U.S. Department of Energy Office of Science Office of Scientific and Technical Information

In the OSTI Collections: From “1 or 0” to “1 or 0 and Both”—Toward Real Quantum Computers

This year’s Nobel Prize in physics is being awarded for very useful methods of manipulating matter by using certain of its quantum-physical properties. Further development of similar methods and their uses are now the focus of several research programs around the world, including many sponsored by the Department of Energy. One of the incentives for this research is the construction of a new type of computer able to solve practical problems that present-day computers could not, even if they literally had all the time in the world.

 

Digital computers treat all information as bits, representing the bits by things that come in one of two stable conditions, and represent mathematical operations by physical manipulations of those things. For example, a computer may represent bits by sections of a magnetic material whose magnetic moments[Wikipedia] have a certain strength pointing either up or down, according to whether a large fraction of the section’s elementary particles have their individual magnetic moments pointing up or down. The mathematical operations can then be represented by flipping some particles’ moments into directions opposite to their initial ones, thus changing 1s to 0s and vice versa, while leaving other magnetic moments alone.

 

Whether the bits are represented by the directions of magnetic moments or by some other means, a set of bits that expresses a problem can be transformed by an appropriate sequence of operations into a different set of bits that expresses the solution. The number of operations it takes to arrive at the solution determines how many steps the computer requires to solve the problem. Essentially, the basic operations of present-day computers amount to nothing but changes of appropriate bits to their exact opposites at each step of a computation. This kind of operation is enough for computers to solve many problems very quickly, but some problems would require such an enormous number of bit-reversing stages that even a very fast computer would take longer than the age of the universe to solve them.

 

But other operations are possible. If an upward- or downward-pointing magnetic moment represents a 1 or a 0, a left- or right-pointing moment can represent both a 1 and a 0 simultaneously. So a set of N particles whose magnetic moments all point, say, to the right can represent every possible combination of N 1s and 0s at the same time. A computer that can not only change particles’ vertical orientations to their exact opposites, but reorient particles and their magnetic moments to any new direction, not just vertical or horizontal ones, could represent a wider range of mathematical operations efficiently and, for some problems, decrease the number of required operations drastically enough to make solutions feasible.

 

The possible advantages of such computers are even greater than this may suggest, because of the quantum-physical properties mentioned above that become most obvious with individual quanta of matter and energy. As one example of these properties, a particle’s magnetic moment not only has a definite orientation parallel or antiparallel to one particular axis; it will generally be found to have some definite orientation either parallel or antiparallel to any axis one examines. Because individual quanta can represent both a definite bit (a 1 or a 0) and also an intermediate, indefinite bit (both 1 and 0) in this way, quanta that do so are said to represent “quantum bits”, or “qubits”.

 

Given that a quantum’s magnetic moment is oriented parallel or antiparallel to some specific axis, the probability of finding it oriented parallel or antiparallel to any other axis depends on the angle between the two axes (see Figure 1). If the probability that a set of magnetic moments has particular orientations at the end of a computation is 100%, a single computation will produce a reliable solution to its problem; but a computation resulting in moments that just have a very high probability (say 99.99%) of representing the solution can still be useful, if the computation can be repeated a few times quickly; if the same result comes up multiple times, the computation is practically certain to represent the solution.

 

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Figure 1. For the case of an atom whose net angular momentum in any direction has a magnitude of Planks Constant /2,[Wikipedia] if its magnetic moment’s vertical component is originally aligned upward, or at a 0° angle (blue arrows), the probability that its magnetic moment along any other axis at angle theta from the vertical is parallel to that axis, or P(theta|0°), equals cos2(theta/2) (green arrows). The probability that the magnetic moment is antiparallel to the axis at angle theta is 1- cos2(theta/2), so the probabilities for any direction and the exact opposite direction sum to 1, or 100%.

 

Many different physical systems besides magnetic moments can conceivably represent operations on sets of bits in a quantum-physical computer, but a sampling of recent research sponsored by the Department of Energy suggests that magnetic systems are a significant focus of attention. Applications of several magnetic systems to computing are at various stages of investigation or development by different research groups. These applications require addressing a major problem that this year’s announcement of the Nobel Prize in physics alludes to: although quantum computations tend to be disrupted when the computers’ working components interact with their environment, completely isolating the components from their environment means their output can’t be observed. A different problem, for at least some types of quantum processors, is how to produce the pieces in quantity, so individual processors can, first, represent enough qubits to solve large-scale problems and, second, be mass-produced.

 

Real Atomic Qubits in Electromagnetic Traps and in Silicon

 

Progress in making devices that represent bits by the magnetic moments of individual atoms is evident from the Sandia National Laboratories reports “Advanced atom chips with two metal layers”[Information Bridge] and “Ion-Photon Quantum Interface: Entanglement Engineering”.[Information Bridge] The first report describes a design for a chip that can magnetically trap individual atoms and transport them controllably to different chip locations where they can be operated on in various ways. The second report describes an actual small-scale device that can trap electrically charged atoms (ions) that each store one qubit of information (a 1 and/or 0); the ions are efficiently “entangled” with photons so that each photon’s polarization in a particular pair of directions indicates its “entangled” ion’s magnetic moment along a single axis. The photon with its polarization can be directed from the ion to other places, thus transmitting the information that the ion stores. While large-scale ion-photon devices in academic laboratories have demonstrated that information can be stored and transmitted this way, if not reliably, microscale devices like the ones described in these reports can work faster and very reliably, and be more readily mass-produced.

 

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Figure 2. From “Ion-Photon Quantum Interface: Entanglement Engineering”[Information Bridge] by Matthew Glenn Blain, Francisco M. Benito, Jonathan David Sterk, and David Lynn Moehring: SEM images of the ion trap. Top: Full view of die. The two 105 micrometer holes for the cavity and ion loading are indicated. Bottom Left: Top view of the ion trap. Bottom Right: Zoom of one of the holes and the adjacent electrodes.

 

 

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Figure 3. Images of ytterbium ions. (From “Ion-Photon Quantum Interface: Entanglement Engineering”[Information Bridge] by Matthew Glenn Blain, Francisco M. Benito, Jonathan David Sterk, and David Lynn Moehring.)

 

Trapping isolated atoms and moving them around with electromagnetic fields to perform different operations on them provides one way to use the atoms for quantum computation. Another way to handle the atoms in a quantum-computer processor is to embed them in solids made of atoms of a different type, which won’t react as the embedded atoms will to the bit-processing manipulations. A Lawrence Livermore National Laboratory report, “Single Ion Implantation and Deterministic Doping”,[Information Bridge] and a Sandia National Laboratories patent, “Isolating and moving single atoms using silicon nanocrystals”,[DOepatents] describe different ways to construct devices whose working atoms are embedded in silicon by ion implantation[Wikipedia]. Both methods address the disruption of the working atoms’ function due to proximity to surfaces of the embedding material—an instance of the general problem mentioned in this year’s Nobel physics prize announcement—and the precise positioning of the working atoms.

 

The Lawrence Livermore report notes some difficulties with implanting ions into a single piece of material. For one, the further the working ions are implanted below the embedding material’s surface to avoid disrupting their function, the less uniformly those ions are positioned; for another, the thermal annealing that repairs the damage to the embedding material caused by ion implantation also causes the ions to diffuse away from where the implantation put them, which also limits how precisely they’re positioned. The report describes how to address these problems through controlling the size of the implanted-ion beam, implanting ions of more massive elements rather than less massive ones, and exploiting different elements’ particular diffusion properties.

 

The Sandia patent addresses the positioning problem a different way. It describes a method of device construction that begins by implanting working ions into silicon nanocrystals, so that most nanocrystals contain exactly one working ion, although some will have more than one and some will have none. After the implantation, an atomic-force microscope is used to first locate which nanocrystals have exactly one implanted ion and then to arrange those nanocrystals so their working ions are properly positioned. The patent points out that the construction method is compatible with existing atomic-force microscopy tools and conventional silicon-device fabrication technology.

 

Theory of Superconductor Qubits, Molecular Qubits, and Control Pulses


While actual devices are being made to represent qubits by individual atoms’ magnetic orientations, mathematical analyses are showing how other kinds of magnetic qubits might be used, and how computing operations might be performed on magnetic qubits in general.

 

Superconducting QUantum Interference Devices (known as SQUIDs)[Wikipedia] have magnetic fields and are nowadays normally used to measure other very small magnetic fields in their environment. But the nature of SQUIDs’ supercurrents and the supercurrents’ own magnetic fields suggests that SQUIDs could also represent qubits much as single atoms can. However, many SQUIDs’ magnetic fields fluctuate too much to be practical qubit storage media, so there’s interest in understanding the precise reasons for the fluctuations in order to find a way to reduce or eliminate them. Progress in figuring out the reasons is described in two reports from Lawrence Berkeley National Laboratory, “Model for 1/f Flux Noise in SQUIDs and Qubits”[Information Bridge] and “Localization of metal-induced gap states at the metal-insulator interface: Origin of flux noise in SQUIDs and superconducting qubits”.[Information Bridge]

 

The first report describes how a SQUID’s magnetic field would be affected if the ordinary thermal motions of its electrons led to some of them being trapped for varying lengths of time at defects in the SQUID’s material; the electrons’ magnetic moments would be randomly stuck for those times, either adding to or subtracting from the magnetic field of the SQUID’s superconducting current. The magnetic-field fluctuations produced by this mechanism would have several characteristics in common with the fluctuations seen in actual SQUIDs. The second report addresses what kind of material defects, of all the kinds that exist, actually trap electrons at random intervals to produce the fluctuations, and offers evidence that the defects occur at the metal-insulator junction essential to the SQUID’s operation; it concludes that improving SQUID and superconducting-qubit performance requires understanding how to reduce the disorder at metal-insulator interfaces by, e.g., using different fabrication methods.

 

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Figure 4. Magnetic flux[Wikipedia] per Bohr magneton[Wikipedia] coupled to SQUID loop by a current loop moved along the line indicated. “In plane” and “perpendicular” refer to the orientation of the magnetic moment. The SQUID’s outer and inner widths are 52 Micro signm and 41.6 Micro signm respectively, while its thickness is 0.1 Micro signm. (From “Model for 1/f Flux Noise in SQUIDs and Qubits”[Information Bridge] by Roger H. Koch, David P. DiVincenzo, and John Clarke.)

 

 

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Figure 5. From “Localization of Metal-Induced Gap States at the Metal-Insulator Interface: Origin of Flux Noise in SQUIDs and Superconducting Qubits”[Information Bridge] by SangKook Choi, Dung-Hai Lee, Steven G. Louie, and John Clarke. (a) The metal (M) is assumed to have a simple cubic structure with one atom per unit cell and the insulator (I) a cesium chloride structure with two atoms per unit cell. (b) Interfacial region (D) consists of 2 layers of metal unit cells and 2 layers of insulator unit cells. The size of the unit cell is taken as 0.15 nanometers (0.15 nm). (c-e) Computed density of states (DOS). (c) Typical metal with bandwidth of 10 electron-volts (10 eV). (d) Typical insulator with a 2 eV band gap separating two bands of about 8 eV and 4 eV. (e) Metal-insulator interface with metal-induced gap states in the band gap of the insulator produced by the presence of the metal.

 

If the fluctuations of SQUIDs’ magnetic fields can be eliminated or reduced enough to make them useful as qubit storage media, how well would they work? A set of slides from Los Alamos National Laboratory, “Theory, modeling and simulation of superconducting qubits”,[Information Bridge] describes extensive mathematical analyses of the physical characteristics needed by SQUIDs and their measuring instruments so that the qubits could be read with various high fidelities from 80% to 99.99% using a new measuring method. The analyses account for interactions of SQUIDs with each other, and also with the measuring instruments and their thermal and electromagnetic environment—another instance of the problem described in this year’s Nobel physics prize announcement.

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Figure 6. A representative conjugated metallorganic molecule containing an ion, Fe III. The surrounding ligands are phenanthroline, a strong ligand used in various complexes. One of the phenanthroline ligands is decorated by two dithiol (i.d., SH) groups at the ends for good contact with the electrodes. (From “Spin Properties of Transition Metallorganic Self-Assembled Molecules”[Information Bridge] by Zhi Gang Yu.)

 

A similarly extensive analysis of a different system for representing qubits is described in the report “Spin Properties of Transition-Metallorganic Self-Assembled Molecules”[Information Bridge] from the nonprofit research institute SRI International. The report points out that nanostructures with integrated magnetic and charge components could provide “sophisticated functions with much simpler circuitry and less demanding fabrication” for magnetoelectronics[Wikipedia] and quantum computing. The Department of Energy funded SRI International to systematically and fundamentally study electronic and transport properties of two types of nanostructure: transition-metallorganic self-assembled molecules, and fullerenes whose inner spheres contain additional atoms or clusters. [Wikipedia] SRI’s results give much technical detail that should be useful for designing computers based on molecular qubits. Another study involving molecules had some similar motivations among others. “Calix[4]arene Based Single-Molecule Magnets”,[Information Bridge] which involved work at Lawrence Berkeley National Laboratory’s Advanced Light Source, describes single-molecule magnets of a new type, based on three-dimensional metal clusters or single lanthanide ions housed in a sheath. The use of sheathing of different kinds offers much potential for adding desirable features to the molecules or removing undesirable ones.

 

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Figure 7. A representative endohedral fullerene[Wikipedia] N@C60, where a nitrogen atom with spin 3/2 is located at the center of a C60 cage. (From “Spin Properties of Transition Metallorganic Self-Assembled Molecules”[Information Bridge] by Zhi Gang Yu.)

Just having devices that can represent qubits is not enough to produce a useful quantum computer; at most, they’d only make a quantum memory unit. To perform computations with qubits requires some means of manipulating them, and the manipulators need to be designed just as the qubit storage media do.

 

A standard technique for reorienting atoms and molecules (and thus their magnetic moments) in specific ways is to expose them to electromagnetic pulses of specific shape. The Los Alamos National Laboratory report “Second-order shaped pulsed for solid-state quantum computation”[Information Bridge] describes a method for calculating appropriate pulse shapes. A pulse shape’s design is not only a function of the desired reorientation, but of random disturbances from the pulse’s environment that could change the pulse in unpredictable ways. To keep these disturbances from corrupting the qubit orientations and thereby messing up the computation, the report describes pulse shapes that would produce the desired qubit reorientations in spite of the random disturbances. An additional feature of this pulse-design method is that, for qubit arrays in which each qubit is predominantly affected by its closest neighbors and little influenced if any by more distant qubits, the pulse designs don’t depend on the number of qubits the quantum computer uses. The report also goes beyond the general design formulas for arbitrary pulses and gives specific results for pulses designed to perform some specific qubit manipulations.

 

References

 

Wikipedia

 

Resesarch Organizations

 

Reports Available through OSTI’s Information Bridge and DOepatents

 

  • “Advanced atom chips with two metal layers” [Abstract and full text via OSTI’s Information Bridge]
  • “Ion-Photon Quantum Interface: Entanglement Engineering” [Abstract and full text via OSTI’s Information Bridge]
  • “Single Ion Implantation and Deterministic Doping” [Abstract and full text via OSTI’s Information Bridge]
  • “Isolating and moving single atoms using silicon nanocrystals” [Abstract and full text via OSTI’s DOepatents]
  • “Model for 1/f Flux Noise in SQUIDs and Qubits” [Abstract and full text via OSTI’s Information Bridge]
  • “Localization of metal-induced gap states at the metal-insulator interface: Origin of flux noise in SQUIDs and superconducting qubits” [Abstract and full text via OSTI’s Information Bridge]
  • “Theory, modeling and simulation of superconducting qubits” [Abstract and full text via OSTI’s Information Bridge]
  • “Spin Properties of Transition-Metallorganic Self-Assembled Molecules” [Abstract and full text via OSTI’s Information Bridge]
  • “Calix[4]arene Based Single-Molecule Magnets” [Abstract and full text via OSTI’s Information Bridge]
  • “Second-order shaped pulsed for solid-state quantum computation” [Abstract and full text via OSTI’s Information Bridge]

 

Additional References

 

 

Acknowledgements

 

Prepared by Dr. William N. Watson, Physicist
DOE Office of Scientific and Technical Information

 

Last updated on Friday 28 February 2014