Quantum computing is the study of a currently hypothetical model of computation. Whereas traditional models of computing such as the Turing machine or Lambda calculus rely on "classical" representations of computational memory, a quantum computation could transform the memory into a quantum superposition of possible classical states. A quantum computer is a device that could perform such computation.
Quantum computing began in the early 1980s when physicist Paul Benioff proposed a quantum mechanical model of the Turing machine. Richard Feynman and Yuri Manin later suggested that a quantum computer could perform simulations that are out of reach for classical computers. In 1994, Peter Shor developed a polynomial-time quantum algorithm for factoring integers. This was a major breakthrough in the subject: an important method of asymmetric key exchange known as RSA
is based on the belief that factoring integers is computationally
difficult. The existence of a polynomial-time quantum algorithm proves
that one of the most widely-used cryptographic protocols is vulnerable
to an adversary who possesses a quantum computer.
Experimental efforts towards building a quantum computer began after a slew of results known as fault-tolerance threshold theorems.
These theorems proved that a quantum computation could be efficiently
corrected against the effects of large classes of physically realistic
noise models. One early result demonstrated parts of Shor's algorithm in a liquid-state nuclear magnetic resonance experiment. Other notable experiments have been performed in superconducting systems, ion-traps, and photonic systems.
Despite rapid and impressive experimental progress, most
researchers believe that "fault-tolerant quantum computing [is] still a
rather distant dream".
As of September 2019, no scalable quantum computing hardware has been
demonstrated. Nevertheless, there is an increasing amount of investment
in quantum computing by governments, established companies, and
start-ups. Current research focusses on building and using near-term intermediate-scale devices and demonstrating quantum supremacy alongside the long-term goal of building and using a powerful and error-free quantum computer.
The field of quantum computing is closely related to quantum information science, which includes quantum cryptography and quantum communication.
Basic concept
In most models of classical computation, the computer has access to memory.
This is a system that can be found in one of a finite set of possible
states, each of which is physically distinct. It is frequently
convenient to represent the state of this memory as a string of symbols;
most simply, as a string of the symbols 0 and 1. In this scenario, the
fundamental unit of memory is called a bit and we can measure the "size" of the memory in terms of the number of bits needed to represent fully the state of the memory.
If the memory obeys the laws of quantum physics, the state of the memory could be found in a quantum superposition
of different possible "classical" states. If the classical states are
to be represented as a string of bits, the quantum memory could be found
in any superposition of the possible bit strings. In the quantum
scenario, the fundamental unit of memory is called a qubit.
The defining property of a quantum computer is the ability to
turn classical memory states into quantum memory states, and vice-versa.
This is not possible with present-day computers because they are
carefully designed to ensure that the memory never deviates from clearly
defined informational states. To clarify this point, consider that
information is normally transmitted through the computer as an
electrical signal that could have one of two easily distinguished voltages. If the voltages were to become indistinct (in a classical or quantum sense), the computer would no longer operate correctly.
Of course, in the end we are classical beings and we can only
observe classical states. That means the quantum computer must complete
its task by returning to us a classical output. To produce these
classical outputs, the quantum computer is obliged to measure parts of
the memory at various times throughout the computation. The measurement process is inherently probabilistic,
meaning that the output of a quantum algorithm is frequently random.
The task of a quantum algorithm designer is to ensure that the
randomness is tailored to the needs of the problem at hand. For example,
if the quantum computer is searching a quantum database for one of
several marked items, we can ask the quantum computer to return one of
the marked items at random. The quantum computer succeeds in this task
as long as it is unlikely to return an unmarked item.
Quantum operations
The prevailing model of quantum computation describes the computation in terms of a network of quantum logic gates. What follows is a brief treatment of the subject based upon Chapter 4 of Nielsen and Chuang.
We may represent the state of a computer memory as a vector whose
length is equal to the number of possible states of the memory. So a
memory consisting of bits of information has possible states, and the vector representing that memory state has
entries. In the classical view, all but one of the entries of this
vector would be zero and the remaining entry would be one. The vector
should be viewed as a probability vector and represents the fact that the memory is to be found in a particular state with 100% probability (i.e. a probability of one).
In quantum mechanics, probability vectors are generalised to density operators. This is the technically rigorous mathematical foundation for quantum logic gates,
but the intermediate quantum state vector formalism is usually
introduced first because it is conceptually simpler. Here we focus only
on the quantum state vector formalism for simplicity.
We begin by considering a simple memory consisting of only one
bit. This memory may be found in one of two states: the zero state or
the one state. We may represent the state of this memory using Dirac notation so that
A quantum memory may then be found in any quantum superposition of the two classical states and :
In general, the coefficients and are complex numbers. In this scenario, we say that one qubit of information can be encoded into the quantum memory. The state
is not itself a probability vector but can be connected with a
probability vector via a measurement operation. If we choose to measure
the quantum memory to determine if the state is or (this is known as a computational basis measurement), we would observe the zero state with probability and the one state with probability . Please see the article on quantum amplitudes for further information.
To manipulate the state of this one-qubit quantum memory, we imagine applying quantum logic gates analogous to classical logic gates. One obvious gate is the NOT gate, which can be represented by a matrix
We can formally apply this logic gate to a quantum state vector through matrix multiplication. Thus we find and
as expected. But this is not the only interesting single-qubit quantum
logic gate. We might, for example, imagine applying one of the other two
Pauli matrices.
We may imagine extending single qubit gates to operate on
multiqubit quantum memories in two important ways. One way to operate a
single qubit gate on a multiqubit memory is simply to select a qubit and
apply that gate to the target qubit whilst leaving the remainder of the
memory unaffected. Another way is to apply the gate to its target only
if another part of the memory is in a desired state. We illustrate this
with another example.
Consider a two-qubit quantum memory. Its possible states are
We may then define the CNOT gate as the following matrix:
It is easy to check that , , , and . In other words, the CNOT applies a NOT gate ( from before) to the second qubit if and only if the first qubit is in the state . If the first qubit is , nothing is done to either qubit.
The preceding discussion is of course a very brief
introduction to the concept of a quantum logic gate. Please see the
article on quantum logic gates for further information.
To put the story together, we can describe a quantum computation
as a network of quantum logic gates and measurements. One can always
'defer' a measurement to the end of a quantum computation, though this
can come at a computational cost according to some cost models. Because
of this possibility of deferring a measurement, most quantum circuits
depict a network consisting only of quantum logic gates and no
measurements. For more details on the sequences of operations used for
various quantum algorithms, see universal quantum computer, Shor's algorithm, Grover's algorithm, Deutsch–Jozsa algorithm, amplitude amplification, quantum Fourier transform, quantum gate, quantum adiabatic algorithm and quantum error correction.
One can represent any quantum computation as a network of quantum
logic gates from a fairly small family of gates. A choice of gate
family that enables this construction is known as a universal gate set.
One common such set includes all single-qubit gates as well as the CNOT
gate from above. This means any quantum computation can be performed by
executing a sequence of single-qubit gates together with CNOT gates.
Though this gate set is infinite, it can be replaced with a finite gate
set by appealing to the Solovay-Kitaev theorem.
Potential
Cryptography
Integer factorization, which underpins the security of public key cryptographic
systems, is believed to be computationally infeasible with an ordinary
computer for large integers if they are the product of few prime numbers (e.g., products of two 300-digit primes). By comparison, a quantum computer could efficiently solve this problem 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 digits 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 or the discrete logarithm problem, both of which can be solved by Shor's algorithm. In particular, the RSA, Diffie–Hellman, and elliptic curve Diffie–Hellman
algorithms could be broken. 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.
However, other cryptographic algorithms do not appear to be broken by those algorithms.
Some public-key algorithms are based on problems other than the integer
factorization and discrete logarithm problems to which Shor's algorithm
applies, like the McEliece cryptosystem based on a problem in coding theory. Lattice-based cryptosystems are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the dihedral hidden subgroup problem, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a symmetric (secret key) algorithm by brute force requires time equal to roughly 2n/2 invocations of the underlying cryptographic algorithm, compared with roughly 2n in the classical case,
meaning that symmetric key lengths are effectively halved: AES-256
would have the same security against an attack using Grover's algorithm
that AES-128 has against classical brute-force search. Quantum cryptography
could potentially fulfill some of the functions of public key
cryptography. Quantum-based cryptographic systems could, therefore, be
more secure than traditional systems against quantum hacking.
Quantum search
Besides
factorization and discrete logarithms, quantum algorithms offering a
more than polynomial speedup over the best known classical algorithm
have been found for several problems, including the simulation of quantum physical processes from chemistry and solid state physics, the approximation of Jones polynomials, and solving Pell's equation.
No mathematical proof has been found that shows that an equally fast
classical algorithm cannot be discovered, although this is considered
unlikely. However, quantum computers offer polynomial speedup for some problems. The most well-known example of this is quantum database search, which can be solved by Grover's algorithm
using quadratically fewer queries to the database than that are
required by classical algorithms. In this case, the advantage is not
only provable but also optimal, it has been shown that Grover's
algorithm gives the maximal possible probability of finding the desired
element for any number of oracle lookups. Several other examples of
provable quantum speedups for query problems have subsequently been
discovered, such as for finding collisions in two-to-one functions and
evaluating NAND trees.
Problems that can be addressed with Grover's algorithm have the following properties:
- There is no searchable structure in the collection of possible answers,
- The number of possible answers to check is the same as the number of inputs to the algorithm, and
- There exists a boolean function which evaluates each input and determines whether it is the correct answer
For problems with all these properties, the running time of Grover's algorithm
on a quantum computer will scale as the square root of the number of
inputs (or elements in the database), as opposed to the linear scaling
of classical algorithms. A general class of problems to which Grover's algorithm can be applied is Boolean satisfiability problem. In this instance, the database through which the algorithm is iterating is that of all possible answers. An example (and possible) application of this is a password cracker that attempts to guess the password or secret key for an encrypted file or system. Symmetric ciphers such as Triple DES and AES are particularly vulnerable to this kind of attack. This application of quantum computing is a major interest of government agencies.
Quantum simulation
Since
chemistry and nanotechnology rely on understanding quantum systems, and
such systems are impossible to simulate in an efficient manner
classically, many believe quantum simulation will be one of the most important applications of quantum computing.
Quantum simulation could also be used to simulate the behavior of atoms
and particles at unusual conditions such as the reactions inside a collider.
Quantum annealing and adiabatic optimization
Quantum annealing or Adiabatic quantum computation
relies on the adiabatic theorem to undertake calculations. A system is
placed in the ground state for a simple Hamiltonian, which is slowly
evolved to a more complicated Hamiltonian whose ground state represents
the solution to the problem in question. The adiabatic theorem states
that if the evolution is slow enough the system will stay in its ground
state at all times through the process.
Solving linear equations
The Quantum algorithm for linear systems of equations
or "HHL Algorithm", named after its discoverers Harrow, Hassidim, and
Lloyd, is expected to provide speedup over classical counterparts.
Quantum supremacy
John Preskill has introduced the term quantum supremacy to refer to the hypothetical speedup advantage that a quantum computer would have over a classical computer in a certain field. Google announced in 2017 that it expected to achieve quantum supremacy by the end of the year though that did not happen. IBM
said in 2018 that the best classical computers will be beaten on some
practical task within about five years and views the quantum supremacy
test only as a potential future benchmark. Although skeptics like Gil Kalai doubt that quantum supremacy will ever be achieved, Google has been reported to have done so, with calculations more than 3,000,000 times as fast as those of Summit, generally considered the world's fastest computer. Bill Unruh doubted the practicality of quantum computers in a paper published back in 1994. Paul Davies argued that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the holographic principle.
Obstacles
There are a number of technical challenges in building a large-scale quantum computer, and thus far quantum computers have yet to solve a problem faster than a classical computer. David DiVincenzo, of IBM, listed the following requirements for a practical quantum computer:
- scalable physically to increase the number of qubits;
- qubits that can be initialized to arbitrary values;
- quantum gates that are faster than decoherence time;
- universal gate set;
- qubits that can be read easily.
Quantum decoherence
One of the greatest challenges is controlling or removing quantum decoherence.
This usually means isolating the system from its environment as
interactions with the external world cause the system to decohere.
However, other sources of decoherence also exist. Examples include the
quantum gates, and the lattice vibrations and background thermonuclear
spin of the physical system used to implement the qubits. Decoherence is
irreversible, as it is effectively non-unitary, and is usually
something that should be highly controlled, if not avoided. Decoherence
times for candidate systems in particular, the transverse relaxation
time T2 (for NMR and MRI technology, also called the dephasing time), typically range between nanoseconds and seconds at low temperature.
Currently, some quantum computers require their qubits to be cooled to
20 millikelvins in order to prevent significant decoherence.
As a result, time-consuming tasks may render some quantum
algorithms inoperable, as maintaining the state of qubits for a long
enough duration will eventually corrupt the superpositions.
These issues are more difficult for optical approaches as the
timescales are orders of magnitude shorter and an often-cited approach
to overcoming them is optical pulse shaping.
Error rates are typically proportional to the ratio of operating time
to decoherence time, hence any operation must be completed much more
quickly than the decoherence time.
As described in the Quantum threshold theorem,
if the error rate is small enough, it is thought to be possible to use
quantum error correction to suppress errors and decoherence. This allows
the total calculation time to be longer than the decoherence time if
the error correction scheme can correct errors faster than decoherence
introduces them. An often cited figure for the required error rate in
each gate for fault-tolerant computation is 10−3, assuming the noise is depolarizing.
Meeting this scalability condition is possible for a wide range
of systems. However, the use of error correction brings with it the cost
of a greatly increased number of required qubits. The number required
to factor integers using Shor's algorithm is still polynomial, and
thought to be between L and L2, where L
is the number of qubits in the number to be factored; error correction
algorithms would inflate this figure by an additional factor of L. For a 1000-bit number, this implies a need for about 104 bits without error correction. With error correction, the figure would rise to about 107 bits. Computation time is about L2 or about 107 steps and at 1 MHz, about 10 seconds.
A very different approach to the stability-decoherence problem is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.
Developments
Quantum computing models
There
are a number of quantum computing models, distinguished by the basic
elements in which the computation is decomposed. The four main models of
practical importance are:
- Quantum gate array (computation decomposed into a sequence of few-qubit quantum gates)
- One-way quantum computer (computation decomposed into a sequence of one-qubit measurements applied to a highly entangled initial state or cluster state)
- Adiabatic quantum computer, based on quantum annealing (computation decomposed into a slow continuous transformation of an initial Hamiltonian into a final Hamiltonian, whose ground states contain the solution)
- Topological quantum computer (computation decomposed into the braiding of anyons in a 2D lattice)
The quantum Turing machine
is theoretically important but the direct implementation of this model
is not pursued. All four models of computation have been shown to be
equivalent; each can simulate the other with no more than polynomial
overhead.
Physical realizations
For
physically implementing a quantum computer, many different candidates
are being pursued, among them (distinguished by the physical system used
to realize the qubits):
- Superconducting quantum computing (qubit implemented by the state of small superconducting circuits (Josephson junctions))
- Trapped ion quantum computer (qubit implemented by the internal state of trapped ions)
- Optical lattices (qubit implemented by internal states of neutral atoms trapped in an optical lattice)
- Quantum dot computer, spin-based (e.g. the Loss-DiVincenzo quantum computer) (qubit given by the spin states of trapped electrons)
- Quantum dot computer, spatial-based (qubit given by electron position in double quantum dot)
- Coupled Quantum Wire (qubit implemented by a pair of Quantum Wires coupled by a Quantum Point Contact)
- Nuclear magnetic resonance quantum computer (NMRQC) implemented with the nuclear magnetic resonance of molecules in solution, where qubits are provided by nuclear spins within the dissolved molecule and probed with radio waves
- Solid-state NMR Kane quantum computers (qubit realized by the nuclear spin state of phosphorus donors in silicon)
- Electrons-on-helium quantum computers (qubit is the electron spin)
- Cavity quantum electrodynamics (CQED) (qubit provided by the internal state of trapped atoms coupled to high-finesse cavities)
- Molecular magnet (qubit given by spin states)
- Fullerene-based ESR quantum computer (qubit based on the electronic spin of atoms or molecules encased in fullerenes)
- Linear optical quantum computer (qubits realized by processing states of different modes of light through linear elements e.g. mirrors, beam splitters and phase shifters)
- Diamond-based quantum computer (qubit realized by the electronic or nuclear spin of nitrogen-vacancy centers in diamond)
- Bose-Einstein condensate-based quantum computer
- Transistor-based quantum computer – string quantum computers with entrainment of positive holes using an electrostatic trap
- Rare-earth-metal-ion-doped inorganic crystal based quantum computers (qubit realized by the internal electronic state of dopants in optical fibers)
- Metallic-like carbon nanospheres based quantum computers
A large number of candidates demonstrates that the topic, in spite of
rapid progress, is still in its infancy. There is also a vast amount of
flexibility.
Timeline
In 1980, Paul Benioff
describes the first quantum mechanical model of a computer. In this
work, Benioff showed that a computer could operate under the laws of
quantum mechanics by describing a Schrodinger equation description of Turing machines, laying a foundation for further work in quantum computing. The paper was submitted in June 1979 and published in April of 1980. Russian mathematician Yuri Manin then motivates the development of quantum computers.
In 1981, at the First Conference on the Physics of Computation held at MIT and co-organized by MIT and IBM, Paul Benioff and Richard Feynman
give talks on quantum computing. Benioff built on his earlier 1980 work
showing that a computer can operate under the laws of quantum
mechanics. The talk was titled “Quantum mechanical Hamiltonian models of
discrete processes that erase their own histories: application to
Turing machines”. In Feynman’s talk, he observed that it appeared to be
impossible to efficiently simulate an evolution of a quantum system on a
classical computer, and he proposed a basic model for a quantum
computer.
Urging the world to build a quantum computer, he said, "Nature isn't
classical, dammit, and if you want to make a simulation of nature, you'd
better make it quantum mechanical, and by golly, it's a wonderful
problem because it doesn't look so easy."
In 1982, Paul Benioff further develops his original model of a quantum mechanical Turing machine.
In 1984, IBM scientists Charles Bennett and Gilles Brassard published BB84, the world's first quantum cryptography protocol.
In 1985, David Deutsch describes the first universal quantum computer. Just as a Universal Turing machine can simulate any other Turing machine efficiently (Church-Turing thesis), so the universal quantum computer is able to simulate any other quantum computer with at most a polynomial slowdown.
In 1989, Bikas K. Chakrabarti
& collaborators proposes the idea that quantum fluctuations could
help explore rough energy landscapes by escaping from local minima of
glassy systems having tall but thin barriers by tunneling (instead of
climbing over using thermal excitations), suggesting the effectiveness
of quantum annealing over classical simulated annealing.
In 1992, David Deutsch and Richard Jozsa propose a computational problem that can be solved efficiently with the determinist Deutsch–Jozsa algorithm
on a quantum computer, but for which no deterministic classical
algorithm is possible. This was perhaps the earliest result in the computational complexity of quantum computers, proving that they were capable of performing some well-defined computational task more efficiently than any classical computer.
In 1993, an international group of six scientists, including Charles Bennett, showed that perfect quantum teleportation is possible in principle, but only if the original is destroyed.
In 1994, Peter Shor, at AT&T's Bell Labs,
discovered an important quantum algorithm, which allows a quantum
computer to factor large integers exponentially much faster than the
best known classical algorithm. Shor's algorithm can theoretically break many of the Public-key cryptography systems in use today, sparking a tremendous interest in quantum computers.
In 1996, the DiVincenzo's criteria
are published, which are a list of conditions that are necessary for
constructing a quantum computer, proposed by the theoretical physicist David P. DiVincenzo in his 2000 paper "The Physical Implementation of Quantum Computation".
In 2001, researchers demonstrated Shor's algorithm to factor 15 using a 7-qubit NMR computer.
In 2005, researchers at the University of Michigan built a semiconductor chip ion trap. Such devices from standard lithography may point the way to scalable quantum computing.
In 2009, researchers at Yale University created the first solid-state quantum processor. The 2-qubit superconducting chip had artificial atom qubits made of a billion aluminum atoms that acted like a single atom that could occupy two states.
A team at the University of Bristol also created a silicon chip based on quantum optics, able to run Shor's algorithm.
Further developments were made in 2010.
Springer publishes a journal, Quantum Information Processing, devoted to the subject.
In February 2010, Digital Combinational Circuits like an adder,
subtractor etc. are designed with the help of Symmetric Functions
organized from different quantum gates.
In April 2011, a team of scientists from Australia and Japan made a breakthrough in quantum teleportation,
successfully transferring a complex set of quantum data with full
transmission integrity, without affecting the qubits' superpositions.
In 2011, D-Wave Systems announced the first commercial quantum annealer, the D-Wave One, claiming a 128-qubit processor. On 25 May 2011, Lockheed Martin agreed to purchase a D-Wave One system. Lockheed and the University of Southern California (USC) will house the D-Wave One at the newly formed USC Lockheed Martin Quantum Computing Center.
D-Wave's engineers designed the chips with an empirical approach,
focusing on solving particular problems. Investors liked this more than
academics, who said D-Wave had not demonstrated that they really had a
quantum computer. Criticism softened after a D-Wave paper in Nature that proved that the chips have some quantum properties.
Two published papers have suggested that the D-Wave machine's operation
can be explained classically, rather than requiring quantum models. Later work showed that classical models are insufficient when all available data is considered.
Experts remain divided on the ultimate classification of the D-Wave
systems though their quantum behavior was established concretely with a
demonstration of entanglement.
During the same year, researchers at the University of Bristol created an all-bulk optics system that ran a version of Shor's algorithm to successfully factor 21.
In September 2011, researchers proved quantum computers can be made with a Von Neumann architecture (separation of RAM).
In November 2011, researchers factorized 143 using 4 qubits.
In February 2012, IBM scientists said that they had made several
breakthroughs in quantum computing with superconducting integrated
circuits.
In April 2012, a multinational team of researchers from the University of Southern California, the Delft University of Technology, the Iowa State University of Science and Technology, and the University of California, Santa Barbara
constructed a 2-qubit quantum computer on a doped diamond crystal that
can easily be scaled up and is functional at room temperature. Two
logical qubit directions of electron spin and nitrogen kernels spin were
used, with microwave pulses. This computer ran Grover's algorithm,
generating the right answer on the first try in 95% of cases.
In September 2012, Australian researchers at the University of New South Wales
said the world's first quantum computer was just 5 to 10 years away,
after announcing a global breakthrough enabling the manufacture of its
memory building blocks. A research team led by Australian engineers
created the first working qubit based on a single atom in silicon,
invoking the same technological platform that forms the building blocks
of modern-day computers.
In October 2012, Nobel Prizes were awarded to David J. Wineland and Serge Haroche for their basic work on understanding the quantum world, which may help make quantum computing possible.
In November 2012, the first quantum teleportation from one macroscopic object to another was reported by scientists at the University of Science and Technology of China.
In December 2012, 1QBit, the first dedicated quantum computing software company, was founded in Vancouver, BC.
1QBit is the first company to focus exclusively on commercializing
software applications for commercially available quantum computers,
including the D-Wave Two. 1QBit's research demonstrated the ability of superconducting quantum annealing processors to solve real-world problems.
In February 2013, a new technique, boson sampling,
was reported by two groups using photons in an optical lattice that is
not a universal quantum computer, but may be good enough for practical
problems.
In May 2013, Google announced that it was launching the Quantum Artificial Intelligence Lab, hosted by NASA's Ames Research Center, with a 512-qubit D-Wave quantum computer. The Universities Space Research Association (USRA) will invite researchers to share time on it with the goal of studying quantum computing for machine learning.
Google added that they had "already developed some quantum machine
learning algorithms" and had "learned some useful principles", such as
that "best results" come from "mixing quantum and classical computing".
In early 2014, based on documents provided by former NSA contractor Edward Snowden, it was reported that the U.S. National Security Agency
(NSA) is running a $79.7 million research program titled "Penetrating
Hard Targets", to develop a quantum computer capable of breaking
vulnerable encryption.
In 2014, a group of researchers from ETH Zürich, USC, Google, and Microsoft
reported a definition of quantum speedup, and were not able to measure
quantum speedup with the D-Wave Two device, but did not explicitly rule
it out.
In 2014, researchers at University of New South Wales used
silicon as a protectant shell around qubits, making them more accurate,
increasing the length of time they will hold information, and possibly
making quantum computers easier to build.
In April 2015, IBM scientists claimed two critical advances
towards the realization of a practical quantum computer, claiming the
ability to detect and measure both kinds of quantum errors
simultaneously, as well as a new, square quantum bit circuit design that
could scale to larger dimensions.
In October 2015, QuTech successfully conducted the Loophole-free
Bell inequality violation test using electron spins separated by 1.3
kilometres.
In October 2015, researchers at the University of New South Wales built a quantum logic gate in silicon for the first time.
In December 2015, NASA publicly displayed the world's first fully operational quantum computer made by D-Wave Systems at the Quantum Artificial Intelligence Lab at its Ames Research Center.
The device was purchased in 2013 via a partnership with Google and
Universities Space Research Association. The presence and use of quantum
effects in the D-Wave quantum processing unit is more widely accepted. In some tests, it can be shown that the D-Wave quantum annealing processor outperforms Selby’s algorithm. Only two of these computers have been made so far.
In May 2016, IBM Research announced
that for the first time ever it is making quantum computing available
to members of the public via the cloud, who can access and run
experiments on IBM’s quantum processor, calling the service the IBM Quantum Experience. The quantum processor is composed of five superconducting qubits and is housed at IBM's Thomas J. Watson Research Center.
In August 2016, scientists at the University of Maryland successfully built the first reprogrammable quantum computer.
In October 2016, the University of Basel
described a variant of the electron-hole based quantum computer, which
instead of manipulating electron spins, uses electron holes in a
semiconductor at low (mK) temperatures, which are much less vulnerable
to decoherence. This has been dubbed the "positronic" quantum computer,
as the quasi-particle behaves as if it has a positive electrical charge.
In March 2017, IBM announced an industry-first initiative, called IBM Q, to build commercially available universal quantum computing systems. The company also released a new API for the IBM Quantum Experience
that enables developers and programmers to begin building interfaces
between its existing 5-qubit cloud-based quantum computer and classical
computers, without needing a deep background in quantum physics.
In May 2017, IBM announced
that it had successfully built and tested its most powerful universal
quantum computing processors. The first is a 16-qubit processor that
will allow for more complex experimentation than the previously
available 5-qubit processor. The second is IBM's first prototype
commercial processor with 17 qubits, and leverages significant
materials, device, and architecture improvements to make it the most
powerful quantum processor created to date by IBM.
In July 2017, a group of U.S. researchers announced a quantum simulator with 51 qubits. The announcement was made by Mikhail Lukin of Harvard University at the International Conference on Quantum Technologies in Moscow.
A quantum simulator differs from a computer. Lukin’s simulator was
designed to solve one equation. Solving a different equation would
require building a new system, whereas a computer can solve many
different equations.
In September 2017, IBM Research scientists used a 7-qubit device
to model beryllium hydride molecule, the largest molecule to date by a
quantum computer. The results were published as the cover story in the peer-reviewed journal Nature.
In October 2017, IBM Research scientists successfully "broke the 49-qubit simulation barrier" and simulated 49- and 56-qubit short-depth circuits, using the Lawrence Livermore National Laboratory's Vulcan supercomputer, and the University of Illinois' Cyclops Tensor Framework (originally developed at the University of California).
In November 2017, the University of Sydney research team successfully made a microwave circulator, an important quantum computer part, that was 1000 times smaller than a conventional circulator, by using topological insulators to slow down the speed of light in a material.
In December 2017, IBM announced
its first IBM Q Network clients. The companies, universities, and labs
that will explore practical business and science quantum applications,
using IBM Q 20-qubit commercial systems, include: JPMorgan Chase,
Daimler AG, Samsung, JSR Corporation, Barclays, Hitachi Metals, Honda,
Nagase, Keio University, Oak Ridge National Lab, Oxford University and
University of Melbourne.
In December 2017, Microsoft released a preview version of a "Quantum Development Kit", which includes a programming language, Q# that can be used to write programs that are run on an emulated quantum computer.
In 2017, D-Wave was reported to be selling a 2,000-qubit quantum computer.
In late 2017 and early 2018, IBM, Intel, and Google
each reported testing quantum processors containing 50, 49, and 72
qubits, respectively, all realized using superconducting circuits. By
number of qubits, these circuits are approaching the range in which
simulating their quantum dynamics is expected to become prohibitive on
classical computers, although it has been argued that further
improvements in error rates are needed to put classical simulation out
of reach.
In February 2018, scientists reported, for the first time, the discovery of a new form of light, which may involve polaritons, that could be useful in the development of quantum computers.
In February 2018, QuTech reported successfully testing a silicon-based two-spin-qubits quantum processor.
In June 2018, Intel began testing a silicon-based spin-qubit processor, manufactured in the company's D1D Fab in Oregon.
In July 2018, a team led by the University of Sydney achieved the
world's first multi-qubit demonstration of a quantum chemistry
calculation performed on a system of trapped ions, one of the leading
hardware platforms in the race to develop a universal quantum computer.
In December 2018, IonQ reported that its machine could be built as large as 160 qubits.
In January 2019, IBM launched IBM Q System One, its first integrated quantum computing system for commercial use. IBM Q System One is designed by industrial design company Map Project Office and interior design company Universal Design Studio.
In March 2019, a group of Russian scientists used the open-access IBM quantum computer to demonstrate a protocol for the complex conjugation of the probability amplitudes needed for time reversal of a physical process, in this case, for an electron scattered on a two-level impurity, a two-qubit experiment. However, for the three-qubit experiment, the amplitude fell below 50%
(failure of time reversal, due to its increased complexity).
In September 2019 Google AI Quantum and NASA published a paper "Quantum supremacy using a programmable superconducting processor" and supplementary material which was later removed from NASA.
Relation to computational complexity theory
The class of problems that can be efficiently solved by quantum computers is called BQP, for "bounded error, quantum, polynomial time". Quantum computers only run probabilistic algorithms, so BQP on quantum computers is the counterpart of BPP
("bounded error, probabilistic, polynomial time") on classical
computers. It is defined as the set of problems solvable with a
polynomial-time algorithm, whose probability of error is bounded away
from one half.
A quantum computer is said to "solve" a problem if, for every instance,
its answer will be right with high probability. If that solution runs
in polynomial time, then that problem is in BQP.
BQP is contained in the complexity class #P (or more precisely in the associated class of decision problems P#P), which is a subclass of PSPACE.
BQP is suspected to be disjoint from NP-complete and a strict superset of P, but that is not known. Both integer factorization and discrete log
are in BQP. Both of these problems are NP problems suspected to be
outside BPP, and hence outside P. Both are suspected to not be
NP-complete. There is a common misconception that quantum computers can
solve NP-complete problems in polynomial time. That is not known to be
true, and is generally suspected to be false.
The capacity of a quantum computer to accelerate classical
algorithms has rigid limits—upper bounds of quantum computation's
complexity. The overwhelming part of classical calculations cannot be
accelerated on a quantum computer. A similar fact prevails for particular computational tasks, like the search problem, for which Grover's algorithm is optimal.
Bohmian Mechanics
is a non-local hidden variable interpretation of quantum mechanics. It
has been shown that a non-local hidden variable quantum computer could
implement a search of an N-item database at most in steps. This is slightly faster than the steps taken by Grover's algorithm. Neither search method will allow quantum computers to solve NP-Complete problems in polynomial time.
Although quantum computers may be faster than classical computers
for some problem types, those described above cannot solve any problem
that classical computers cannot already solve. A Turing machine can simulate these quantum computers, so such a quantum computer could never solve an undecidable problem like the halting problem. The existence of "standard" quantum computers does not disprove the Church–Turing thesis. It has been speculated that theories of quantum gravity, such as M-theory or loop quantum gravity, may allow even faster computers to be built. Currently, defining computation in such theories is an open problem due to the problem of time,
i.e., there currently exists no obvious way to describe what it means
for an observer to submit input to a computer and later receive output.