Related papers: Synthesizing Quantum Circuits for Simple Periodic …
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…
Time-periodic form or expression is a ubiquitous natural and man-made phenomenon observable in all the scientific and engineering disciplines. In this article, we propose a theory of periodic sequence (TPS), which can be formulated as a…
Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We…
Pauli channels are fundamental in the context of quantum computing as they model the simplest kind of noise in quantum devices. We propose a quantum algorithm for simulating Pauli channels and extend it to encompass Pauli dynamical maps…
In this paper, we use the methods found in quant-ph/0201095 to create a continuous variable analogue of Shor's quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function F:R-->R…
Quantum compiling, a process that decomposes the quantum algorithm into a series of hardware-compatible commands or elementary gates, is of fundamental importance for quantum computing. We introduce an efficient algorithm based on deep…
The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there are no standard ways to…
Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits, following a recent report that a one-dimensional…
Mutually unbiased bases (MUBs) play a crucial role in numerous applications within quantum information science, such as quantum state tomography, error correction, entanglement detection, and quantum cryptography. Utilizing \(2^n + 1\) MUB…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
We present numerical results which show how two-bit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a…
We first consider the basic requirements for a quantum computer, arguing for the attractiveness of nuclear spins as information-bearing entities, and light for the coupling which allows quantum gates. We then survey the strengths of and…
I give analytical estimates and numerical simulation results for the performance of Kitaev's 2d topological error-correcting codes. By providing methods for the execution of an encoded three-qubit Toffoli gate, I complete a universal gate…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…
Improving over an earlier construction by Kaye and Zalka, Maslov et al. describe an implementation of Shor's algorithm which can solve the discrete logarithm problem on binary elliptic curves in quadratic depth O(n^2). In this paper we show…
Basic logic gates and their operations in ternary quantum domain are involved in the synthesis of ternary quantum circuits. Only a few works define ternary algebra for ternary quantum logic realization. In this paper, a ternary logic…
In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T,…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic operations on quantum data, e.g., reversible arithmetic circuits. In physical implementations, however, TOFFOLI gates are decomposed into six CNOT gates…