Simulating quantum dynamics on a quantum computer

arXiv (Cornell University), 2021

Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically involves multiple ancilla qubits and multi-qubit control gates. In order to simulate a certain class of n-qubit random Hamiltonians, we propose a drastically simplified quantum circuit that we refer to as the minimal QSVT circuit, which uses only one ancilla qubit and no multi-qubit controlled gates. We formulate a simple metric called the quantum unitary evolution score (QUES), which is a scalable quantum benchmark and can be verified without any need for classical computation. Under the globally depolarized noise model, we demonstrate that QUES is directly related to the circuit fidelity, and the potential classical hardness of an associated quantum circuit sampling problem. Under the same assumption, theoretical analysis suggests there exists an 'optimal' simulation time t opt ≈ 4.81, at which even a noisy quantum device may be sufficient to demonstrate the potential classical hardness.

Scientific Reports, 2020

Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. in this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. the Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-nagy theorem. this allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.

Physical Review Letters, 2001

We propose a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics described by the quantum sawtooth map. The numerical study of the effect of static imperfections in the quantum computer hardware shows that the main elements of the phase space structures are accurately reproduced up to a time scale which is polynomial in the number of qubits. The errors generated by these imperfections are more significant than the errors of random noise in gate operations.

Physical Review Letters, 2002

We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum information. For a collection of harmonic oscillators, any quantum process that begins with unentangled Gaussian states, performs only transformations generated by Hamiltonians that are quadratic in the canonical operators, and involves only measurements of canonical operators (including finite losses) and suitable operations conditioned on these measurements can be simulated efficiently on a classical computer.

Computer Science, 2015

In this paper, we analyze existing quantum computer simulation techniques and their realizations to minimize the impact of the exponential complexity of simulated quantum computations. As a result of this investigation, we propose a quantum computer simulator with an integrated development environment-QuIDE-supporting the development of algorithms for future quantum computers. The simulator simplifies building and testing quantum circuits and understanding quantum algorithms in an efficient way. The development environment provides flexibility of source code edition and ease of the graphical building of circuit diagrams. We also describe and analyze the complexity of algorithms used for simulation as well as present performance results of the simulator as well as results of its deployment during university classes.

Journal of Mathematical Physics, 2012

We analyze a quantum evolution of the system where the problem Hamiltonian H F is of small rank. We show the running time τ is bounded from below by O( √ N ), where N is a dimension of the Hilbert space. In a Gedanken experiment, we construct an initial Hamiltonian and non-adiabatic parametrization such that τ = O( √ N ). We also prove that for a robust adiabatic computational device τ cannot be much smaller than O(N/ ln N ).

Cornell University - arXiv, 2020

Due to complexity of the systems and processes it addresses, the development of computational quantum physics is influenced by the progress in computing technology. Here we overview the evolution, from the late 1980s to the current year 2020, of the algorithms used to simulate dynamics of quantum systems. We put the emphasis on implementation aspects and computational resource scaling with the model size and propagation time. Our minireview is based on a literature survey and our experience in implementing different types of algorithms.

ACM Transactions on Quantum Computing, 2021

In the last few years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised: on the one hand, “direct” quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit; on the other hand, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work, we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the “direct” quantum algorithm: the wave equation solver devised in [32]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great detail the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some ...

Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.

arXiv (Cornell University), 2021