Computers that harness the weirdness of quantum mechanics could smash conventional encryption systems by factoring gigantic numbers fast-and factoring the product of two large prime numbers is the only way standard codes can be broken. The job would take conventional computers decades, not minutes. Encrypted data is still safe for the moment, because a powerful enough quantum computer is still many years away. But physicists have now demonstrated that quantum calculations can be done in a version of a quantum computer that could, in theory at least, be scaled up sufficiently. Rainer Blatt and his colleagues at the University of Innsbruck (Austria), in collaboration with Isaac Chuang of the Massachusetts Institute of Technology (MIT), have run a simple quantum algorithm in a computer that consists of only a single, very cold calcium ion. They employed a standard ion-trapping technique and a series of carefully tuned laser pulses to turn the ion into a computer that calculates using qubits-bits that can exist, seemingly paradoxically, as both a 1 and a 0 simultaneously. The Innsbruck-M IT team put this property of qubits to work in the Deutsch-Jozsa algorithm.
Computers that harness the weirdness of quantum mechanics could smash conventional encryption systems by factoring gigantic numbers fast-and factoring the product of two large prime numbers is the only way standard codes can be broken. The job would take conventional computers decades, not minutes. Encrypted data is still safe for the moment, because a powerful enough quantum computer is still many years away. But physicists have now demonstrated that quantum calculations can be done in a version of a quantum computer that could, in theory at least, be scaled up sufficiently. Rainer Blatt and his colleagues at the University of Innsbruck (Austria), in collaboration with Isaac Chuang of the Massachusetts Institute of Technology (MIT), have run a simple quantum algorithm in a computer that consists of only a single, very cold calcium ion. They employed a standard ion-trapping technique and a series of carefully tuned laser pulses to turn the ion into a computer that calculates using qubits-bits that can exist, seemingly paradoxically, as both a 1 and a 0 simultaneously. The Innsbruck-M IT team put this property of qubits to work in the Deutsch-Jozsa algorithm.
A full-scale quantum computer would work like the standard desktop computer, in that it would have a place to store data, a place where a program manipulates the data, and interconnections to move the data from one to the other. In the computer you are using now, bits of data - stored as quantity of charge or its absence - are transferred from memory to a processor in the form of levels of voltage. At the processor the computer's program determines which logic operations the bits will be subjected to. Once the logic operations are completed, the bits are converted to amounts of charge and stored in memory again. Similarly, in an ion-trap computer, stored qubits would be called from a storage trap to a logic trap, the kind we've been building so far. The two traps would be connected by a long trap that acts like an interconnect or a data bus. It sounds simple, but such a structure would have to be repeated and connected many dozens of times on the same chip to handle the number of ions we'd need. Therefore, a quantum computer equivalent of very-large-scale integration would be required to handle the control circuitry just to move the ions around. The small-scale quantum algorithms that scientists are running today and plan to run in the near future will almost certainly lead to insights that could make full-scale quantum computing, if not easy, at least more tractable.
Trapped ions, trapped atoms, and NMR spin systems are all fine ways of building small “toy” quantum computers, each with its own advantages and disadvantages. There are also many other techniques which have been suggested, although these three so far remain in the lead for general-purpose quantum computing. However, the most powerful general-purpose quantum computers constructed to date have only about a dozen qubits, and this is not nearly large enough to make quantum computers useful rather than merely interesting. (Larger systems have been used to demonstrate particular quantum information processing techniques, but these cannot as yet be used to implement arbitrary quantum algorithms.) Although it is not completely clear how complex a general-purpose quantum computer needs to be, it is clear that such a device will involve thousands or even millions of qubits, rather than the dozens involved today. It is, therefore, important to consider whether there is any hope of scaling up these technologies to useful sizes, and we will consider each of the three approaches in turn, before turning briefly to alternative technologies which have not been discussed so far. Trapped ions Trapped ions initially look very promising as a candidate for scaling up, as it is possible to trap thousands of ions while keeping a reasonable distance between them. Early experiments relied on particular tricks which only work with systems of two ions, but this is not true of more recent work, and there is no reason in principle why these large strings of ions could not be controlled.
A product is on the way that relies on the quantum properties of photons to keep out eavesdroppers. All of them. The battle between codemakers and codebreakers is centuries old, but at the start of the 21st century, could it finally be drawing to a close? Physicists are putting the finishing touches to a method of encrypting messages that is more secure than anything that has gone before. Unlike the ciphers of the past, this new method has the potential to be absolutely unbreakable, not just practically unbreakable, but theoretically unbreakable. Mathematicians believe they can prove it. Central to the technique are the strange laws of quantum mechanics. Already experimental messages encrypted using quantum mechanics are being sent over tens of kilometers of optical fibers and received securely. Researchers are confident that it will not be long before ultra-secret messages are routinely transmitted in this way. But while quantum cryptography may be perfect in theory, practical considerations introduce security loopholes that an eavesdropper can exploit. The seriousness of these is still unclear, and physicists believe they can plug most of the holes with more efficient equipment. Still, enough cracks remain to maintain a healthy interest among cryptographers.
Quantum computers can solve certain problems more efficiently compared to conventional classical methods. In the endeavor to build a quantum computer, several competing platforms have emerged that can implement certain quantum algorithms using a few qubits. However, the demonstrations so far have been done usually by tailoring the hardware to meet the requirements of a particular algorithm implemented for a limited number of instances. Although such proof of principal implementations are important to verify the working of algorithms on a physical system, they further need to have the potential to serve as a general purpose quantum computer allowing the flexibility required for running multiple algorithms and be scaled up to host more qubits. Here we demonstrate a small programmable quantum computer based on five trapped atomic ions each of which serves as a qubit. By optically resolving each ion we can individually address them in order to perform a complete set of single-qubit and fully connected two-qubit quantum gates and alsoperform efficient individual qubit measurements. We implement a computation architecture that accepts an algorithm from a user interface in the form of a standard logic gate sequence and decomposes it into fundamental quantum operations that are native to the hardware using a set of compilation instructions that are defined within the software. These operations are then effected through a pattern of laser pulses that perform coherent rotations on targeted qubits in the chain. The architecture implemented in the experiment therefore gives us unprecedented flexibility in the programming of any quantum algorithm while staying blind to the underlying hardware. As a demonstration we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms on the five-qubit processor and achieve average success rates of 95 and 90 percent, respectively. We also implement a five-qubit coherent quantum Fourier transform and examine its performance in the period finding and phase estimation protocol. We find fidelities of 84 and 62 percent, respectively. While maintaining the same computation architecture the system can be scaled to more ions using resources that scale favorably (O(N^2)) with the number of qubits N.
A quantum computer is a digital computer capable of exploiting quantum coherence among the physical two-state systems that store the binary arithmetic information. To factor an integer is to find its (unique) expression as a product of prime numbers. The most impressive, most important, and best-known thing a quantum computer can do is to factor with spectacular efficiency the product of two enormous prime numbers. But what on earth can quantum mechanics have to do with factoring? This question bothered me for four years, from the time I heard about the discovery that a quantum computer was spectacularly good at factoring until I finally took the trouble to find out how it was done. The answer, you will be relieved—but, if you're like me, also a little disappointed—to learn, is that quantum mechanics has nothing at all directly to do with factoring. But it does have a lot to do with waves. Many important waves are periodic, so it is not very surprising that quantum mechanics might be useful in efficiently revealing features associated with periodicity. Quantum mechanics is connected to factoring through periodicity. It turns out, for purely arithmetic reasons having nothing to do with quantum mechanics, that if we have an efficient way to find the period of a periodic function, then, as we shall see below, we can easily factor the product of two enormous prime numbers. And a quantum computer provides an extremely efficient way to find periods. All of the above is of considerable practical importance, because the great difficulty in factoring such a product—where the two enormous prime numbers are typically each several hundred digits long—is the basis for the security of the most widely used encryption scheme (called RSA [1] encryption) for protecting private information sent over the internet. In 1994 Peter Shor discovered [2] that a quantum computer would be super-efficient at period finding and thereby pose a potential threat to innumerable secrets. Whence the explosion of interest in developing quantum computation. The threat is only potential because no quantum computer capable of anything like serious period finding currently exists. I suspect the emphasis has been put on factoring rather than period finding because factoring is more famously associated with RSA code breaking, although, as it happens, period finding can be used directly to crack the RSA code, without any need for a detour into factoring.
We investigate the problem of factorization of large numbers on a quantum computer which we imagine to be realized within a linear ion trap. We derive upper bounds on the size of the numbers that can be factorized on such a quantum computer. These upper bounds are independent of the power of the applied laser. We investigate two possible ways to implement qubits, in metastable optical transitions and in Zeeman sublevels of a stable ground state, and show that in both cases the numbers that can be factorized are not large enough to be of practical interest. We also investigate the effect of quantum error correction on our estimates and show that in realistic systems the impact of quantum error correction is much smaller than expected. Again no number of practical interest can be factorized.