3 research outputs found
Disordered Phase in Ising and Metastability in Cellular Potts Models Hint at Glassy Dynamics
In this paper, quantum algorithms are to be used to simulate glassy systems
in toy models. To look for glassy behavior, the energy landscape and spin
configurations of the transverse field Ising model in a longitudinal field are
studied. The Variational Quantum Eigensolver (VQE) is used to obtain the
ground-state energies and corresponding eigenstates for a Ising
lattice using 36 qubits and a 1-dimensional Ising chain of length 25. For the
Cellular Potts model, the original Hamiltonian is converted to an
Ising formulation for the VQE to reduce to its ground state. The energy change
during minimization is carefully analyzed to find whether the effects of
interfacial tension among cells could probably induce glassiness in the cell
system
Intermediate Qutrit-based Improved Quantum Arithmetic Operations with Application on Financial Derivative Pricing
In some quantum algorithms, arithmetic operations are of utmost importance
for resource estimation. In binary quantum systems, some efficient
implementation of arithmetic operations like, addition/subtraction,
multiplication/division, square root, exponential and arcsine etc. have been
realized, where resources are reported as a number of Toffoli gates or T gates
with ancilla. Recently it has been demonstrated that intermediate qutrits can
be used in place of ancilla, allowing us to operate efficiently in the
ancilla-free frontier zone. In this article, we have incorporated intermediate
qutrit approach to realize efficient implementation of all the quantum
arithmetic operations mentioned above with respect to gate count and
circuit-depth without T gate and ancilla. Our resource estimates with
intermediate qutrits could guide future research aimed at lowering costs
considering arithmetic operations for computational problems. As an application
of computational problems, related to finance, are poised to reap the benefit
of quantum computers, in which quantum arithmetic circuits are going to play an
important role. In particular, quantum arithmetic circuits of arcsine and
square root are necessary for path loading using the re-parameterization
method, as well as the payoff calculation for derivative pricing. Hence, the
improvements are studied in the context of the core arithmetic circuits as well
as the complete application of derivative pricing. Since our intermediate
qutrit approach requires to access higher energy levels, making the design
prone to errors, nevertheless, we show that the percentage decrease in the
probability of error is significant owing to the fact that we achieve circuit
robustness compared to qubit-only works.Comment: 11 pages, 6 figure
QuDiet: A classical simulation platform for qubitâqudit hybrid quantum systems
Abstract In recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the stateâofâtheâart classical simulators are only limited to binary quantum systems, which restrict the classical simulation of higherâdimensional quantum computing systems. Through recent developments in higherâdimensional quantum computing systems, it is realised that implementing qudits improves the overall performance of a quantum algorithm by increasing memory space and reducing the asymptotic complexity of a quantum circuit. Hence, in this article, QuDiet, a stateâofâtheâart userâfriendly pythonâbased higherâdimensional quantum computing simulator is introduced. QuDiet offers multiâvalued logic operations by utilising generalised quantum gates with an abstraction so that any naive user can simulate qudit systems with ease as compared to the existing ones. Various benchmark quantum circuits is simulated in QuDiet and show the considerable speedup in simulation time as compared to the other simulators without loss in precision. Finally, QuDiet provides a full qubitâqudit hybrid quantum simulator package with quantum circuit templates of wellâknown quantum algorithms for fast prototyping and simulation. Comprehensive simulation up to 20 qutrits circuit on depth 80 on QuDiet was successfully achieved. The complete code and packages of QuDiet is available at https://github.com/LegacYFTw/QuDiet