient for implementing the Fredkin gate(the controlled swap gate), which settles the open problem introduced in [Smolin and DiVincenzo, Phys. Rev. A, 53, 2855 (1996)]. The Fredkin gate is one of the most important quantum logic gates because it is universal alone for classical reversible computation, and thus with little help, universal for quantum computation. Before our work, a five two-qubit gates decomposition of the Fredkin gate was already known, and numerical evidence of showing five is optimal is found.
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 computers are very efficient in terms of speed and security. Decoherence and architectural complexity restrict the control of sensitive quantum information as the number of qubits in a quantum computer increases. Therefore, it is more convenient to make a device with multiple quantum processors with small number of qubits instead of making a device with a large number of qubits quantum processors. The implementation of controlled unitary gates is a problem in such nonlocal systems. The methods in the literature for this problem use entangled qubit pairs, classical communication channels and classical bits. The existing methods perform some unitary operations on the target state for reconstruction after sending information through classical communication channels and applying quantum measurements on control states. In this study, a generalized method for nonlocal implementation of multi-qubit controlled unitary quantum gates with quantum channel is proposed. The proposed method can implement any controlled gate on the control and target qubits that are far from each other in terms of location. The method does not require classical channels and classical bits, any extra unitary operation for reconstruction. The proposed method is both more secure and uses less resources for operations than the other hybrid methods in the literature. Comparisons with existing studies are given in terms of required entangled qubit pairs, classical channels and bits, extra unitary operations for reconstruction the target state, and the advantages of the proposed method are revealed.
Abstract 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.
One of the greatest challenges in modern science is the realisation of quantum computers which, as their scale increases, will allow enhanced performance of tasks across many areas of quantum information processing. Quantum logic gates play a vital role in realising these applications by carrying out the elementary operations on the qubits; a key aim is minimising the resources needed to build these gates into useful circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, e.g., single- and two-qubit gates, difficulties in scaling quantum systems to encode and manipulate multiple qubits has hindered demonstrations of more complex operations. This is exemplified by the classical Fredkin (or controlled-SWAP) gate [1] for which, despite many theoretical proposals [2,3] relying on concatenating multiple two-qubit gates, a quantum analogue has yet to be realised. Here, by directly adding control to a two-qubit SWAP unitary [4], we use photonic qubit logic to report the first experimental demonstration of a quantum Fredkin gate [5]. Our scheme uses linear optics and improves on the overall probability of success by an order of magnitude over previous proposals [2,3]. This optical approach allows us to add control an arbitrary black-box unitary which is otherwise forbidden in the standard circuit model [6]. Additionally, the action of our gate exhibits quantum coherence allowing the generation of the highest fidelity three-photon GHZ states to date. The quantum Fredkin gate has many applications in quantum computing, quantum measurements [7] and cryptography [8,9]. Using our scheme, we apply the Fredkin gate to the task of direct measurements of the purity and state overlap of a quantum system [7] without recourse to quantum state tomography.