Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation

Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure non-stabilizer states which can be distilled from certain mixed non-stabilizer states via Clifford group operations alone. Because of the Gottesman-Knill theorem, mixtures of Pauli eigenstates are not expected to be magic state distillable, but it has been an open question whether all mixed states outside this set may be distilled. In this Letter we show that, when resources are finitely limited, non-distillable states exist outside the stabilizer octahedron. In analogy with the bound entangled states, which arise in entanglement theory, we call such states bound states for magic state distillation.Comment: Published version. This paper builds on a theorem proven in "On the Structure of Protocols for Magic State Distillation", arXiv:0908.0838. These two papers jointly form the content of a talk entitled "Neither Magical nor Classical?", which was presented at TQC 2009, Waterlo

How good must single photon sources and detectors be for efficient linear optical quantum computation?

We present a scheme for linear optical quantum computation (LOQC) which is highly robust to imperfect single photon sources and inefficient detectors. In particular we show that if the product of the detector efficiency with the source efficiency is greater than 2/3, then efficient LOQC is possible. This threshold is many orders of magnitude more relaxed than those which could be inferred by application of standard results in fault tolerance. The result is achieved within the cluster state paradigm for quantum computation.Comment: New version contains an Added Appendi

Loss tolerant linear optical quantum memory by measurement-based quantum computing

We give a scheme for loss tolerantly building a linear optical quantum memory which itself is tolerant to qubit loss. We use the encoding recently introduced in Varnava et al 2006 Phys. Rev. Lett. 97 120501, and give a method for efficiently achieving this. The entire approach resides within the 'one-way' model for quantum computing (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 5188–91; Raussendorf et al 2003 Phys. Rev. A 68 022312). Our results suggest that it is possible to build a loss tolerant quantum memory, such that if the requirement is to keep the data stored over arbitrarily long times then this is possible with only polynomially increasing resources and logarithmically increasing individual photon life-times

Impulse Generation by an Open Shock Tube

We perform experimental and numerical studies of a shock tube with an open end. The purpose is to investigate the impulse due to the exhaust of gases through the open end of the tube as a model for a partially filled detonation tube as used in pulse detonation engine testing. We study the effects of the pressure ratio (varied from 3 to 9.2) and the volume ratio (expressed as fill fractions) between the driver and driven section. Two different driver gases, helium and nitrogen, and fill fractions between 5 and 100% are studied; the driven section is filled with air. For both driver gases, increasing the pressure ratio leads to larger specific impulses. The specific impulse increases for a decreasing fill fraction for the helium driver, but the impulse is almost independent of the fill fraction for the nitrogen driver. Two-dimensional (axisymmetric) numerical simulations are carried out for both driver gases. The simulation results show reasonable agreement with experimental measurements at high pressure ratios or small fill fractions, but there are substantial discrepancies for the smallest pressure ratios studied. Empirical models for the impulse in the limits of large and small fill fractions are also compared with the data. Reasonable agreement is found for the trends with fill fractions using the Gurney or Sato model at large fill fractions, but only Cooper’s bubble model is able to predict the small fill fraction limit. Computations of acoustic impedance and numerical simulations of unsteady gas dynamics indicate that the interaction of waves with the driver-driven gas interface and the propagation of waves in the driven gas play an essential role in the partial-fill effect

Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions

Two-level quantum systems, qubits, are not the only basis for quantum computation. Advantages exist in using qudits, d-level quantum systems, as the basic carrier of quantum information. We show that color codes, a class of topological quantum codes with remarkable transversality properties, can be generalized to the qudit paradigm. In recent developments it was found that in three spatial dimensions a qubit color code can support a transversal non-Clifford gate, and that in higher spatial dimensions additional non-Clifford gates can be found, saturating Bravyi and K\"onig's bound [Phys. Rev. Lett. 110, 170503 (2013)]. Furthermore, by using gauge fixing techniques, an effective set of Clifford gates can be achieved, removing the need for state distillation. We show that the qudit color code can support the qudit analogues of these gates, and show that in higher spatial dimensions a color code can support a phase gate from higher levels of the Clifford hierarchy which can be proven to saturate Bravyi and K\"onig's bound in all but a finite number of special cases. The methodology used is a generalisation of Bravyi and Haah's method of triorthogonal matrices [Phys. Rev. A 86 052329 (2012)], which may be of independent interest. For completeness, we show explicitly that the qudit color codes generalize to gauge color codes, and share the many of the favorable properties of their qubit counterparts.Comment: Authors' final cop

J0316+4328: a Probable "Asymmetric Double" Lens

We report a probable gravitational lens J0316+4328, one of 19 candidate asymmetric double lenses (2 images at a high flux density ratio) from CLASS. Observations with the Very Large Array (VLA), MERLIN and the Very Long Baseline Array (VLBA) imply that J0316+4328 is a lens with high confidence. It has 2 images separated by 0.40", with 6 GHz flux densities of 62 mJy and 3.2 mJy. The flux density ratio of ~19 (constant over the frequency range 6-22 GHz) is the largest for any 2 image gravitational lens. High resolution optical imaging and deeper VLBI maps should confirm the lensing interpretation and provide inputs to detailed lens models. The unique configuration will give strong constraints on the lens galaxy's mass profile.Comment: Accepted to MNRAS Letters. 5 pages, 6 figures, 3 table

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