ArQTiC is an open-source, full-stack software package built for the simulations of materials on quantum computers. It currently can simulate materials that can be modeled by any Hamiltonian derived from a generic, one-dimensional, time-dependent Heisenberg Hamiltonian. ArQTiC includes modules for generating quantum programs for real- and imaginary-time evolution, quantum circuit optimization, connection to various quantum backends via the cloud, and post-processing of quantum results. By enabling users to seamlessly design, execute, and analyze materials simulations on quantum computers, ArQTiC opens this field to a broader community of scientists from a wider range of scientific domains.

As a central thermodynamic property, free energy enables the calculation of virtually any equilibrium property of a physical system, allowing for the construction of phase diagrams and predictions about transport, chemical reactions, and biological processes. Thus, methods for efficiently computing free energies, which in general is a difficult problem, are of great interest to broad areas of physics and the natural sciences. The majority of techniques for computing free energies target classical systems, leaving the computation of free energies in quantum systems less explored. Recently developed fluctuation relations enable the computation of free energy differences in quantum systems from an ensemble of dynamic simulations. While performing such simulations is exponentially hard on classical computers, quantum computers can efficiently simulate the dynamics of quantum systems. Here, we present an algorithm utilizing a fluctuation relation known as the Jarzynski equality to approximate free energy differences of quantum systems on a quantum computer. We discuss under which conditions our approximation becomes exact, and under which conditions it serves as a strict upper bound. Furthermore, we successfully demonstrate a proof of concept of our algorithm using the transverse field Ising model on a real quantum processor. As quantum hardware continues to improve, we anticipate that our algorithm will enable computation of free energy differences for a wide range of quantum systems useful across the natural sciences.

Quantum computers hold the potential to unlock new discoveries in complex quantum systems by enabling the simulation of physical systems that have heretofore been impossible to implement on classical computers due to intractability. A system of particular interest is that of dirty bosons, whose physics highlights the intriguing interplay of disorder and interactions in quantum systems, playing a central role in describing, for instance, ultracold gases in a random potential, doped quantum magnets, and amorphous superconductors. Here, we demonstrate how quantum computers can be used to elucidate the physics of dirty bosons in one and two dimensions. Specifically, we explore the disorder-induced delocalized-to-localized transition using adiabatic state preparation. In one dimension, the quantum circuits can be compressed to small enough depths for execution on currently available quantum computers. In two dimensions, the compression scheme is no longer applicable, thereby requiring the use of large-scale classical state vector simulations to emulate quantum computer performance. In addition, simulating interacting bosons via emulation of a noisy quantum computer allowed us to study the effect of quantum hardware noise on the physical properties of the simulated system. Our results suggest that scaling laws control how noise modifies observables versus its strength, the circuit depth, and the number of qubits. Moreover, we observe that noise impacts the delocalized and localized phases differently. A better understanding of how noise alters the observed properties of the simulated system is essential for leveraging near-term quantum devices for simulation of dirty bosons, and indeed for condensed matter systems in general.

In this work [1], we extend our recently introduced algebraic circuit compression algorithms [2], [3] that can compress time evolution circuits of free fermionic Hamiltonians on an n-site 1D chain, equation H(t)=∑i=1n-1 (hi(t)cici+1+pi(t)cici+1)+h.c., 1 equation in three significant ways: (1) we allow for compression of free fermionic Hamiltonians on arbitrary lattices, (2) we incorporate particle creation/annihilation operators into the compression schemes, and (3) we extend the compression scheme to controlled time-evolution operators. We illustrate the effectiveness of our approach by simulating the dynamics of a fermion on a 4× 4 2D square lattice on ibmq_washington, both in the presence and absence of disorder. Our quantum simulations show a remarkably high fidelity which is enabled through the compressed circuits.

Unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elements are limited to a subset of SU(4) - or equivalently, when the Hamiltonian may be mapped onto free fermionic models - several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates using algebraic relations between adjacent circuit elements. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

A highly anticipated application for quantum computers is as a universal simulator of quantum many-body systems, as was conjectured by Richard Feynman in the 1980s. The last decade has witnessed the growing success of quantum computing for simulating static properties of quantum systems, i.e., the ground state energy of small molecules. However, it remains a challenge to simulate quantum many-body dynamics on current-to-near-future noisy intermediate-scale quantum computers. Here, we demonstrate successful simulation of nontrivial quantum dynamics on IBM's Q16 Melbourne quantum processor and Rigetti's Aspen quantum processor; namely, ultrafast control of emergent magnetism by THz radiation in an atomically-thin two-dimensional material. The full code and step-by-step tutorials for performing such simulations are included to lower the barrier to access for future research on these two quantum computers. As such, this work lays a foundation for the promising study of a wide variety of quantum dynamics on near-future quantum computers, including dynamic localization of Floquet states and topological protection of qubits in noisy environments.

A composable design scheme is presented for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. The proposed object-oriented approach is based on constructing an expressive set of common data structures and methods that enables programming of a broad variety of complex hybrid quantum simulation applications. The abstract core of the scheme is distilled from the analysis of the current quantum simulation algorithms. Subsequently, it allows synthesis of new hybrid algorithms and workflows via the extension, specialisation, and dynamic customisation of the abstract core classes defined by the proposed design. The design scheme is implemented using the hardware-agnostic programming language QCOR into the QuaSiMo library. To validate the implementation, the authors test and show its utility on commercial quantum processors from IBM and Rigetti, running some prototypical quantum simulations.