Related papers: Random sampling of permutations through quantum ci…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…
We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
We give a polynomial time classical algorithm for sampling from the output distribution of a noisy random quantum circuit in the regime of anti-concentration to within inverse polynomial total variation distance. This gives strong evidence…
Genetic information is encoded in a linear sequence of nucleotides, represented by letters ranging from thousands to billions. Mutations refer to changes in the DNA or RNA nucleotide sequence. Thus, mutation detection is vital in all areas…
Sampling from probability distributions of quantum circuits is a fundamentally and practically important task which can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In the present work, we examine…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
We investigate the relationship between two distinct classical approaches to quantum systems: direct simulation from a classical description and sample-based learning from measurement data. While both tasks ultimately aim to reproduce…
If classical algorithms have been successful in reproducing the estimation of expectation values of observables of some quantum circuits using off-the-shelf computing resources, matching the performance of the most advanced quantum devices…
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…