**Experimental Quantum Computing to Solve Systems of Linear Equations**

X.-D. Cai et al

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

Read more: http://prl.aps.org/abstract/PRL/v110/i23/e230501

Read also: http://physicsworld.com/cws/article/news/2013/jun/12/quantum-computer-solves-simple-linear-equations

# Tag Archives: Quantum computing

# Solving systems of linear equations on a quantum computer

**Stefanie Barz, Ivan Kassal, Martin Ringbauer, Yannick Ole Lipp, Borivoje Dakic, Alán Aspuru-Guzik, Philip Walther**

Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers, making for one of the most promising applications of quantum computation. Here, we demonstrate this quantum algorithm by implementing various instances on a photonic quantum computing architecture. Our implementation involves the application of two consecutive entangling gates on the same pair of polarisation-encoded qubits. We realize two separate controlled-NOT gates where the successful operation of the first gate is heralded by a measurement of two ancillary photons. Our work thus demonstrates the implementation of a quantum algorithm with high practical significance as well as an important technological advance which brings us closer to a comprehensive control of photonic quantum information.

Read more: http://arxiv.org/pdf/1302.1210v1.pdf

# Landmark in quantum computing

## Australians Create 1-Atom Silicon Quantum Computing Bit (quBit)

World’s first ever single-atom silicon quantum bit opens the door to new quantum computers based on traditional materials

Using a silicon circuit with a phosphorous donor atom, researchers at the University of New South Wales have achieved a critical step forward in the path to quantum computers.

Past efforts have been limited to making nanostructures to read spin, or to making quBits that stored it. This work represents a bold step forward as it’s reportedly the first single-atom silicon quBit system endowed with both the ability to read and write the bit coherently.

The bit showed excellent coherence, lasting for 200 micro-seconds (0.2 milliseconds), or about 400,000 clock cycles on a 2 GHz CPU. The paper suggests that with tighter control of the phosphorous doping, coherence could be extended to last for seconds.

The quBit system was manufactured using standard complementary metal-oxide-semiconductor (CMOS) techniques. Nanostructures were grown on silicon-dioxide.

Electron spin was first set by 1 Tesla magnetic field — around the intensity of the magnetic field at the surface of a Neodymium magnet (by contrast the Earth’s magnetic field is a near 31 microTeslas at the Equator).

The electron temperature was then brought down to 300 milliKelvin (note to readers: milliKelvin coolers are pretty expensive, as one might think — but work is being done to bring down prices).

Reads were accomplished given a technique called single-shot projective measurement.The long term goal of this kind of research is to create nanostructure quBits that use traditional processes, with some extra tweaks (cooling, high power magnetic sync) to encode information in the spins of electrons, and then use other nanostructures to read that stored information coherently.

QuBits could then be applied to one of two purposes.

First, quBits could be used with traditional transistor circuitry to provide dense storage, as one quBit (with the right read/write nanostructure equipment) could store multiple states (0, 1, 2, 3, …) (via different electron spins) versus a traditional bit, which only can have two states (0, 1).

Second, quBits could be coupled together to produce a quantum computer capable of solving certain types of problems like integer factorization far faster than traditional computers.

The new work still has some issues before its ready for prime-time — relatively short coherence, the need for intense cooling — but it also is promising given its use of traditional materials and manufacturing techniques

The work was presented in the prestigious peer-review journal *Nature*. The first author was Jarryd Pla and the senior author was Professor Andrea Morello. The work was funded by the US Army Research Office and the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology.

Read more: www.dailytech.com

# Quantum computing with microwaves

Two independent groups of physicists have made important breakthroughs in the control of quantum computers based on trapped ions. Instead of controlling quantum bits (qubits) using multiple laser beams, the teams have used microwave sources, which are much easier to control and integrate within quantum circuits. The work could lead to practical quantum computers that incorporate large numbers of qubits on a single chip.

The most successful quantum-computing system so far has been the ion trap – in which information is encoded in the electron spin states of ions that are confined by electric fields. In such systems, the electron spins of multiple ions can be put into a single quantum state in which they are no longer independent of one another. In this “entangled” state, which has no analogue in classical physics, correlations between ions can be used to perform certain logical operations that would take an unfeasibly long time for a classical computer….. Continue reading Quantum computing with microwaves