The Present and Future of Discrete Logarithm Problems on Noisy Quantum Computers

The discrete logarithm problem (DLP) is the basis for several cryptographic primitives. Since Shor’s work, it has been known that the DLP can be solved by combining a polynomial-size quantum circuit and a polynomial-time classical postprocessing algorithm. The theoretical result corresponds the situation where a quantum device working with a medium number of qubits of […]

A Distributed Learning Scheme for Variational Quantum Algorithms

Variational quantum algorithms (VQAs) are prime contenders to gain computational advantages over classical algorithms using near-term quantum machines. As such, many endeavors have been made to accelerate the optimization of modern VQAs in past years. To further improve the capability of VQAs, here, we propose a quantum distributed optimization scheme (dubbed as QUDIO), whose back […]

Classically Optimal Variational Quantum Algorithms

Hybrid quantum-classical algorithms, such as variational quantum algorithms (VQAs), are suitable for implementation on noisy intermediate-scale quantum computers. In this article, we expand an implicit step of VQAs: the classical precomputation subroutine, which can nontrivially use classical algorithms to simplify, transform, or specify problem instance-specific variational quantum circuits. In VQA, there is a tradeoff between […]

Quantum Circuit Architecture Optimization for Variational Quantum Eigensolver via Monto Carlo Tree Search

The advent of noisy intermediate-scale quantum (NISQ) devices provide crucial promise for the development of quantum algorithms. Variational quantum algorithms have emerged as one of the best hopes to utilize NISQ devices. Among these is the famous variational quantum eigensolver (VQE), where one trains a parameterized and fixed quantum circuit (or an ansatz) to accomplish […]

Efficient Boolean Methods for Preparing Uniform Quantum States

As each quantum algorithm requires a specific initial quantum state, quantum state preparation is an important task in quantum computing. The preparation of quantum states is performed by a quantum circuit consisting of controlled-NOT (CNOT) and single-qubit gates. Known algorithms to prepare arbitrary n -qubit quantum states create quantum circuits in O(2n) runtime and use O(2n) CNOTs, which are more expensive […]

Reducing the Depth of Linear Reversible Quantum Circuits

In quantum computing the decoherence time of the qubits determines the computation time available, and this time is very limited when using current hardware. In this article, we minimize the execution time (the depth) for a class of circuits referred to as linear reversible circuits, which has many applications in quantum computing (e.g., stabilizer circuits, […]

One-Dimensional Lazy Quantum Walk in Ternary System

Quantum walks play an important role for developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional lazy quantum walk in the ternary quantum domain and show its equivalence for circuit realization in ternary quantum logic. Using an appropriate logical mapping of the position space on which a walker evolves […]

Survey on Quantum Circuit Compilation for Noisy Intermediate-Scale Quantum Computers: Artificial Intelligence to Heuristics

Computationally expensive applications, including machine learning, chemical simulations, and financial modeling, are promising candidates for noisy intermediate scale quantum (NISQ) computers. In these problems, one important challenge is mapping a quantum circuit onto NISQ hardware while satisfying physical constraints of an underlying quantum architecture. Quantum circuit compilation (QCC) aims to generate feasible mappings such that […]

Compiler Design for Distributed Quantum Computing

In distributed quantum computing architectures, with the network and communications functionalities provided by the Quantum Internet, remote quantum processing units can communicate and cooperate for executing computational tasks that single, noisy, intermediate-scale quantum devices cannot handle by themselves. To this aim, distributed quantum computing requires a new generation of quantum compilers, for mapping any quantum […]