Gravitational waves (GWs) are one of the key signatures of cosmic strings. If GWs from cosmic strings are detected in future experiments, not only their existence can be confirmed, but also their properties might be probed. In this paper, we study the determination of cosmic string parameters through direct detection of GW signatures in future ground-based GW experiments. We consider two types of GWs, bursts and the stochastic GW background, which provide us with different information about cosmic string properties. Performing the Fisher matrix calculation on the cosmic string parameters, such as parameters governing the string tension G$\mu${} and initial loop size $\alpha${} and the reconnection probability p, we find that the two different types of GWs can break degeneracies in some of these parameters and provide better constraints than those from each measurement.

We study future observational constraints on cosmic string parameters from various types of next-generation experiments: direct detection of gravitational waves (GWs), pulsar timing array, and the cosmic microwave background. We consider both GW burst and stochastic GW background searches by ground- and space-based interferometers as well as GW background detection in pulsar timing experiments. We also consider cosmic string contributions to the cosmic microwave background temperature and polarization anisotropies. These different types of observations offer independent probes of cosmic strings and may enable us to investigate cosmic string properties if the signature is detected. In this paper, we evaluate the power of future experiments to constrain cosmic string parameters, such as string tension $G$\mu${}$, initial loop size $$\alpha${}$, and reconnection probability $p$, by performing Fisher information matrix calculations. We find that combining the information from the different types of observations breaks parameter degeneracies and provides more stringent constraints on the parameters. We also find future space-borne interferometers independently provide a highly precise determination of the parameters.

It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In many problems in finance to which Monte Carlo simulation is applied, many random numbers are required to obtain one sample value of the integrand, since those problems are extremely high-dimensional integrations, for example, risk measurement of credit portfolio. This leads to the situation that the required qubit number is too large in the naive implementation where a quantum register is allocated per random number. In this paper, we point out that we can reduce qubits keeping quantum speed up if we perform calculation similar to the classical one, that is, estimate the average of integrand values sampled by a pseudo-random-number generator (PRNG) implemented on a quantum circuit. We present not only the overview of the idea but also concrete implementation of PRNG and application to credit risk measurement. Actually, reduction of qubits is a trade-off against increase of circuit depth. Therefore, full reduction might be impractical, but such a trade-off between speed and memory space will be important in adjustment of calculation setting considering machine specs, if large-scale Monte Carlo simulation by quantum computer is in operation in the future.

Gravitational waves emitted by kinks on infinite strings are investigated using detailed estimations of the kink distribution on infinite strings. We find that gravitational waves from kinks can be detected by future pulsar timing experiments such as SKA for an appropriate value of the string tension, if the typical size of string loops is much smaller than the horizon at their formation. Moreover, the gravitational wave spectrum depends on the thermal history of the Universe and hence it can be used as a probe into the early evolution of the Universe.

Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this article, we focus on derivative pricing based on solving the Black–Scholes partial differential equation by the finite-difference method (FDM), which is a suitable approach for some types of derivatives but suffers from the curse of dimensionality , that is, exponential growth of complexity in the case of multiple underlying assets. We propose a quantum algorithm for FDM-based pricing of multi-asset derivative with exponential speedup with respect to dimensionality compared with classical algorithms. The proposed algorithm utilizes the quantum algorithm for solving differential equations, which is based on quantum linear system algorithms. Addressing the specific issue in derivative pricing, that is, extracting the derivative price for the present underlying asset prices from the output state of the quantum algorithm, we present the whole of the calculation process and estimate its complexity. We believe that the proposed method opens the new possibility of accurate and high-speed derivative pricing by quantum computers.

We investigate the cosmological and astrophysical constraints on superconducting cosmic strings (SCSs). SCS loops emit strong bursts of electromagnetic waves, which might affect various cosmological and astrophysical observations. We take into account the effect on the CMB anisotropy, CMB blackbody spectrum, BBN, observational implications on radio wave burst and X-ray or γ-ray events, and stochastic gravitational wave background measured by pulsar timing experiments. We then derive constraints on the parameters of SCS from current observations and estimate prospects for detecting SCS signatures in on-going observations. As a result, we find that these constraints exclude broad parameter regions, and also that on-going radio wave observations can probe large parameter space.