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April 28, 2009

Considering Possibilities for a Room Temperature Quantum Computer


Fig 1: Optically controlled spintronic patches might be linked by flying qubits to form a larger processor. Even 20 qubits linked within a patch would provide only a very modest quantum computer. Linking 10 or 12 patches would be much more impressive. This figure shows schematically such a linkage to form a larger processor. If each patch is to be accessed by separate optical inputs, the spacings must be more than optical wavelengths, so of order 1–2 microns

Marshall Stoneham of the
London Centre for Nanotechnology and Department of Physics and Astronomy has written a paper that considers if a room temperature quantum computers are possible.


Marshall concentrates on two proposals as examples, with apologies to those whose suggestions I am omitting. Both of the proposals use optical methods to control spins, but do so in wholly different ways. The first is a scheme for optically controlled spintronics that Marhall Stoneham, Andrew Fisher, and Thornton Greenland proposed. The second route exploits entanglement of states of distant atoms by interference in the context of measurement-based quantum computing.

What would you do with a quantum computer if you had one? Proposals that do not demand room temperature range from probable, like decryption or directory searching, to the possible, like modeling quantum systems, and even to the difficult yet perhaps conceivable, like modeling turbulence. More frivolous applications, like the computer games that drive many of today’s developments, make much more sense if they work at ambient temperatures. And available quantum processing at room temperature would surely stimulate inventive new ideas, just as solid-state lasers led to compact disc technology.

Summing up, where do we stand? At liquid nitrogen temperatures, say 77 K, quantum computing is surely possible, if quantum computing is possible at all. At dry ice temperatures, say 195 K, quantum computing seems reasonably possible. At temperatures that can be reached by thermoelectric or thermomagnetic cooling, say 260 K, things are harder, but there is hope. Yet we know that small (say 2–3 qubit) quantum devices operate at room temperature. It seems likely, to me at least, that a quantum computer of say 20 qubits will operate at room temperature. I do not say it will be easy. Will such a QIP device be as portable as a laptop? I won’t rule that out, but the answer is not obvious on present designs.

Why do we need a quantum computer? The major reasons stem from challenges to mainstream silicon technology. Markets demand enhanced power efficiency, miniaturization, and speed. These enhancements have their limits. Future technology scenarios developed for the semiconductor industry’s own roadmap imply that the number of electrons needed to switch a transistor should fall to just 1 (one single electron) before 2020. Should we follow this innovative yet incremental roadmap, and trust to new tricks, or should we seek a radical technology, with wholly novel quantum components operating alongside existing silicon and photonic technologies? Any device with nanoscale features inevitably displays some types of quantum behavior, so why not make a virtue of necessity and exploit quantum ideas? Quantum-based ideas may offer a major opportunity, just as the atom gave the chemical industry in the 19th century, and the electron gave microelectronics in the 20th century. Quantum sciences could transform 21st century technologies.

Why choose the solid state for quantum computing? Quantum devices nearly always mean nanoscale devices, ultimately because useful electronic wave functions are fairly compact. Complex devices with controlled features at this scale need the incredible know-how we have acquired with silicon technology. Moreover, quantum computers will be operated by familiar silicon technology. Operation will be easier if classical controls can be integrated with the quantum device, and easiest if the quantum device is silicon compatible. And scaling up, the linking of many basic and extremely small units is a routine demand for silicon devices. With silicon technologies, there are also good ways to link electronics and photonics. So an ideal quantum device would not just meet quantum performance criteria, but would be based on silicon; it would use off-the-shelf techniques (even sophisticated ones) suitable for a near-future generation fabrication plant. A cloud on the horizon concerns decoherence: can entanglement be sustained long enough in a large enough system for a useful quantum calculation?



Fig 2: Larger arrays of diamond center qubits could be linked together for scale-up to a quantum computer. The many pairwise entanglements can be linked via a fast-switched optical multiplexer, in readiness for the final measurement step.






It can’t be done: serious quantum computing simply isn’t possible anyway. Could any quantum computer work at all? Is it credible that we can build a system big enough to be useful, yet one that isn’t defeated by loss of entanglement or degraded quantum coherence? Certainly there are doubters, who note how friction defeated 19th century mechanical computers. Others have given believable arguments that computing based on entanglement is possible. Of course, it may prove that some hybrid, a sort of quantum-assisted classical computing, will prove the crucial step.

It can’t be done: quantum behavior disappears at higher temperatures. Confusion can arise because quantum phenomena show up in two ways. In quantum statistics, the quantal ħ appears as ħω/kT. When statistics matter most, near equilibrium, high temperatures T oppose the quantum effects of ħ. However, in quantum dynamics, ħ can appear unassociated with T, opening new channels of behavior. Quantum information processing relies on staying away from equilibrium, so the rates of many individual processes compete in complex ways: dynamics dominate. Whatever the practical problems, there is no intrinsic problem with quantum computing at high temperatures.

It can’t be done: the right qubits don’t exist. True, some qubits are not available at room temperature. These include superconducting qubits and those based on Bose-Einstein condensates. In Kane’s seminal approach, the high polarizability needed for phosphorus-doped silicon (Si:P) corresponds to a low ionization donor energy, so the qubits disappear (or decohere) at room temperature. In what follows, I shall look at methods without such problems.



Optically controlled spintronics. Think of a thin film of silicon, perhaps 10 nm thick, isotopically pure to avoid nuclear spins, on top of an oxide substrate (Fig. 1). The simple architecture described is essentially two dimensional. Now imagine the film randomly doped with two species of deep donor—one species as qubits, the other to control the qubits. In their ground states, these species should have negligible interactions. When a control donor is excited, the electron’s wave function spreads out more, and its overlap with two of the qubit donors will create an entangling interaction between those two qubits. Shaped pulses of optical excitation of chosen control donors guide the quantum dance (entanglement) of chosen qubit donors.

For controlling entanglement in this way, typical donor spacings in silicon must be of the order of tens of nanometers. Optically, one can only address regions of the order of a wavelength across, say 1000 nm. The limit of optical spatial resolution is a factor 100 larger than donor spacings needed for entanglement. How can one address chosen pairs of qubits? The smallest area on which we can focus light contains many spins. The answer is to exploit the randomness inevitable in standard fabrication and doping. Within a given patch of the film a wavelength across, the optical absorptions will be inhomogeneously broadened from dopant randomness. Even the steps at the silicon interfaces are helpful because the film thickness variations shift transition energies from one dopant site to another. Light of different wavelengths will excite different control donors in this patch, and so manipulate the entanglements of different qubits. Reasonable assumptions suggest one might make use of perhaps 20 gates or so per patch. Controlled links among 20 qubits would be very good by present standards, though further scale up—the linking of patches—would be needed for a serious computer. The optically controlled spintronics strategy separates the two roles: qubit spins store quantum information, and controls manipulate quantum information. These roles require different figures of merit.

To operate at room temperature, qubits must stay in their ground states, and their decoherence—loss of quantum information—must be slow enough. Shallow donors like Si:P or Si:Bi thermally ionize too readily for room-temperature operations, though one could demonstrate principles at low temperatures with these materials. Double donors like Si:Mg+ or Si:Se+ have ionization energies of about half the silicon band gap and might be deep enough. Most defects in diamond are stable at room temperature, including substitutional N in diamond and the NV- center on which so many experiments have been done.

What about decoherence? First, whatever enables entanglement also causes decoherence. This is why fast switching means fast decoherence, and slow decoherence implies slow switching. Optical control involves manipulation of the qubits by stimulated absorption and emission in controlled optical excitation sequences, so spontaneous emission will cause decoherence. For shallow donors, like Si:P, the excitation energy is less than the maximum silicon phonon energy; even at low temperatures, one-phonon emission causes rapid decoherence. Second, spin-lattice relaxation in qubit ground states destroys quantum information. Large spin-orbit coupling is bad news, so avoiding high atomic number species helps. Spin lattice relaxation data at room temperature are not yet available for those Si donors (like Si:Se+) where one-phonon processes are eliminated because their first excited state lies more than the maximum phonon energy above the ground state. In diamond at room temperature, the spin-lattice relaxation time for substitutional nitrogen is very good (~1 ms) and a number of other centers have times ~0.1 ms. Third, excited state processes can be problems, and two-photon ionization puts constraints on wavelengths and optical intensities. Fourth, the qubits could lose quantum information to the control atoms. This can be sorted out by choosing the right form of excitation pulses. Fifth, interactions with other spins, including nuclear spins, set limits, but there are helpful strategies, like using isotopically pure silicon.

The control dopants require different criteria. The wave functions of electronically excited controls overlap and interact with two or more qubits to manipulate entanglements between these qubits. The transiently excited state wave function of the control must have the right spatial extent and lifetime. While centers like Si:As could be used to show the ideas, for room-temperature operation one would choose perhaps a double donor in silicon, or substitutional phosphorus in diamond. The control dopant must have sharp optical absorption lines, since what determines the number of independent gates available in a patch is the ratio of the spread of excitation energies, inhomogeneously broadened, to the (homogeneous) linewidth. The spread of excitation energies—inhomogeneous broadening is beneficial in this optical spintronics approach—has several causes, some controllable. Randomness of relative control-qubit positions and orientations is important, and it seems possible to improve the distribution by using self-organization to eliminate unusable close encounters. Steps on the silicon interfaces are also helpful, provided there are no unpaired spins. Overall, various experimental data and theoretical analyses indicate likely inhomogeneous widths are a few percent of the excitation energy.

A checklist of interesting systems as qubits or controls shows some significant gaps in knowledge of defects in solids. Surprisingly little is known about electronic excited states in diamond or silicon, apart from energies and (sometimes) symmetries. Little is known about spin lattice relaxation and excited state kinetics at temperatures above liquid nitrogen, except for the shallow donors that are unlikely to be good choices for a serious quantum computer. There are few studies of stabilities of several species present at one time. Can we be sure to have isolated P in diamond? Would it lose an electron to substitutional N to yield the useless species P+ and N- ? Will most P be found as the irrelevant (spin S=0) PV- center?

What limits the number of gates in a patch is the number of control atoms that can be resolved spectroscopically one from another. As the temperature rises, the lines get broader, so this number falls and scaling becomes harder. Note the zero phonon linewidth need not be simply related to the fraction of the intensity in the sidebands. Above liquid nitrogen temperatures, these homogeneous optical widths increase fast. Thus we have two clear limits to room-temperature operation. The first is qubit decoherence, especially from spin lattice relaxation. The second is control linewidths becoming too large, reducing scalability, which may prove a more powerful limit.

Entangled states of distant atoms or solid-state defects created by interference. See Fig 2 above. A wholly different approach generates quantum entanglement between remote systems by performing measurements on them in a certain way. The systems might be two diamonds, each containing a single NV- center prepared in specific electron spin states, the two centers tuned to have exactly the same optical energies. The measurement involves “single shot” optical excitation. Both systems are exposed to a weak laser pulse that, on average, will achieve one excitation. The single system excited will emit a photon that, after passing though beam splitters and an interferometer, is detected without giving information as to which system was excited. “Remote entanglement” is achieved, subject to some strong conditions. The electronic quantum information can be swapped to more robust nuclear states (a so-called brokering process). This brokered information can then be recovered when needed to implement a strategy of measurement-based quantum information processing.

The materials and equipment needs, while different from those of optically controlled spintronics, have features in common. For remote entanglement, a random distribution of centers is used, with one from each zone chosen because of their match to each other. The excitation energies of the two distant centers must stay equal very accurately, and this equality must be stable over time, but can be monitored. There are some challenges here, since there will be energy shifts when other defect species in any one of the systems change charge or spin state (the difficulty is present but less severe for the optical control approach). As for optically controlled spintronics, scale-up requires narrow lines, and becomes harder at higher temperatures, though there are ways to reduce the problem. Remote entanglement needs interferometric stability, avoiding problems when there are different temperature fluctuations for the paths from the separate systems. Again, there are credible strategies to reduce the effects.

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