Noise Robustness of Quantum Relaxation for Combinatorial Optimization
Relaxation is a common way for dealing with combinatorial optimization problems.
Quantum Approximate Bayesian Optimization Algorithms With Two Mixers and Uncertainty Quantification
The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently, a quantum approximate Bayesian optimization algorithm (QABOA) that includes two mixers was developed, where surrogate-based Bayesian optimization is applied to improve the sampling efficiency of the classical optimizer. A continuous-time quantum walk mixer […]
Bayesian Optimization for QAOA
The quantum approximate optimization algorithm (QAOA) adopts a hybrid quantum-classical approach to find approximate solutions to variational optimization problems. In fact, it relies on a classical subroutine to optimize the parameters of a quantum circuit. In this article, we present a Bayesian optimization procedure to fulfill this optimization task, and we investigate its performance in […]
Shor’s Algorithm Using Efficient Approximate Quantum Fourier Transform
Shor’s algorithm solves the integer factoring and discrete logarithm problems in polynomial time. Therefore, the evaluation of Shor’s algorithm is essential for evaluating the security of currently used public-key cryptosystems because the integer factoring and discrete logarithm problems are crucial for the security of these cryptosystems. In this article, a new approximate quantum Fourier transform […]
Analysis of the Vehicle Routing Problem Solved via Hybrid Quantum Algorithms in the Presence of Noisy Channels
The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global […]
Efficient Quantum State Preparation for the Cauchy Distribution Based on Piecewise Arithmetic
The benefits of the quantum Monte Carlo algorithm heavily rely on the efficiency of the superposition state preparation. So far, most reported Monte Carlo algorithms use the Grover–Rudolph state preparation method, which is suitable for efficiently integrable distribution functions. Consequently, most reported works are based on log-concave distributions, such as normal distributions. However, non-log-concave distributions […]
Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers
Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this article, inspired by the variational quantum eigensolver (VQE), we propose an iterative layer VQE (L-VQE) approach. We present a large-scale numerical study, simulating circuits with […]
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 […]
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, […]
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