What leaps in technology would be needed to scan the total state of
the human brain?

Preface
In 2016, the "Small Mammal BPF Prize" was won, see: http://www.brainpreservation.org/small-mammal-announcement/. It's the first of two stages of competition for brain preservation (BP) achievements. This competition is doing for BP what XPRIZE is doing for space innovation with competitions like the Ansari X Prize.
Researchers from 21st Century Medicine have developed a new technique
to allow long term storage of a near-perfect mammalian brain. It’s a
breakthrough that could have serious implications for cryonics, and
the futuristic prospect of bringing the frozen dead back to life.
By using a chemical compound to turn a rabbit’s brain into a near
glass-like state, and then cooling it to -211 degrees Fahrenheit (-135
degrees Celsius), a research team from California-based 21st Century
Medicine (21CM) showed that it’s possible to enable near-perfect,
long-term structural preservation of an intact mammalian brain. The
achievement has earned not just accolades from the scientific
community, but a prestigious award as well; the 21CM researchers are
today being awarded the $26,735 Small Mammal Brain Preservation Prize,
which is run by the Brain Preservation Foundation (BPF). — http://gizmodo.com/brain-preservation-breakthrough-could-usher-in-a-new-er-1758022181
Answer
If you consider focused ion beam scanning electron microscopy (FIBSEM)-level scanning to be adequate, than the technology is already available:
In the types of electron microscopy neuroscientists commonly use
(FIBSEM, etc.), preserved neural tissue can be visualized down to
about a 6 nanometer resolution. This allows them to directly see each
neuron’s synapses and dendrites (connections to other neurons). This
level of detail also includes the ability to image, directly and
indirectly (via molecular probes), many elements of the “synaptome,”
the number and types of special proteins (vesicles, signaling
proteins, cytoskeleton), receptors (Glutamate, etc.), and
neurotransmitters (at least six types in human neurons) that are known
to be involved in long-term learning and memory at each synapse in the
brain, and elements of the “epigenome” (learning-based DNA methylation
and histone modifications) in the nucleus of each neuron.
— http://www.brainpreservation.org/tech-prize
If you don't consider FIBSEM-level scanning to be adequate, then the leaps in technology needed for this feat are on the horizon:
Our ability to scan and verify is also rapidly improving. New types of
electron microscopy, such as Cryo-TEM, can image at an amazing 3
angstrom resolution, 50 times greater magnification than FIBSEM, a
scale where brain proteins and even individual atoms can be directly
seen.
— http://www.brainpreservation.org/tech-prize/
In conclusion, the scanning technology is either currently adequate or will be in the near future. The major leap, will be the actual preservation of a large mammalian brain: BPF Prize Stage 2.
Related Topic
perhaps the state of the neurons will continue to work properly the
next time synaptic input is introduced and the mind will "wake up".
In regard to the "wake up" part, (IMO) once mapping the brain's connectome is achievable, the next step is virtualization including a "runtime" wikipedia.org/wiki/Run_time_(program_lifecycle_phase) by applying what's already known from scientific research:
… self-emerged oscillatory timing is the brain's fundamental organizer
of neuronal information. The small-world-like connectivity of the
cerebral cortex allows for global computation on multiple spatial and
temporal scales. The perpetual interactions among the multiple network
oscillators keep cortical systems in a highly sensitive "metastable"
state and provide energy-efficient synchronizing mechanisms via weak links. — https://global.oup.com/academic/product/rhythms-of-the-brain-9780199828234
John Smart, VP of the BPF, via io9's article, "How to Live Forever By Turning Your Brain Into Plastic":
"We appear to be our special, complex patterns," Smart told io9, "not
our matter, or even our type of matter." He notes that each of the
250,000 or so people who have had cochlear implants has had one small
nervous system pattern replaced, or "uploaded", into technology.
Retinal implants are coming next. It's the pattern replication that we
care about, not the matter, or "substrate."
Patternism, in conjunction with connectomics, may eventually reveal
our neural correlates of identity — and allow us to preserve
capacities like memories, thoughts, emotions, even consciousness.
"Consciousness is transitory, it's like a pattern in a stream," said
Smart, "and it's also overrated. You don't have it when you sleep, and
it's rebooted, at a later time, from much more durable cellular and
molecular patterns when you are knocked unconscious, given anesthesia,
drowned for an hour in cold water with no EEG, and so on."
Identity, argues Smart, is what really matters — those patterns that
are stored in our neural architectures. — http://io9.gizmodo.com/5943304/how-to-preserve-your-brain-by-turning-it-into-plastic