Quantum simulation of open quantum systems.
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Date
2016
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Abstract
Over the last two decades the field of quantum simulations has experienced incredible
growth, which, coupled with progress in the development of controllable quantum
platforms, has recently begun to allow for the realisation of quantum simulations of a
plethora of quantum phenomena in a variety of controllable quantum platforms. Within
the context of these developments, we investigate within this thesis methods for the
quantum simulation of open quantum systems.
More specically, in the first part of the thesis we consider the simulation of Markovian
open quantum systems, and begin by leveraging previously constructed universal
sets of single-qubit Markovian processes, as well as techniques from Hamiltonian simulation,
for the construction of an efficient algorithm for the digital quantum simulation
of arbitrary single-qubit Markovian open quantum systems. The algorithm we provide,
which requires only a single ancillary qubit, scales slightly superlinearly with respect
to time, which given a recently proven no fast-forwarding theorem for Markovian dynamics,
is therefore close to optimal. Building on these results, we then proceed to
explicitly construct a universal set of Markovian processes for quantum systems of any
dimension. Specifically, we prove that any Markovian open quantum system, described
by a one-parameter semigroup of quantum channels, can be simulated through coherent
operations and sequential simulations of processes from the universal set. Under the assumption
that these universal Markovian processes can be efficiently implemented, this
allows us to propose an efficient algorithm for a wide class of Markovian open quantum
systems, while simultaneously providing a tool for combining and exploiting existing
simulation methods.
In the second part of this thesis we then consider the simulation of many-body non-
Markovian open quantum systems. In particular, we develop an algorithmic procedure
for the quantum simulation of system propagators which are not completely positive
maps, which allows us to provide an explicit algorithm for the digital quantum simulation
of many-body locally-indivisible non-Markovian open quantum systems described by
time-dependent master equations. Finally we construct generalised Suzuki-Lie-Trotter
theorems which allow us to analyse the efficiency of our method, which is expected to
be experimentally achievable for a variety of interesting cases.
Description
Doctor of Philosophy n Physics, University of KwaZulu-Natal, Westville, 2016.