Chin-Yung Lu

An XQDD-Based Verification Method for Quantum Circuits

Synthesis of quantum circuits is essential for building quantum computers. It is important to verify that the circuits designed perform the correct functions. In this paper, we propose an algorithm which can be used to verify the quantum circuits synthesized by any method. The proposed algorithm is based on BDD (Binary Decision Diagram) and is called X-decomposition Quantum Decision Diagram (XQDD). In this method, quantum operations are modeled using a graphic method and the verification process is based on comparing these graphic diagrams. We also develop an algorithm to verify reversible circuits even if they have a different number of garbage qubits. In most cases, the number of nodes used in XQDD is less than that in other representations. In general, the proposed method is more efficient in terms of space and time and can be used to verify many quantum circuits in polynomial time.

Modified Karnaugh map for quantum Boolean circuits construction

Karnaugh map is an efficient method of minimization for conventional logic design. Unfortunately, it is usually used for 3 or 4 variables, at most 6 variables. In this paper, we modify the Karnaugh map and propose a set of reduction rules for quantum Boolean circuit optimization. By applying these rules, we can efficiently simplify a quantum Boolean circuit that has an arbitrary number of input variables. In terms of the space consumption, we use only one auxiliary qubit as the output qubit, and keep all the input qubits unchanged.

Quantum switching and quantum string matching

Applications of quantum string matching can be found in quantum signature scheme and quantum fingerprinting. The major benefit of these applications is computation complexity. Quantum Boolean circuits can check the equivalence function: all in puts are quantum digital state. However, it is difficult to verify quantum strings if all input qubits are quantum superposition state. Quantum switching could be reversible circuits. These circuits have two major benefits: information lossless and energy saving. In this paper, we use quantum circuits to design the control module that can verify the equivalence of quantum strings and satisfy the following condition: all inputs qubits could be quantum superposition state. In the pro posed circuits, the control module can form a special correlation between input sequence and output sequence. This correlation can design the equivalence function of quantum strings to solve the problem: input strings with superposition. In regard to the performance, the scalability of the proposed circuits can be achieved.

QUANTUM SECURE DIRECT COMMUNICATION WITH A CONSTANT NUMBER OF EPR PAIRS

In this paper, we propose a quantum secure direct communication (QSDC) protocol based on Einstein–Podolsky–Rosen (EPR) pairs. Previous QSDC protocols usually consume one EPR pair to transmit a single qubit. If Alice wants to transmit an n-bit message, she needs at least n/2 EPR pairs when a dense coding scheme is used. In our protocol, if both Alice and Bob preshare 2c + 1 EPR pairs with the trusted server, where c is a constant, Alice can transmit an arbitrary number of qubits to Bob. The 2c EPR pairs are used by Alice and Bob to authenticate each other and the remaining EPR pair is used to encode and decode the message qubit. Thus the total number of EPR pairs used for one communication is a constant no matter how many bits will be transmitted. It is not necessary to transmit EPR pairs before transmitting the secret message except for the preshared constant number of EPR pairs. This reduces both the utilization of the quantum channel and the risk. In addition, after the authentication, the server is not involved in the message transmission. Thus we can prevent the server from knowing the message.

Quantum blind signature based on quantum circuit

Quantum circuit is a reversible circuit that can be designed the control module to derive the correlation between quantum input sequence and quantum output sequence. In addition, in this paper we use the control module of the quantum circuit to verify the equivalence of the quantum state such that quantum blind signature can achieve the security requirement of the signature scheme and resist eavesdropping from the outsider. The core concept of the proposed signature is based on the correlation of quantum entangled state to investigate that the message string and the signatory string is consistent. In regard to the security, the blindness and the failure of eavesdropping can be preserved by this work. The proposed signature can achieve impossibility of forgery and impossibility of disavowal.

Quantum Boolean circuits construction using tabulation method

The tabulation method can be used with a computer to simplify Boolean logic functions with up to 6 or more variables, especially with a large number of variables. For the various applications, their circuits usually are complex and we must simplify the circuit design to the best of our ability. In this paper, we present an algorithm that can efficiently simplify a quantum Boolean circuit with an arbitrary number of input variables by using the tabulation method. In terms of the space consumption, we use only one auxiliary qubit as the output qubit, and keep all the input qubits unchanged.

A novel quantum key in distributed networks

In the distributed network, quantum teleportation can teleport a quantum state from one quantum device to a remote site by using quantum entangled particles. Quantum entangled particles have the correlation among sharing party of distributed node to form a special relation for transmitting quantum message and classical message. In the paper, we derive a novel quantum key with indirect communication among sharing party. In the deriving process, random measurement outcome can resist eavesdropping from the outsider. An attacker is unable to break a secret quantum key in the deriving process. In addition, several types of attack in the transmission security can be considered in the distributed networks.

Quantum switching and quantum walks

Quantum walks can be implemented in the hypercube and general graphs, where hypercube is a regular graph. According to quantum walk algorithm, unitary property of quantum walks can be preserved. In the regular graph, to develop quantum walks algorithm is focused on quantum search algorithm. Quantum switching is the reversible and parallel computation circuits, where parallel computation circuit can achieve the better performance in time complexity and space complexity. Especially, this switching can trace the behavior of quantum walks from input sequence to output sequence, looking as quantum search algorithm. Furthermore, application of unicasting and multicasting can be implemented in this circuit.

Quantum circuit and Byzantine generals problem

This paper designs quantum circuit to detect the fault components in the Byzantine generals problem. This circuit is verification circuit that can investigate the equivalence of quantum input particles. In this problem, reach agreement and liar detection are two major issues. In the quantum field, quantum secret sharing can support a special correlation among sharing party. By using this relation, quantum circuit can detect the behavior of the traitor to obtain the consistence of the Byzantine agreement. In regard to the performance, quantum solution can obtain little message exchange and more tolerant faulty components. Furthermore, the proposed circuit is scalable.

An Extended XQDD Representation for Multiple-Valued Quantum Logic

X-decomposition Quantum Decision Diagram (XQDD) can represent a quantum operation and perform matrix operations. It can be used to verify quantum and reversible circuits even if the reversible circuits have different number of garbage qubits. It is efficient in terms of space and time. In this paper, we extend the original XQDD to multiple-valued quantum logic. The extended XQDD can represent a multiple-valued quantum operation and perform matrix operations. It can be used to check the equivalence of two multiple-valued quantum or reversible circuits which are synthesized by different approaches. In this paper, we show that the space in multiple-valued XQDD is less than other representations and it is much better than multiple-valued QuIDD and very close to QMDD in terms of time.