Don't Discount the Tachyon!

NEWS & VIEWS consequences for quantum-state but not necessarily found, on a classical interactions can be replaced by pair-wise preparation, quantum computation and computer. The quantum analogue of interactions such that the relative difference quantum complexity theory. this result was derived by again making in the ground-state energies remains One way of performing quantum use of the aforementioned gadgets: arbitrarily small (here the local reduction computation is by encoding the solution determining the ground-state energy of is independent of the rest of the system). of a computational problem into the pair-wise interacting qubits on a square The question of whether approximating ground state of a Hamiltonian. The desired lattice is as hard as such a problem the ground-state energy up to such a state is then obtained by approaching its can get; seemingly more complicated relative error has the same computational Hamiltonian adiabatically from a simple interactions or geometries do not yield complexity is the basis of one of the initial one whose ground state is easily harder problems2,3. In a similar vein, the major conjectures of quantum complexity prepared. Typically, one would like the complexity of widespread methods such as theory — the ‘quantum PCP theorem’. interactions involved to be two-body, Hartree–Fock or density functional theory Whether or not these methods shed geometrically local and requiring control can be pinpointed6. new light on complexity, the acquired tools of only a few local degrees of freedom Usually, perturbation theory comes and gadgets certainly have the potential (say two, as in a qubit). Proof that this with a catch: the perturbative term has to to be of use in many corners of theoretical is indeed possible — for example on a be sufficiently small. In the context of the physics where reductions are necessary two-dimensional square lattice — was one work on many-body systems, in which and perturbations ubiquitous. And where of the first successes of the perturbation- low-energy properties must be preserved, gadgets don’t work, there may be other theory gadgets2,3. ‘small’ is defined with respect to the widgets and gizmos to play with. A related result concerns the energy of excitations. Extensivity of the complexity of determining the ground- perturbations’ energy thus seems to require References state energy of a quantum system. It is that the energy of the lowest excitations 1. Bravyi, S., DiVincenzo, D. P., Loss, D. & Terhal, B. M. Phys. Rev. known that, for classical systems, obtaining (the spectral gap) grows linearly with the Lett. 101, 070503 (2008). 2. Kempe, J., Kitaev, A. & Regev, O. SIAM J. Comput. 35, a minimum-energy configuration of a spin system size. Although unphysical, this is 1070–1097 (2006). glass with nearest-neighbour interactions what was assumed in the earlier reductions. 3. Oliveira, R. I. & Terhal, B. M. Preprint at <http://arxiv.org/abs/ on a square lattice is the hardest problem Bravyi et al.1 have now shown that this quant-ph/0504050> (2005). 4. Jordan, S. & Farhi, E. Phys. Rev. A 77, 062329 (2008). in a notorious complexity class called shortcoming can be circumvented: the 5. Biamonte, J. D. & Love, P. J. Phys. Rev. A 78, 012352 (2008). NP. This class encompasses all problems coupling strength can remain independent 6. Schuch, N. & Verstraete, F. Preprint at <http://arxiv.org/ whose solutions can be efficiently verified, of the system size. Nevertheless, many-body abs/0712.0483> (2007). PARTICLE PHYSICS Don’t discount the tachyon! It makes regular appearances in case that the lightest supersymmetric science fiction — from the novels of particle is the gravitino (partner of Isaac Asimov, to TV’s Dr Who and the graviton), the parameter space of Babylon 5 — but the tachyon is less the MSSM extends to negative mass- popular in science fact. squared values. This hypothetical particle travels This, say Ellis et al., should not faster than light and the square of be discounted. The point is that any its rest mass is negative. So far, so tachyonic spin-zero fields that might unphysical. However, the proper exist do so at very high energy scales; in treatment of tachyonic fields within evolving down to the much lower energy quantum field theory does not allow scales of our present Universe — a any violation of causality, and writing trick that theorists perform using the in Physical Review D, John Ellis and mathematics of the ‘renormalization co-authors make a plea to theorists group’ — the sign of the tachyonic mass- to resist “unreasoning tachyophobia” squared can change, if the actual size of (Phys. Rev. D 78, 075006; 2008). It could the mass-squared was sufficiently small be that tachyons feature in an extended up at the unification scale. standard model. Models like this do, however, raise The standard model is not the whole other issues: for example, whether our story for particle physics, and it is Universe exists in a true minimum of hoped that data from the Large Hadron potential or only a local minimum, Collider will direct us to the physics and whether there is a danger of needed to extend, even if not complete, SPL introducing charge and colour-charge the picture. Supersymmetry — a broken non-conservation. But these, the authors symmetry that would endow each form of the ‘minimal supersymmetric stress, are points that can be reasonably fundamental particle with a heavier standard model’, or MSSM. Working considered (or calculated) without supersymmetric partner — is a favoured with certain constraints to tie the model wantonly discarding the tachyon. addition to the model, typically in the in with grand unified theory, and in the Alison Wright nature physics | VOL 4 | NOVEMBER 2008 | www.nature.com/naturephysics 835 © 2008 Macmillan Publishers Limited. All rights reserved. .

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