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Topic Name: Researchers Demonstrated Basic Building Blocks for Distributed Quantum Computing Using Entangled Photons
Category: Quantum Computing
Research persons: Prem Kumar
Location: Center for Photonic Communication and Computing, United States
Details
For now, full-fledged quantum computers are the stuff of
science fiction — in last summer's blockbuster movie Transformers, the bad guys
use quantum computing to break into the
U.S. Army's secure files in
just 10 seconds flat.
But Prem Kumar, the AT&T Professor of Information Technology in the Department
of Electrical Engineering and Computer Science and the director of the
Center for Photonic
Communication and Computing, and his research group are one step closer to
realizing that technology — though for far better purposes. The group recently
demonstrated one of the basic building blocks for distributed quantum computing
using entangled photons generated in optical fibers, and their research was
published in the April 4 edition of Physical Review Letters.
"Because it is done with fiber and the technology that is already globally
deployed, we think that it is a significant step in harnessing the power of
quantum computers," Kumar says.
Quantum computing differs from classical computing in that a classical computer
works by processing “bits” that exist in two states, either one or zero. Quantum
computing uses quantum bits, or qubits, which, in addition to being one or zero
can also be in a "superposition," which is both one and zero simultaneously.
This is possible because qubits are quantum units like atoms, ions, or photons
that operate under the rules of quantum mechanics instead of classical
mechanics.
The "superposition" state allows a quantum computer to process significantly
more information than a classical computer and in a much shorter time.
The area of quantum computing took off about 14 years ago after
mathematician/physicist Peter Shor created a quantum algorithm that could factor
large integers much more efficiently than a classical computer. Such an
algorithm put the computer world in a tizzy because many web sites secure
information like credit card and bank account numbers over the Internet through
the public-key cryptography method known as RSA, after its inventors Rivest,
Shamir, and Adleman. This method is based on the assumption that it is
computationally infeasible to factor very large integers on classical computers.
Though researchers are still many years away from creating a quantum computer
capable of running the Shor algorithm, progress has been made. Kumar’s group,
which uses photons as qubits, found that they can entangle two indistinguishable
photons together in an optical fiber very efficiently by using the fiber’s
inherent nonlinear response. They also found that no matter how far you separate
the two photons in standard transmission fibers they remain entangled and are
"mysteriously" connected to each other’s quantum state.
For this paper, Kumar and his team used the fiber-generated indistinguishable
photons to implement the most basic quantum computer task – a controlled-NOT
gate, which allows two photonic qubits to interact.
"This device that we demonstrated in the lab is a two-qubit device — nowhere
near what’s needed for a quantum computer — so what can you do with it?" Kumar
says. "It’s nice to demonstrate something useful to give a boost to the field,
and there are some problems at hand that can be solved right now using what we
have."
The Defense Advanced Research
Projects Agency has funded the group’s next effort to study how to implement
a quantum network for physically demonstrating efficient public goods
strategies, which are similar to the mechanism design theory that Nobel laureate
Roger Myerson laid the foundation for while at Northwestern.
Kumar says such a network could help out with high stakes auctions, like if, for
example, the Department of Defense wanted to build an expensive airplane and
sends out a request for bids. No one company can build the entire airplane, and
there could be 15 companies that can build some part of the airplane, whether
it’s a navigation system or an engine.
But instead of just giving the project to the lowest bidder, the government
could save public dollars by allowing these companies to bid in a complicated
way that makes the process more efficient. Maybe the engine company has worked
with the fuselage company before and, if they worked together again, could be
more efficient and less expensive than another two companies working together.
They could then send in a conditional set of bids, along with regular bids if
the two companies were to work with other companies as well.
"Figuring out the best possible outcome is possible with quantum computers,"
Kumar says. "Based on these fiber-type gates that we are building utilizing
entanglement, the auctioneer has an efficient way of determining optimal
outcomes when bidders make conditional bids. When the computation is done, it
reveals only the winning strategy, and all other bids disappear."
Kumar says they hope to perform this experiment sometime in the next year.
Note for Quantum Computer
A quantum computer is hypothetical device for computation that makes direct use
of distinctively quantum mechanical phenomena, such as superposition and
entanglement, to perform operations on data. In a classical (or conventional)
computer, information is stored as bits; in a quantum computer, it is stored as
qubits (quantum bits). The basic principle of quantum computation is that the
quantum properties can be used to represent and structure data, and that quantum
mechanisms can be devised and built to perform operations with this data.
Although quantum computing is still in its infancy, experiments have been
carried out in which quantum computational operations were executed on a very
small number of qubits. Research in both theoretical and practical areas
continues at a frantic pace, and many national government and military funding
agencies support quantum computing research to develop quantum computers for
both civilian and national security purposes, such as cryptanalysis.
If large-scale quantum computers can be built, they will be able to solve
certain problems much faster than any of our current classical computers (for
example Shor's algorithm). Quantum computers are different from other computers
such as DNA computers and traditional computers based on transistors. Some
computing architectures such as optical computers may use classical
superposition of electromagnetic waves, but without some specifically quantum
mechanical resources such as entanglement, they haven't computational speed-up
as quantum computers.
A classical computer has a memory made up of bits, where each bit holds either a
one or a zero. A quantum computer maintains a sequence of qubits. A single qubit
can hold a one, a zero, or, crucially, a quantum superposition of these, and any
two qubits can be in a quantum superposition of 4 states, and three qubits in 8.
In general a quantum computer with n qubits can be in up to 2n different states
simultaneously (this compares to a normal computer that can only be in one of 2n
states at any one time). A quantum computer operates by manipulating those
qubits with (possibly a suite of) quantum logic gates.
An example of an implementation of qubits for a quantum computer could start
with the use of particles with two spin states: "up" and "down" (typically
written and ). But in fact any system possessing an observable quantity A which
is conserved under time evolution and such that A has at least two discrete and
sufficiently spaced consecutive eigenvalues, is a suitable candidate for
implementing a qubit. This is true because any such system can be mapped onto an
effective spin-1/2.
Integer factorization is believed to be computationally infeasible with an
ordinary computer for large integers that are the product of only a few prime
numbers (e.g., products of two 300-digit primes). By comparison, a quantum
computer could solve this problem more efficiently than a classical computer
using Shor's algorithm to find its factors. This ability would allow a quantum
computer to "break" many of the cryptographic systems in use today, in the sense
that there would be a polynomial time (in the number of bits of the integer)
algorithm for solving the problem. In particular, most of the popular public key
ciphers are based on the difficulty of factoring integers, including forms of
RSA. These are used to protect secure Web pages, encrypted email, and many other
types of data. Breaking these would have significant ramifications for
electronic privacy and security. The only way to increase the security of an
algorithm like RSA would be to increase the key size and hope that an adversary
does not have the resources to build and use a powerful enough quantum computer.
Note for Quantum Bit
A quantum bit, or qubit is a unit of quantum information. That information is
described by a state vector in a two-level quantum mechanical system which is
formally equivalent to a two-dimensional vector space over the complex numbers.
Benjamin Schumacher discovered a way of interpreting quantum states as
information. He came up with a way of compressing the information in a state,
and storing the information on a smaller number of states. This is now known as
Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51,
2738), Schumacher states that the term qubit was invented in jest, during his
conversations with Bill Wootters.
A bit is the base of computer information. Regardless of its physical
representation, it is always read as either a 0 or a 1. An analogy to this is a
light switch–the down position can represent 0 (normally equated to off) and the
up position can represent 1 (normally equated to on).
A qubit has some similarities to a classical bit, but is overall very different.
Like a bit, a qubit can have two possible values–normally a 0 or a 1. The
difference is that whereas a bit must be either 0 or 1, a qubit can be 0, 1, or
a superposition of both.
Any two-level system can be used as a qubit. Multilevel systems can be used as
well, if they possess two states that can be effectively decoupled from the rest
(e.g., ground state and first excited state of a nonlinear oscillator). There
are various proposals. Several physical implementations which approximate
two-level systems to various degrees were successfully realized. Similarly to a
classical bit where the state of a transistor in a processor, the magnetization
of a surface in a hard disk and the presence of current in a cable can all be
used to represent bits in the same computer, an eventual quantum computer is
likely to use various combinations of qubits in its design.
Note for Shor's Algorithm
Shor's algorithm is a quantum algorithm for integer factorization. On a quantum
computer, Shor's algorithm takes time O((log N)3) to factor an integer N. This
is exponentially faster than the best-known classical factoring algorithm, which
works in time about . Peter Shor discovered the eponymous algorithm in 1994.
Shor's algorithm is important because it breaks a widely used public-key
cryptography scheme known as RSA. RSA is based on the assumption that factoring
large numbers is computationally infeasible. So far as is known, this assumption
is valid for classical computers. No classical algorithm is known that can
factor in time polynomial in log N. However, Shor's algorithm shows that
factoring is efficient on a quantum computer, so a quantum computer could
"break" RSA.
Note for Quantum Superposition
Quantum superposition is the fundamental law of quantum kinematics. It defines
the allowed state space of a quantum mechanical system.
The principle of superposition states that if the world can be in any
configuration, any possible arrangement of particles or fields, and if the world
could also be in another configuration, then the world can also be in a state
which is a mixture of the two, where the amount of each configuration that is in
the mixture is specified by a complex number.
Applying the superposition principle to a quantum mechanical particle, the
configurations of the particle are all positions, so the superpositions make a
complex wave in space. The coefficients of the linear superposition are a wave
which describes the particle as best as is possible, and whose amplitude
interferes according to the Huygens principle.
For any physical quantity in quantum mechanics, there is a list of all the
states where the quantity has some value. These states are necessarily
perpendicular to each other using the Euclidean notion of perpendicularity which
comes from sums-of-squares length, except that they also must not be i multiples
of each other. This list of perpendicular states has an associated value which
is the value of the physical quantity. The superposition principle guarantees
that any state can be written as a combination of states of this form with
complex coefficients.
In addition to Kumar, authors include Jun Chen, Joseph Altepeter, Milja Medic,
Kim Fook Lee, Burc Gokden, all of Northwestern. Robert Hadfield and Sae Woo Nam
of the National Institute of Standard and Technology were also authors.
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