Controlling the Quantum World The Science of Atoms, Molecules, and Photons (2007) / Chapter Skim
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7 Quantum Information with Light and Atoms
7 Quantum Information with Light and Atoms
Pages 137-169
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THE QUANTUM INFORMATION REVOLUTION two of the great scientific, philosophical, and technological revolutions of the 20th century were quantum mechanics and information science. each of these changed our lives in fundamental and lasting ways.
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the new quantum information science promises to be as radical in its effect on human society as quantum physics and information science were individually in the last century. in the next 10 years, it will be one of the major driving forces in AMo physics.
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Quantum information is stored not in bits but in "qubits," quantum bits whose value can be one or zero but can also be both zero and one at the same time. An ordinary transistor cannot be both on and off!
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controlling Quantum world 0 the FIGURE 7-2 Top: A mechanical switch representing a bit of classical information is either on or off, representing a value of one or zero.
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For a modest 300-qubit register, the number of states in the superposition can be 2300, a number that is enormously larger than the number of atoms in the entire universe. in addition to this ability to store exponentially many quantum states, the linear nature of quantum mechanics means that these states can all be manipulated at the same time -- that is, massive "quantum parallelism" is possible.
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Here we describe some aspects of this challenge and how quantum information technology from AMo physics may someday bridge this gap. Despite the dramatic success of quantum mechanics, glaring difficulties remain in reconciling quantum rules of nature with our everyday notions of reality.
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A large-scale quantum information processor can be considered a complex quantum entangled state with many degrees of freedom, but with special archi tecture or controls that delay the onset of decoherence (see Box 7-2)
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controlling Quantum world the BOX 7-1 Entanglement The exponential scaling of quantum information is related to one of the weirdest aspects of quantum theory, entanglement (see Figure 7-1-1)
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Quantum information science is directed at answering these questions. Among the many possible out comes in this quest, two are earth-shattering.
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These states were precisely the entangled states that are now of central interest to quantum information processing, although that was not realized at the time. At the 1994 International Conference on Atomic Physics in Boulder, a lecture by an infor mation theorist brought the topic of quantum computation and mathematician Peter Shor's new factoring algorithm to the atomic physics community.
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Q ua n t u m i n f o r m at i o n light atoms with and FIGURE 7-4 Processing power, measured in millions of instructions per second, has risen because of increased transistor counts. SOURCE: Copyright © 2005 Intel Corporation.
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However, much is still unknown about the capabilities of quantum information. Quantum Cryptography: A Real-World Application coded messages are almost as old as language itself, and today, encryption is essential not only for military and diplomatic purposes but also for industry and commerce.
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QKD exploits this property by using quantum systems for key distribution; with the proper choice of quantum states, it is possible to create the situation where an eavesdropper cannot avoid causing changes that can be detected. in this way it is possible to create a natural "wax seal" on the key; as long as no measurment is made, the seal is intact and the key is known to be secure.
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controlling Quantum world 0 the FIGURE 7-5 Left: To generate the key, the sender (Alice) randomly chooses one of four polarization orientations for a photon (vertical, horizontal, +45 degrees, or −45 degrees)
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. However, the addition of quantum mechanics to this scenario, together with recent experimental advances in AMo physics, has indeed allowed the quantum states of photons and atoms to be teleported, for atoms over very short distances and for photons over distances of several kilometers (see Figure 7-6)
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the difficult synchronization requirements this would introduce are as yet unaddressed. in the meantime, the use of quantum teleportation for moving states of atoms and photons around with high fidelity promises significant advantages for any schemes manipulating quantum states for metrology and high-precision measurements, or for facilitating data transfer in quantum information processing.
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these severe hardware requirements rule out most known physical systems. the most advanced candidates for quantum information processors in the next decade will likely come from atomic, molecular, and optical physics.
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in the context of quantum information processing, the optical lattices described FIGURE 7-7 Top: Array of a few dozen trapped mercury ions. The ions fluoresce from applied laser radiation, and the apparent gaps are different isotopes that fluoresce at different wavelengths.
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. this exciting development underscores the inherent interdisciplinary nature of the field of quantum information science.
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controlling Quantum world the V (x,y)
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once this is accomplished, these single-photon sources can be used for a variety of applications, ranging from secure quantum cryptography to full-blown quantum computing. one source of entangled photons that has been used for many seminal demonstrations of quantum information applications is the nonlinear downcon verter, where a single (blue)
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dimensions. in quantum information processing, storage and communication of qubits will likely take far different forms.
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Simple interconversion methods could lead to the development of quantum networks of qubits and distributed quantum computing, where small numbers of atomic qubit memories are linked within a single device or between remotely located devices with optical fibers. As photonic quantum information propagates through optical fibers over very long distances -- say, across a continent or through space -- the quantum signal will eventually degrade.
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This is similar to the use of conventional repeater circuits, which can, for example, deliver power over large distances. Quantum repeater networks allow stored quantum information to propagate over long distances despite noise and losses en route.
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Right: An alternative method for linking atoms through photons is to allow the photons' quantum information to leak controllably through the mirrors and carry the quantum information to another cavity, possibly remote.
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controlling Quantum world the FIGURE 7-14 Simplified evolution during a quantum algorithm on N = 3 quantum bits. The inputs are prepared in superposition states of all 2N = 8 possible numbers (written in binary)
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Q ua n t u m i n f o r m at i o n light atoms with and of the weights cancel, leaving only a very small number of answers, or even a single answer, as depicted in Figure 7-14b. By measuring this answer (or repeating the computation a few times and recording the distribution of answers)
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controlling Quantum world the BOX 7-4 Shor's Quantum Factoring Algorithm The breakthrough discovery of the quantum factoring algorithm by Peter Shor in 1994 involves a juxtaposition of the disjoint disciplines of number theory and quantum physics. There is no known efficient method for factorizing a number N into a product of two smaller numbers, N = p × q.
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Q ua n t u m i n f o r m at i o n light atoms with and FIGURE 7-15 Public key cryptography. Alice (A)
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Although these are all rudimentary implementations of quantum search, they exemplify the flexibility of AMo systems for quantum information applications and also indicate how to scale up to more complex versions of this and other quantum algorithms in any physical system. the quantum search algorithm has broad applicability to many problems in computer science and our information-oriented society beyond searching of large databases.
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For instance, a model-sized device of 30 qubits would be able to perform calculations on quantum systems that would require an array of 1 billion billion values to be represented in a conventional classical computer, far beyond the memory capacity of any of today's computers. it is increasingly being realized that such quantum simulations can have practi cal utility.
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physics of more complicated systems, their relevance ranges from commercial materials fabrication to basic problems in condensed matter physics. Another ex citing prospect for quantum simulations is to gain insight into the mechanism of high-temperature superconductivity, for which the correct microscopic physics is still unknown.
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After all, the systems currently under study are precisely the "thought experiments" envisioned by einstein, Bohr, Heisenberg, and the other founding figures of quantum theory over 80 years ago. With the new language of quantum information, we hope to gain more insight into the underlying quantum physical principles, just as the classical theory of information ushered in the advances in physics responsible for our current digital age.
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