In 2017 the cryptocurrency Bitcoin
repeatedly made headlines by starting at the beginning of the year valued at
about $1,000 per unit, climbing to over $19,000 in December, and then
precipitously dropping to below $8,000, where it has since remained.In the interest of full disclosure I should say that last year I invested
about $11k in three cryptocurrencies.At
this writing in mid-March, my investment, which had been up in value by more
than a factor of two, has declined and is now barely breaking even.

Also in 2017 IBM announced the initial
operation of a 20-qubit quantum computer that they made available online, and
Google did them 29 times better by announcing the development of
a 49-qubit quantum computer to go into operation by the end of the year.Microsoft, which is developing a decoherence-resistant version of quantum
computing based on the topology of two-dimensional systems, released a new
coding language for quantum computing.Things
moved fast in 2017.

Superficially these two things are
unrelated developments, but they were tied together by an October-2017 preprint
by D. Aggarwal and coauthors based in
Singapore
and
Australia
.The group outlined in some detail
the expected impact of quantum computing on cryptocurrencies like Bitcoin, and
the impacts seem to be more negative than positive.

Let me begin this discussion by reviewing
just what cryptocurrencies are and what quantum computing is.Normal currencies like the US dollar, the UK pound, and the EU euro,
either in the forms of printed bills or of bank balances, have a value (a)
because they are issued and backed by trusted governments that exert some
control over their value and stability, (b) because they can be stored in banks
that keep reliable legers of financial transactions to prevent the spending of
the same on-deposit currency twice, and (c) because regulated exchanges allow
individuals to buy and sell currencies and to speculate on their increase or
decline in value, contributing to their stability.The banks and exchanges normally extract a fee for each transaction that
is sometimes small and sometimes substantial, introducing a kind of "friction" to the system.Further,
there is normally a significant time delay, possibly of days, before a given
transaction is completed.There are
also the concerns in some quarters that governments can manipulate the value of
their currencies for political reasons and can interfere with and snoop on
transactions.

Cryptocurrencies serve essentially the same
purpose, but without the involvement of governments and banks and with less
friction.They are initially issued
by their creators and subsequently new cryptocurrency is created by "mining", an operation that uses high speed computers to competitively
process transaction data in the form of blockchain blocks (see below).In the beginning, the mining computers were just ordinary laptops,
desktops, and workstations, but the operation has evolved into "crypto-farms" with thousands of dedicated specialzed processors located in
cooled warehouses in locations where electrical energy is cheap.Many crypto-mining farms are located in
China
and
South Korea
, but also old mining towns in
Montana
are experiencing a new crypto-mining boom because of the cheap real estate and
low power costs.

Cryptocurrencies are stored in individual
digital "wallets" kept by the owners on their computers and devices and
accessed by a unique digital key. (Don't lose yours!).The transaction records reside in a publically available block of data
shared over the Internet by hundreds or thousands of the mining computers.Transaction fees are small and transaction speeds are fast.All this is possible because of the digital encryption that verifies
ownership while protecting peer-to-peer transactions from scrutiny and
tampering.

To be more specific, each transaction is
represented as an entry in a "block", and each block is an element or link
in the blockchain.Each transaction
entry uniquely identifies the crypto-coin owner using a form of reverse
cryptography and specifies the amounts to be withdrawn from one digital wallet
and deposited into two other wallets.These
transactions are entered until a block is full, at which point a cryptographic
hash code is added that connects it to the previous block of the chain, and it
is published on the Internet.Many
mining computers then compete to process the new block's transactions and to
repetitively compute the smallest possible "nonce", a fixed-length hash-code
based on the digital structure of the block.For a nonce to win the mining competition, its value must be less than a
previously established value.The
mining processor that produces the smallest nonce the fastest is awarded a fee
paid in the newly-minted cybercurrency, and all the mining computers of the
system then move on to competitively process the next block in the blockchain.In this way, the public
digital ledger is updated, cryptocurrencies are transferred, newly minted
cryptocurrency enters the system, and all is well.

A
quantum computer is a device first suggested in 1978 by Richard Feynman that
uses the manipulation of quantum states to process information and to solve
problems.Feynman himself was
particularly interested in applying such a device to problems involving quantum
mechanics itself, but later enthusiasts seem to be more focused on database
searches and cryptography. A quantum
computer is a completely new kind of data processing device that is today
emerging from the academic and industrial laboratories of the planet, ready or
not, and finding its initial applications in the real world.

A
conventional computer has a memory in which bits of information are stored in
definite binary states of 1 or 0 and has a processor that operates on this
stored information. For example, the
memory may contain two numbers stored in binary representation and a program
specifying the locations of these numbers and calling for them to be multiplied
together and the result stored in another location. With
the execution of the program by the processor, the numbers are fetched,
multiplied, and their product in binary representation stored in the memory.

A
quantum computer differs from this computing scheme in one important way: the
definite-state memory units, the 0-or-1 bits in the conventional computer, are
replaced by indefinite-state qubits (short for quantum bits). The
qubits are possible states in a quantum system and may be indefinite until they
are "collapsed" to a 1 or 0.

Of
course, a quantum computer needs more than just qubits for its operation. The
qubits must be well enough insulated from the random scrambling effects of
environmental noise (called decoherence) that the coherent state of the quantum
system is preserved for at least long enough to set up a calculation, perform
it, and read out the results.Because
of this decoherence problem, a major part of quantum computer architecture
involves correcting the errors that inevitably arise from decoherence.

A
quantum computer must have the ability to initialize any qubit in a specified
state and to measure the state of any specific qubit. It
must have "universal quantum gates", logical elements capable of arranging
any desired logical relationship between the states of qubits. It
must also have a processor capable of interlinking such quantum gates to
establish rules and boundary conditions for their inter-relationships. In a
quantum computation, the arrangement of quantum gates is set by the programmer
to connect the qubits in a logical pattern, according to a program or algorithm.
After an interval, the qubits assigned to the final result are read out. If this
is done properly, the quantum computer can be made to perform calculations in a
way that is qualitatively different from calculations performed on a
conventional computer. In fact, computations easily performed with a quantum
computer in some cases would require a computation time with a conventional
computer greater than the age of the universe.

It
is relatively easy to visualize the operation of a quantum computer by using the
transactional interpretation of quantum mechanics (see The
Quantum Handshake below). The
programming of the quantum computer that sets up the problem has created a set
of conditions such that the quantum mechanical wave function can only
form a final transaction and collapse to a definite state by solving the problem
(for example, by finding the prime factors of an input number).

The
advanced and retarded waves emanating from the initial qubits, describing all
the possible qubit states of the system, propagate through the computer, seeking
the ultimate multi-vertex quantum handshake that solves the problem and permits
a transaction to form. This process converges very rapidly because the
propagation duration of the advanced waves requires a negative time. The net
result is that the solution transaction forms, the wave function collapses into
the solution state, the problem is solved, and the results are read out. In
particular, quantum computers can be used to rapidly determine the two numerical
factors that, when multiplied together, form the large product that is the
problem's input.This capability
can be used to break most codes in contemporary cryptography.

This
brings us to the question of how the quantum computers now becoming available
can be expected to impact cryptocurrencies.The impacts are expected to lie in two areas: (1) Cracking: i.e.,
breaking the cryptographic encoding within the blockchain to identify
cryptocurrency owners and discover the keys to their digital wallets, and (2)
Mining: i.e., out-competing existing cryptocurrency miners to win every race
with the smallest nonce and to corrupt transactions by marshalling more
computing power than all the rest of the blockchain system combined.

For
the Cracking problem, Aggarwal, et al,
estimate that by the year 2027 the current blockchain signature scheme can be
broken by a quantum computer in less than 10 minutes.This should be of great concern to the cryptocurrency community.

On
the other hand, for the Mining problem they predict, projecting out as far as
the year 2042, that quantum computing may perform very profitable blockchain
mining operations using what is called the Grover algorithm but will not be able to overwhelm the standard hardware system and corrupt
it.This is in part because the
specialized ASIC systems developed specifically to mine quantum currency are
extremely fast and cannot be easily overwhelmed in the near future.

There
may be alternative signature algorithms on the horizon that will make it more
difficult for quantum computers to impact the Cracking problem.However, Aggarwal, et al, analyze eleven of these schemes and conclude that they would
not be of much help in protecting against a quantum attack.

Of course, it is very
early in this hypothetical battle between quantum computers and
cryptocurrencies.So far in this war
not a single shot has been fired.Moreover,
new developments not considered in the Aggarwal analysis are possible in both
areas that could radically change everything.We live in interesting times.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional
interpretation of quantum mechanics, The Quantum Handshake -
Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is
available online as a hardcover or eBook at: http://www.springer.com/gp/book/9783319246406
or https://www.amazon.com/dp/3319246402.

Alternate View Columns Online: Electronic reprints of 212 or more
"The Alternate View" columns by John G. Cramer published in Analog
between 1984 and the present are currently available online at: http://www.npl.washington.edu/av
.

References:

Quantum
Computing and Bitcoin:

"Quantum
attacks on Bitcoin, and how to protect against them", Divesh Aggarwal, Gavin
K. Brennen, Troy Lee, Miklos Santha, and Marco Tomamichel, (October-2017); arXiv:1710.10377
[quant-ph]