Simulating and Visualizing Quantum Annealing in Julia

07/27/2022, 8:00 PM8:30 PM UTC
Purple

Abstract:

QuantumAnnealing.jl provides a toolkit for performing simulations of Adiabatic Quantum Computers on classical hardware. The package includes functionality for rapid simulation of the Schrodinger evolution of the system, processing annealing schedules used by real world annealing hardware, implementing custom annealing schedules, and more.

Description:

The field of Quantum Computation has been rapidly growing in recent years. One driving factor behind this growth is the computational intractability of simulating quantum systems. The classical overhead for simulating quantum systems grows exponentially as the system size increases, making quantum computers an appealing option for performing these simulations. Algorithms have also been developed to perform actions such as search and optimization on quantum computers. Quantum Annealing is an optimization method which makes use of an adiabatic quantum computer to try to find a global minima. It relies on the Adiabatic Theorem which states that if a quantum system is prepared in its ground state, if the system evolves slowly enough it will stay in its ground state. A few companies have created quantum annealing hardware, most notably D-Wave Systems, so it is useful to be able to simulate small anneals to look for signatures that imply that the quantum annealing hardware is behaving as expected. To accomplish this, we can solve the Schrodinger equation with the time varying Hamiltonian for the quantum annealer we wish to simulate.

That is where this package comes into play. QuantumAnnealing.jl allows for the simulation of a quantum annealer with arbitrary annealing schedule (two functions which dictate how the system evolves from the initial "easy" state to the final "problem" state), and arbitrary target hamiltonian (the encoding of the problem which is supposed to be solved by the quantum annealer). This package also provides functionality for implementing controls on the annealing schedules, such as holding the schedules constant for a set amount of time (often called a pause) or increasing the speed of the anneal (often called a quench), as well as the ability to directly process D-Wave hardware schedules from CSV files into annealing schedule functions used by the simulator. The simulation can be performed either by using a wrapper around DifferentialEquations.jl, or by using a specialized solver we have written to quickly and accurately simulate the closed system evolution of the quantum annealing hamiltonian. This solver makes use of the Magnus Expansion and includes hard-coded implementations up to the fourth order, as well as a general implementation if a higher order solver is needed. This hardcoded solver has empirically produced a 20-30x speed improvement over the DifferentialEquations.jl wrapper.

Alongside QuantumAnnealing.jl, we have released a plotting package, QuantumAnnealingAnalytics.jl which provides useful plotting functionality for common use-cases of the QuantumAnnealing.jl package. QuantumAnnealingAnalytics.jl includes functions to plot the instantaneous ground state of the Hamiltonian (useful for determining how quickly it is expected that the system can evolve without leaving the ground state), plotting the probabilities of various energy levels for the final system (useful for comparing output statistics from hardware), and plotting output statistics from data files in the bqpjson format. This allows for much easier understanding of the system the user is working with and can be used to quickly reproduce figures found in seminal works in the field of Quantum Annealing.

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