Abstract Quantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix operations of row addition, row swapping, trace calculation and transpose are obtained. In particular, the complexities of these quantum algorithms are presented, too.

Abstract In classical logic design, there are machine learning methods based on converting a set of input-output traces to non-deterministic automata that are then converted to deterministic automata and synthesized using logic gates. This approach has not yet been extended to quantum automata. In this paper, we present a method to convert a set of input-output traces to a non-deterministic automaton, which is then converted to an incompletely specified multi-output Boolean function. The existing logic synthesis approaches for designing quantum circuits are insufficient to handle incompletely specified functions. So, we present a novel algorithm to synthesize logic functions with don’t cares using permutative quantum gates. The original MMD (D.M.Miller, D. Maslov, and G.W.Dueck) algorithm minimizes only completely specified reversible functions using cascades of reversible gates. In this paper, this algorithm is modified to allow for the inclusion of don’t cares within the given function’s truth table (reversible or irreversible). The distinguishing property of our presented algorithm QAS, is that it does not add any ancilla qubits if it is not necessary. This algorithm solves the problem of synthesizing deterministic and non-deterministic quantum state machines, both completely specified and incompletely specified.

Abstract In recent years, quantum computing has gradually extended its influence beyond the realm of physics research into the fields of electrical engineering and computer science. Most researchers and programmers remain more familiar with traditional algorithmic techniques based on conventional computer architectures. To address this gap, this study proposes a quantum algorithmic circuit design framework with Grover’s search speedup technique and provides theoretical proofs for some design techniques, aiming to facilitate knowledge transfer and ease the learning curve for designers entering the field of quantum algorithm development. Since combinatorial optimization problems in graph theory serve as the foundation for many practical applications, this study adopts the well-known Connected Dominating Set (CDS) problem as a design example to illustrate the practical applicability of the proposed quantum algorithmic design framework and presents a quantum circuit as a potential solution for addressing realworld challenges in network optimization and related applications. In addition, the circuit proposed in this paper can serve as a quantum oracle to identify connected dominating sets (CDSs) of a graph. When the oracle is applied to a superposition of vertex subsets, Grover’s search algorithm achieves a quadratic speedup. We designed a method for adjusting the initial amplitudes so that the search can be biased toward smaller CDSs, which maximizes the probability of finding the minimum CDS.

Our previous work delt with the zeta function for the interacting particle system (IPS) including quantum cellular automaton (QCA) as a typical model in the study of ``IPS/Zeta Correspondence". On the other hand, the absolute zeta function is a zeta function over $\mathbb{F}_1$ defined by a function satisfying an absolute automorphy. This paper proves that a new zeta function given by QCA is an absolute automorphic form of weight depending on the size of the configuration space. As an example, we calculate an absolute zeta function for a tensor-type QCA, and show that it is expressed as the multiple gamma function. In addition, we obtain its functional equation by the multiple sine function.

Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. However, we find that the PEA is not an unbiased estimation, which prevents the estimation error from achieving an arbitrarily small level. In this paper, we propose an unbiased phase estimation algorithm (UPEA) based on the original PEA. We also show that a maximum likelihood estimation (MLE) post-processing step applied on UPEA has a smaller mean absolute error than MLE applied on PEA. In the end, we apply UPEA to quantum counting, and use an additional correction step to make the quantum counting algorithm unbiased.

In this paper, we present a polynomial-complexity algorithm to construct a special orthogonal matrix for the deterministic remote state preparation (DRSP) of an arbitrary $n$-qubit state, and prove that if $n > 3$, such matrices do not exist. Firstly, the construction problem is split into two sub-problems, i.e., finding a solution of a semi-orthogonal matrix and generating all semi-orthogonal matrices. Through giving the definitions and properties of the matching operators, it is proved that the orthogonality of a special matrix is equivalent to the cooperation of multiple matching operators, and then the construction problem is reduced to the problem of solving an XOR linear equation system, which reduces the construction complexity from exponential to polynomial level. Having proved that each semi-orthogonal matrix can be simplified into a unique form, we use the proposed algorithm to confirm that the unique form does not have any solution when $n > 3$, which means it is infeasible to construct such a special orthogonal matrix for the DRSP of an arbitrary $n$-qubit state.

In this paper, we propose an estimation of quantum resources necessary for recovering a key using Known Plain Text Attack (KPA) model for SPARKLE family of LWC authenticated block ciphers - SCHWAEMM. The procedure is based on a general attack using Grover's search algorithm with encryption oracle over key space in superposition. The paper explains step by step how to evaluate the cost of each operation type in encryption oracle in terms of various quantum and reversible gates. The result of this paper is an implementation of the simplified version of this cipher using quantum computer and summary table which shows the depth of quantum circuit, the size of quantum register and how many gates of NCT family are required for implementing the ciphers and attacks on them.

Rinton Press, a science and technology publisher, is founded by a team of scholars and publication professionals, and is based in Princeton, New Jersey. Rinton Press serves the scientific and academic community by publishing, marketing and distributing journals, books and proceedings, through a progressively wide variety of media such as CD-ROM and Internet in addition to conventional print on paper.

Rinton Press, a science and technology publisher, is founded by a team of scholars and publication professionals, and is based in Princeton, New Jersey. Rinton Press serves the scientific and academic community by publishing, marketing and distributing journals, books and proceedings, through a progressively wide variety of media such as CD-ROM and Internet in addition to conventional print on paper.

Rinton Press, a science and technology publisher, is founded by a team of scholars and publication professionals, and is based in Princeton, New Jersey. Rinton Press serves the scientific and academic community by publishing, marketing and distributing journals, books and proceedings, through a progressively wide variety of media such as CD-ROM and Internet in addition to conventional print on paper.