Researchers prove quantum algorithm works by solving linear equations on a quantum computer

Jun 14, 2013 by report
Graph sample of linear equations. Credit: Wikipedia.

(Phys.org) —A research team composed of members from China, Singapore and Canada has built a simple quantum computer that has proven a quantum algorithm developed in 2009. In their paper published in Physical Review Letters, the team describes how they built their simple quantum computer and how it might be developed into a more powerful machine.

As scientists continue their quest to build a true quantum computer, they take baby steps by creating quantum-based devices capable of carrying out quantum algorithms. In this latest effort, the research team built a simple device that uses entangled photons to solve 2x2 linear equations.

Back in 2009, a team of researchers developed an algorithm that they believed could be used by a quantum computer to solve linear equations. To find out if that algorithm truly would work as proposed, the research team built a simple to run it. They started by firing a laser beam at barium-borate crystals to create two pairs of entangled photons—each of the pairs had the same polarization. The photon pairs were then sent through a that separated them from the others. The four photons were used to represent which were processed by an . Afterwards, the photons were detected by a sensor—their polarization state represented the solution to the linear equations given at the onset. The device doesn't give an exact answer, but instead provides what it's most likely to be. In this case, the algorithm developed in 2009 proved to be reasonably accurate, providing fidelity of 0.993 to 0.825.

The simple device created by the team demonstrates the working principle of the algorithm, and opens the door to solving much larger equations by upping the number of entangled photons. Its creation also suggests that similar devices could be created to solve different types of equations. The team points out that that there are two elements of their device they would like to improve. The first is that it's limited by use of just one photon source. That makes the creation of the photons somewhat unreliable. They'd also like to find a way to implement more efficient photon detectors.

Explore further: Physics team entangles photons that never coexisted in time

More information: Experimental Quantum Computing to Solve Systems of Linear Equations, Phys. Rev. Lett. 110, 230501 (2013) prl.aps.org/abstract/PRL/v110/i23/e230501

Abstract
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.

Related Stories

Efficient distributed quantum computing

Feb 21, 2013

(Phys.org)—A quantum computer doesn't need to be a single large device but could be built from a network of small parts, new research from the University of Bristol has demonstrated. As a result, building ...

Hi-fi single photons

Oct 04, 2012

Many quantum technologies—such as cryptography, quantum computing and quantum networks—hinge on the use of single photons. While she was at the Kastler Brossel Laboratory (affiliated with the Pierre and Marie Curie University, ...

Quantum algorithm breakthrough

Feb 24, 2013

An international research group led by scientists from the University of Bristol, UK, and the University of Queensland, Australia, has demonstrated a quantum algorithm that performs a true calculation for the first time. ...

Recommended for you

CERN: World-record current in a superconductor

17 hours ago

In the framework of the High-Luminosity LHC project, experts from the CERN Superconductors team recently obtained a world-record current of 20 kA at 24 K in an electrical transmission line consisting of two ...

High power laser sources at exotic wavelengths

Apr 14, 2014

High power laser sources at exotic wavelengths may be a step closer as researchers in China report a fibre optic parametric oscillator with record breaking efficiency. The research team believe this could ...

Novel technique opens door to better solar cells

Apr 14, 2014

A team of scientists, led by Assistant Professor Andrivo Rusydi from the Department of Physics at the National University of Singapore's (NUS) Faculty of Science, has successfully developed a technique to ...

User comments : 0

More news stories

CERN: World-record current in a superconductor

In the framework of the High-Luminosity LHC project, experts from the CERN Superconductors team recently obtained a world-record current of 20 kA at 24 K in an electrical transmission line consisting of two ...

Glasses strong as steel: A fast way to find the best

Scientists at Yale University have devised a dramatically faster way of identifying and characterizing complex alloys known as bulk metallic glasses (BMGs), a versatile type of pliable glass that's stronger than steel.

Low Vitamin D may not be a culprit in menopause symptoms

A new study from the Women's Health Initiative (WHI) shows no significant connection between vitamin D levels and menopause symptoms. The study was published online today in Menopause, the journal of The North American Menopa ...

Astronomers: 'Tilt-a-worlds' could harbor life

A fluctuating tilt in a planet's orbit does not preclude the possibility of life, according to new research by astronomers at the University of Washington, Utah's Weber State University and NASA. In fact, ...