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Toward practical quantum computers

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Quantum computers are largely hypothetical devices that could perform some calculations much more rapidly than conventional computers can. Instead of the bits of classical computation, which can represent 0 or 1, quantum computers consist of quantum bits, or qubits, which can, in some sense, represent 0 and 1 simultaneously.

Although quantum systems with as many as 12 qubits have been demonstrated in the lab, building quantum computers complex enough to perform useful computations will require miniaturizing qubit technology, much the way the miniaturization of transistors enabled modern computers.

Trapped ions are probably the most widely studied qubit technology, but they’ve historically required a large and complex hardware apparatus. In today’s Nature Nanotechnology, researchers from MIT and MIT Lincoln Laboratory report an important step toward practical quantum computers, with a paper describing a prototype chip that can trap ions in an electric field and, with built-in optics, direct laser light toward each of them.

“If you look at the traditional assembly, it’s a barrel that has a vacuum inside it, and inside that is this cage that’s trapping the ions. Then there’s basically an entire laboratory of external optics that are guiding the laser beams to the assembly of ions,” says Rajeev Ram, an MIT professor of electrical engineering and one of the senior authors on the paper. “Our vision is to take that external laboratory and miniaturize much of it onto a chip.”

Caged in

The Quantum Information and Integrated Nanosystems group at Lincoln Laboratory was one of several research groups already working to develop simpler, smaller ion traps known as surface traps. A standard ion trap looks like a tiny cage, whose bars are electrodes that produce an electric field. Ions line up in the center of the cage, parallel to the bars. A surface trap, by contrast, is a chip with electrodes embedded in its surface. The ions hover 50 micrometers above the electrodes.

Cage traps are intrinsically limited in size, but surface traps could, in principle, be extended indefinitely. With current technology, they would still have to be held in a vacuum chamber, but they would allow many more qubits to be crammed inside.

“We believe that surface traps are a key technology to enable these systems to scale to the very large number of ions that will be required for large-scale quantum computing,” says Jeremy Sage, who together with John Chiaverini leads Lincoln Laboratory’s trapped-ion quantum-information-processing project. “These cage traps work very well, but they really only work for maybe 10 to 20 ions, and they basically max out around there.”

Performing a quantum computation, however, requires precisely controlling the energy state of every qubit independently, and trapped-ion qubits are controlled with laser beams. In a surface trap, the ions are only about 5 micrometers apart. Hitting a single ion with an external laser, without affecting its neighbors, is incredibly difficult; only a few groups had previously attempted it, and their techniques weren’t  practical for large-scale systems.

Getting onboard

That’s where Ram’s group comes in. Ram and Karan Mehta, an MIT graduate student in electrical engineering and first author on the new paper, designed and built a suite of on-chip optical components that can channel laser light toward individual ions. Sage, Chiaverini, and their Lincoln Lab colleagues Colin Bruzewicz and Robert McConnell retooled their surface trap to accommodate the integrated optics without compromising its performance. Together, both groups designed and executed the experiments to test the new system.

“Typically, for surface electrode traps, the laser beam is coming from an optical table and entering this system, so there’s always this concern about the beam vibrating or moving,” Ram says. “With photonic integration, you’re not concerned about beam-pointing stability, because it’s all on the same chip that the electrodes are on. So now everything is registered against each other, and it’s stable.”

The researchers’ new chip is built on a quartz substrate. On top of the quartz is a network of silicon nitride “waveguides,” which route laser light across the chip. Above the waveguides is a layer of glass, and on top of that are niobium electrodes with tiny holes in them to allow light to pass through. Beneath the holes in the electrodes, the waveguides break into a series of sequential ridges, a “diffraction grating” precisely engineered to direct light up through the holes and concentrate it into a beam narrow enough that it will target a single ion, 50 micrometers above the surface of the chip.

Prospects

With the prototype chip, the researchers were evaluating the performance of the diffraction gratings and the ion traps, but there was no mechanism for varying the amount of light delivered to each ion. In ongoing work, the researchers are investigating the addition of light modulators to the diffraction gratings, so that different qubits can simultaneously receive light of different, time-varying intensities. That would make programming the qubits more efficient, which is vital in a practical quantum information system, since the number of quantum operations the system can perform is limited by the “coherence time” of the qubits.

“As far as I know, this is the first serious attempt to integrate optical waveguides in the same chip as an ion trap, which is a very significant step forward on the path to scaling up ion-trap quantum information processors [QIP] to the sort of size which will ultimately contain the number of qubits necessary for doing useful QIP,” says David Lucas, a professor of physics at Oxford University. “Trapped-ion qubits are well-known for being able to achieve record-breaking coherence times and very precise operations on small numbers of qubits. Arguably, the most important area in which progress needs to be made is technologies which will enable the systems to be scaled up to larger numbers of qubits. This is exactly the need being addressed so impressively by this research.”

“Of course, it’s important to appreciate that this is a first demonstration,” Lucas adds. “But there are good prospects for believing that the technology can be improved substantially. As a first step, it’s a wonderful piece of work.”


Source: http://news.mit.edu/2016/toward-practical-quantum-computers-0808

Quantum

Bell nonlocality with a single shot

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Mateus Araújo1, Flavien Hirsch1, and Marco Túlio Quintino2,1,3

1Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
3Department of Physics, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan

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Abstract

In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a $p$-value it will give for a physical experiment. Here we show that to obtain a small expected $p$-value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality, when it is formulated as a nonlocal game. We develop an algorithm for transforming an arbitrary Bell inequality into an equivalent nonlocal game with the largest possible gap, and show its results for the CGLMP and $I_{nn22}$ inequalities.

We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables with arbitrarily small $p$-value in a single shot, without needing to collect statistics. We also develop an algorithm for calculating local bounds of general Bell inequalities which is significantly faster than the naïve approach, which may be of independent interest.

Nonlocal games are cooperative games between two parties, Alice and Bob, that are not allowed to communicate. The maximal probability with which Alice and Bob can win the game depends on how the world fundamentally works: if it respects classical ideas about locality and determinism, this maximal probability is given by the local bound. On the other hand, if the world works according to quantum mechanics, the maximal probability is given by the Tsirelson bound, which is larger than the local bound. This makes it possible to experimentally falsify the classical worldview: let Alice and Bob play a nonlocal game with quantum devices for many rounds, and if they win more often than the local bound predicts, that’s it.

The number of rounds it takes for a decisive rejection of the classical worldview depends on the statistical power of the nonlocal game: a more powerful game requires fewer rounds to reach a conclusion with the same degree of confidence. We show that in order to get a large statistical power, it is enough to have a large gap between the local bound and the Tsirelson bound of the nonlocal game. Moreover, we show that this gap depends on how precisely a nonlocal game is formulated, so we develop an algorithm to maximise the gap over all possible formulations of a nonlocal game. With this, we derive the most powerful version of several well-known nonlocal games, such as the CHSH game, the CGLMP games, and the Inn22 games.

A natural question to ask is how high can the statistical power of a nonlocal game get. We show that it can get arbitrarily high, by constructing two nonlocal games with gap between their local and Tsirelson bounds arbitrarily close to one. This makes it possible to conclusively falsify the classical worldview with a single round of the nonlocal game, without needing to collect statistics. Unfortunately, neither of these games is experimentally feasible, so the question of whether a single-shot falsification is possible in practice is still open.

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Quantum

Optimization of the surface code design for Majorana-based qubits

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Rui Chao1, Michael E. Beverland2, Nicolas Delfosse2, and Jeongwan Haah2

1University of Southern California, Los Angeles, CA, USA
2Microsoft Quantum and Microsoft Research, Redmond, WA, USA

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Abstract

The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT gates between the data qubits with nearest-neighbor ancilla qubits.

Here, we present surface code error-correction schemes using $textit{only}$ Pauli measurements on single qubits and on pairs of nearest-neighbor qubits. In particular, we provide several qubit layouts that offer favorable trade-offs between qubit overhead, circuit depth and connectivity degree. We also develop minimized measurement sequences for syndrome extraction, enabling reduced logical error rates and improved fault-tolerance thresholds.

Our work applies to topologically protected qubits realized with Majorana zero modes and to similar systems in which multi-qubit Pauli measurements rather than CNOT gates are the native operations.

► BibTeX data

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Classical Simulations of Quantum Field Theory in Curved Spacetime I: Fermionic Hawking-Hartle Vacua from a Staggered Lattice Scheme

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Adam G. M. Lewis1 and Guifré Vidal1,2

1Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario, Canada, N2L 2Y5
2X, The Moonshot Factory, Mountain View, CA 94043

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Abstract

We numerically compute renormalized expectation values of quadratic operators in a quantum field theory (QFT) of free Dirac fermions in curved two-dimensional (Lorentzian) spacetime. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation values of quadratic operators in the continuum. As illustrative applications, we show how to recover the Unruh effect in flat spacetime and how to compute renormalized expectation values in the Hawking-Hartle vacuum of a Schwarzschild black hole and in the Bunch-Davies vacuum of an expanding universe described by de Sitter spacetime. Although here we address a non-interacting QFT using free fermion techniques, the framework described in this paper lays the groundwork for a series of subsequent studies involving simulation of interacting QFTs in curved spacetime by tensor network techniques.

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Cited by

[1] Adam G. M. Lewis, “Hadamard renormalization of a two-dimensional Dirac field”, Physical Review D 101 12, 125019 (2020).

[2] Yue-Zhou Li and Junyu Liu, “On Quantum Simulation Of Cosmic Inflation”, arXiv:2009.10921.

The above citations are from SAO/NASA ADS (last updated successfully 2020-10-28 10:51:27). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2020-10-28 10:51:25: Could not fetch cited-by data for 10.22331/q-2020-10-28-351 from Crossref. This is normal if the DOI was registered recently.

Source: https://quantum-journal.org/papers/q-2020-10-28-351/

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