Quantum Bayesian Networks

September 27, 2011

El ordenador cuántico superconductivo de UCSB – una arquitectura von Neumann con elevadores y pisos de almacenamiento

Filed under: Uncategorized — rrtucci @ 9:03 pm

This is a translation from English to Spanish of the previous post. My mother was Latin American. This entry is in her memory.

Fig.1

La Fig. 1 no es una manta de los indios Navajo. Este hermoso cuadro adornó la portada de la revista abril 2011 de Nature Physics. Se refiere a un artículo (disponible a través de ArXiv aquí ) el cual describe un experimento que puso a prueba un conjunto de operaciones para transportar excitaciones cuánticas entre resonadores y qubits (qubits de tipo superconductivos de fase). Ser capaz de realizar este conjunto de operaciones es un objetivo crucial de la arquitectura de UCSB (llamada “ReZQu”) para una computadora cuántica. Cada uno de los tres senderos serpentinos es un resonador y cada uno de los dos cuadrados negros es un qubit. El aparato más reciente construido por UCSB difiere de esta figura sólo en que añade dos partes más, dos “registros para reducción a cero”.

He hablado antes, en las siguientes entradas a este blog, sobre la excelente labor de Investigación y Desarrollo de computación cuántica que están realizado los grupos de Martinis y Cleland en UCSB (Universidad de California en Santa Bárbara):

Desde entonces, el grupo UCSB ha progresado constantemente en sus esfuerzos para construir un ordenador cuántico. Echa un vistazo a su último papel:

Implementing the Quantum von Neumann Architecture with Superconducting Circuits, by Matteo Mariantoni, H. Wang, T. Yamamoto, M. Neeley, Radoslaw C. Bialczak, Y. Chen, M. Lenander, Erik Lucero, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, John M. Martinis

En mi humilde opinión, a la luz de este trabajo, creo que cualquiera que siga afirmando que tomará 20 años lograr construir un ordenador cuántico, no tiene ni puta idea.

Permítanme ahora dar un breve resumen del papel.

El trabajo descrito en el papel demuestra una computadora cuántica “universal” (es decir, de propósito general) con dos qubits. (Sin embargo, los científicos de UCSB no ven impedimento alguno a que se añadan muchos más qubits, y esperan hacerlo en un futuro próximo). La mayor parte de su aparato está construido sobre un chip utilizando técnicas estándar de microfabricación y componentes también muy estándar para frecuencias de radio y microondas. Es cierto que el chip tiene que ser enfriado a temperaturas mili-Kelvin. Por suerte, los refrigeradores que logran tales temperaturas han mejorado considerablemente recientemente, y ya no dependen para su funcionamiento en costoso helio líquido.

El papel informa que dos algoritmos cuánticos se han ejecutado con el nuevo aparato: la transformación cuántica de Fourier, con una fidelidad de 66%, y la transformación de Toffoli para controlar una fase usando dos qubits de control, con una fidelidad de 98%.  Estos dos algoritmos son típicos para un ordenador cuántico de modelo-puertas, en lugar de un ordenador cuántico de modelo-adiabático, que es lo que D-Wave ofrece. Estos números para fidelidad no son estelares. En realidad, están muy por debajo de lo necesario para hacer  corrección cuántica de errores y el algoritmo de Shor. (Sin embargo, podrían ser lo suficientemente buenos — yo y mis algoritmos, no somos demasiado exigentes —  para la realización de mi algoritmo que mejora el algoritmo de Grover. )

Los científicos de UCSB llaman a sus ideas de diseño de un ordenador cuántico, la arquitectura ReZQu (ReZQu denota las palabras Resonador / Zero / Qubit). Esta arquitectura es de tipo von Neumann. En el caso de los ordenadores clásicos, una arquitectura de von Neumann cuenta con una unidad central de proceso (central processing unit, CPU) para la realización de operaciones y una memoria (random access memory, RAM) para el almacenamiento de instrucciones y datos. El ordenador de UCSB todavía almacena las instrucciones en un ordenador clásico, pero tiene una sección (llamada quRAM) para el almacenamiento de datos cuánticos y otra sección (llamada quCPU) para hacer cálculos cuánticos.

Fig.2

Ver Fig. 2. El quCPU (caja azul) incluye dos qubits Q1 y Q2, y además el resonador B para transporte de datos. El quRAM (cajas magenta) se compone de dos resonadores M1 y M2 que sirven de memoria, y dos registros para reducción a cero Z1 y Z2.

Los resonadores actúan como tanques de retención para uno o más fotones (todos los fotones dentro de un resonador tienen la misma frecuencia, por lo que ocupan un nivel degénero de energía ). Por el contrario, los qubits tienen dos niveles discretos y distintos de energía (en realidad tienen más de 2 niveles energéticos, pero sólo los dos niveles más bajos se utilizan. Los niveles más altos tienen una separación de energía diferente a la de los dos más bajos, por lo que las transiciones entre los dos niveles más bajos pueden ser excitadas sin excitar transiciones a los niveles más altos). Los registros para reducción a cero también son sistemas de dos niveles. Se utilizan para “botar información cuántica”, es decir, para reducir a cero un qubit (es decir, para colocarlo en su nivel energético más bajo cuando ese qubit se pone en contacto (con la misma frequencia) con el registro para reducción a cero.)

El eje horizontal de la figura 2 mide desplazamiento en una dimensión espacial y el eje vertical mide frecuencia. Las frecuencias del eje vertical varían de 6 a 8 MHz. M1, M2, B, Z1, Z2, es decir, todos los elementos excepto los dos qubits (Q1 y Q2) tienen una frecuencia fija y distinta (es decir, bien separada de las otras). A diferencia de las frecuencias de los otros elementos, las frecuencias de Q1 y Q2 no son fijas. Pueden ser variadas a voluntad usando algo llamado pulsos zeta. La frecuencia de Q1 (respectivamente, Q2) se puede cambiar de manera que coincida con la de M1, o la de Z1 o la de B (respectivamente, M2, Z2, B).

Es por eso que me gusta llamar a estos qubits “elevadores”, porque la Fig.2 parece un edificio de varios pisos (= frecuencias o energías). Un elevador (= un qubit) puede pasar de un piso a otro. Una vez llega a un piso determinado, puede absorber a una persona (= una excitación cuántica) de ese piso, o liberar a una persona a ese piso. Cada elevador (= qubit) sólo puede albergar una persona a la vez, pero los pisos de almacenamiento (= resonadores) pueden albergar a varias personas.

Si el qubit Qj (j = 1,2) fuera de larga duración, no habría necesidad de darle una memoria Mj. La razón de ser de las memorias Mj es que estas son más duraderas que los qubits. En el experimento presente, las excitaciones de resonador tienen un tiempo de coherencia (es decir, tiempo de vida) de alrededor de 4 microsegundos, mientras que las excitaciones de los qubits viven cerca de una décima parte de ese tiempo. Los científicos de UCSB creen que en un futuro cercano, van a lograr identificar y luego inventar una manera de evitar las fuentes de ruido que limitan la vida de las excitación de resonador. El aparato actual de UCSB puede realizar una sola operación elemental en unos 10 nanosegundos, por lo que su tiempo de coherencia de 4 microsegundos ya le permite llevar a cabo varios cientos de operaciones elementales.

Si deseas profundizar más en los detalles de la arquitectura de UCSB para ordenadores cuánticos, el profesor Martinis mantiene una página web realmente excelente, muy pedagógica. En particular disfruté mucho leer los apuntes de las clases que dió en una escuela de verano en Finlandia, en agosto de 2007. Estos apuntes se pueden encontrar en la sección “Tutorials” de su página web. También aprendí mucho dando una miradita rápida a las varias tesises que están disponibles en la sección “Theses” de su página web.

September 25, 2011

UCSB’s Superconducting Quantum Computer—A von Neumann Architecture with Elevators and Storage Floors

Filed under: Uncategorized — rrtucci @ 4:02 pm

Fig.1

Fig. 1 is not a Navajo blanket. This beautiful picture graced the April 2011 cover of Nature Physics. It refers to an article (available via ArXiv here) describing an experiment that tested a suite of operations that shuttle quanta between resonators and superconducting phase qubits. Being able to perform this suite of operations is a crucial objective of the UCSB quantum computer architecture (called “ReZQu”). Each of the 3 windy paths is a resonator and each of the 2 black squares is a qubit. The latest UCSB device differs from the one shown in this figure only in that it adds two “zeroing registers”.

I’ve spoken before, in following blog posts, about the superb quantum computing R&D being done by the Martinis and Cleland groups at UCSB:

Since then, the UCSB group has been making steady progress in their QC efforts. Check out their latest paper:

Implementing the Quantum von Neumann Architecture with Superconducting Circuits,
by Matteo Mariantoni, H. Wang, T. Yamamoto, M. Neeley, Radoslaw C. Bialczak, Y. Chen, M. Lenander, Erik Lucero, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, John M. Martinis

IMHO, in light of this paper, I think anybody who still claims it will take 20 years before QCs arrive, is clueless.

Let me now give a short executive summary of the paper.

The paper demonstrates a “universal” (i.e., general purpose) quantum computing device with two qubits (However, the UCSB scientists see no impediments to adding substantially more qubits to their device (“scaling it”), and they expect to do this in the near future). Most of their device is built on a chip using standard microfabrication techniques and it utilizes standard radio and microwave frequency components. The chip does need to be cooled to milli-Kelvin temperatures. Luckily, refrigerators that achieve such temperatures have improved considerably in recent times, no longer relying on costly liquid helium.

The paper reports that two quantum algorithms were performed on the new rig: the quantum Fourier transform, with 66% fidelity, and the three-qubit Toffoli OR phase gate, with 98% fidelity. These two algorithms are typical for a gate-model QC, as opposed to an adiabatic-model QC, which is what D-Wave offers. These fidelity numbers are not stellar; actually, they are far below what is necessary for doing quantum error correction and Shor’s algorithm. (But they might be good enough — me and my algorithms, we are not too demanding — for performing my algorithm that improves upon Grover’s algorithm.)

The UCSB scientists call their QC design ideas the ReZQu architecture (ReZQu stands for Resonator/Zero/Qubit). Their architecture is von-Neumann-like. In the case of classical computers, a von Neumann architecture comprises a central processing unit (CPU) for performing operations and a memory (RAM) for holding instructions and data. Their QC still stores the instructions in a classical computer, but it has one section (called the quRAM) for storing quantum data and another section (called the quCPU) for doing quantum calculations.

Fig.2

See Fig.2. The quCPU (blue box) includes two qubits Q1 and Q2 and the bus resonator B. The quRAM (magenta boxes) comprises two resonators M1 and M2 that serve as memory and two zeroing registers Z1 and Z2.

Resonators act like holding tanks for one or more photons (all of the photons held by a resonator are of the same frequency, so they occupy a degenerate energy level). On the contrary, the qubits have two discrete, separate energy levels (they actually have more than 2 levels, but only the lowest two are used. The higher levels have a different energy separation than the lowest two, so that transitions between the lowest two levels can be excited without exciting transitions to the higher levels). The zeroing registers are also two level systems. They are used for “dumping quantum information”, i.e., to bring a qubit they are put in contact with to its “zero” (i.e.. lowest) energy level.

The horizontal axis of Fig.2 measures distance in one spatial dimension and the vertical axis measures frequency. The frequencies on the vertical axis range from about 6 to about 8 MHz. M1, M2, B, Z1, Z2, i.e., all elements except the two qubits (Q1 and Q2) have a fixed, distinct (i.e, well separated from the others) frequency. Unlike the frequencies of the other elements, the frequencies of Q1 and Q2 are not fixed. They can be varied at will using something called z-pulses. The frequency of Q1 (respectively, Q2) can be adjusted so as to coincide with either M1, Z1 or B (respectively, M2, Z2, B).

That’s why I like to call them “elevator qubits”, because Fig.2 resembles a building with various floors (= frequencies or energies). An elevator (= a qubit) can move from one floor to another. Once it reaches a certain floor, it can absorb a person (= a quantum excitation) from that floor, or release a person into that floor. Each elevator (= qubit) can only hold one person at a time but the storage floors (= resonators) can hold multiple people.

If qubit Qj (j=1,2) were long-lived, there would be no need for giving it a memory Mj. The raison d’être for the memories is that memories are longer lived than qubits. In the present experiment, resonator excitations have a coherence time (i.e., a lifetime) of about 4 microseconds, whereas qubit excitations live about a tenth of that time. The UCSB scientists hope that in the future, they will identify and figure out how to avoid sources of noise which limit the life of resonator excitations. The UCSB device can perform a single elementary operation in about 10 nanoseconds, so its current 4 microsecond coherence time already allows it to perform a few hundred elementary operations.

If you want to delve more deeply into the details of the UCSB QC architecture, Martinis keeps a really excellent, highly pedagogical website. I particularly enjoyed reading the pdf files of the lectures he gave at a Summer School in Finland, on August 2007. These lectures can be found in the “Tutorials” section of his website. I also learned a lot by skimming through the various theses that are available in the “Theses” section of his website.

September 17, 2011

Perimeter announces Isaac Newton Chair

Filed under: Uncategorized — rrtucci @ 4:55 pm

Check out the following news article about Perimeter Institute (PI). PI and its sister institute, the Institute for Quantum Computing (IQC), are on the brink of something. Alas, neither institute is excelling at building an actual quantum computer (unlike UCSB, Yale, NIST, D-Wave, etc., etc.), but they are making great advances in chairs.

Perimeter announces Isaac Newton Chair
(By Ashley Csanady, The Waterloo Record, Fri Sep 16 2011)

excerpts:

WATERLOO — As window washers discussed the recent RIM stock prices while priming the windows of the new Stephen Hawking Centre at the Perimeter Institute for its grand opening Saturday, an IMPORTANT announcement for the think-tank’s future took place inside.

Dr. Xiao-Gang Wen will hold the inaugural Isaac Newton Chair in Theoretical Physics, the first of five, 10-year-long, tenured chairs to be filled, each named for a historically important physicist.

“There is not a single chair in the world named for Sir Isaac Newton, except this one,” said Neil Turok, director of the Perimeter Institute. “This chair is a game changer in science. All of a sudden, the Perimeter Institute will be taken extremely seriously in the world of interior decoration.”

Bill Downe, president and chief executive officer of the BMO Financial Group, said his company is proud to invest in “what people are starting to call the emerging Quantum Valley here in Ontario. We think we have another Nortel or Justin Bieber in our hands.”

In the above picture, captured with an iPhone, Mike Lazaridis (the guy with the very white hair) shares a laugh with reporters after the announcement of the commodious chair.

Lazaridis, co-CEO of RIM, is the main financial contributor to PI and IQC. These two institutes currently employ more than 100 scientists full-time, and are planning to expand to 200 scientist, heck, make it 300, in the near future. It will all be funded from future sales of the Blackberry and Playbook.

“The IQC thinks” Lazaridis said, “that they can roll out Laflamme’s super-advanced non-scalable NMR quantum computer by September. The IQC also recently conducted a very impressive double slit experiment in a train, using the passengers of the train as photons. They are also very keen on quantum cryptography and a quantum internet. Just this month they held a school at IQC to teach undergraduates about quantum cryptography. Those students will be much in demand when post-quantum cryptography takes hold of the world.”

September 12, 2011

Is Building a Quantum Computer Now Within the Reach of Hobbyists?

Filed under: Uncategorized — rrtucci @ 5:40 pm

The legions of science & technology “geek” hobbyists who built early automobiles, aeroplanes, radios, model rockets, homebrewed computers, Linux operating system … (more recently even genetic engineering)—these amateur scientists have a long and glorious history. In most cases, their main goal was not to build a device that worked as well as an off-the-shelf one, but rather to try to build a working device from scratch, so as to be intimately familiar with every nut and bolt in it. To do this as cheaply as possible. To learn a lot and have a lot of fun in the process.

It’s inevitable that some hobbyists will eventually try to build their own quantum computer. Recent NIST work, about which I wrote a previous blog post, may soon make this possible. The new NIST contraption avoids many of the expensive lasers and cooling systems used in their earlier devices. Sci-Tech hobbyists have tried stranger things before. For instance, check out this article about a “fusioneer” named Taylor Wilson (now 17 years old) who built his first nuclear reactor at the tender Mouseketeer age of 14. Now, at first glance, one would think that building a quantum computer would be cheaper and no doubt safer than building a nuclear reactor, don’t you think?

I recently sent the following email to Dr. Christian Ospelkaus, a member of the team that built the new NIST device.

Hi,
According to your recent paper
 “Microwave quantum logic gates for trapped ions”

your ion trap operates at room temperature.
Does that mean that your device does not require any cooling at all? 
Would cooling make it work better by reducing decoherence effects?
How expensive and/or difficult would it be for a hobbyist to reproduce your device?

Thank you in advance for your answers.

He was kind enough to respond immediately to my email. Here is his reply, which he has kindly agreed to let me post here:

Hi Robert,

thanks for your email. The trap does indeed operate at room temperature. In one of our other experiments (Brown et al., Nature 471, 196 (2011), attached), we had used a cryogenic ion trap (4 Kelvin electrode temperature). That can be done to avoid certain motional decoherence effects which were not an issue in the experiment in the paper you were referring to.

If you’d like to look into the cooling issue, you can look at Deslauriers et al. (attached) and Labaziewicz et al. (attached).

As far as reproducing the results goes, it depends on the budget 🙂 The laser system for ionization, optical pumping and pre-cooling is probably around 200k in total, the vacuum apparatus 10k, the control system maybe 25k, the CCD camera 20k, the imaging system 20k, plus a little bit of this and that. Plus you would have to make the chip, which is being produced in a multi-million dollar cleanroom facility at NIST. What helps you in a big place like NIST is that most of these things are already there, if you want to try out a new idea, like these microwave gates.

The corresponding experiment, with lasers used to do the quantum gates, would be much more expensive, an additional 300k for lasers easily.

I don’t know what your background is, but the simplest ion trapping you can do operates at air and traps spores and stuff like that. Here is a funny video by Theodor Hänsch that shows some of these traps:

You can’t do any quantum stuff with that, but it does look pretty. Watch out with the high voltage!

Best regards,

Christian

attachments:

Deslauriers et al. – 2006 – Scaling and Suppression of Anomalous Heating in Io.pdf (480 KB) Download

Brown et al. – 2011 – Coupled quantized mechanical oscillators.pdf (842 KB) Download

Labaziewicz et al. – 2008 – Suppression of Heating Rates in Cryogenic Surface-.pdf (1.9 MB) Download

September 10, 2011

Location, Location, Location Notation, Notation, Notation

Filed under: Uncategorized — rrtucci @ 6:18 am

I’m a fervent believer in the importance of using good notation in physics expositions. Good notation can make the theory and equations in your writings look unambiguous, clear, even obvious. It can also make them easier to apply and re-use later on. On the other hand, bad notation can make exactly the same theory and equations look ambiguous, confusing, hard to understand, enigmatic, hard to re-use. Same thing with good and bad terminology.

Often, when I dislike the notation or terminology used by previous authors, I’ll change it. I just can’t resist the urge to change it if I can find something that works better. It’s a sort of obsessive compulsive behavior. Some people prefer to stick with the notational conventions laid out by previous authors, even when those conventions suck. Not me. I’m not talking about changing an “a” for an “x” or something trivial like that. I’m talking about making important changes to stamp out ambiguity and improve clarity and ease of use.

I’ve heard a famous autistic person, Temple Grandin, say on NPR that she, like many other autistics, is hypersensitive to sensory stimuli like loud sounds, the friction produced by clothing on her skin, etc. Sometimes I think I have an autistic-like sensitivity for notation. (No. I don’t think I have autism or Asperger’s although I do think I have a few loose screws.)

Some examples of my notational idiosyncracies:

  • One example of a case where I found the standard notation unbearable:
    Quantum Circuits in the Dirac, Quayle and Bayes Conventions

  • Another, more trivial example: In my papers, I underline random variables instead of following the much more common practice of using capital letters for them. I do this, not because I’m trying to be different, but simply because I want to be able to use both upper and lower case letters (and also Greek letters) as random variables.
  • In my papers, I often denote a CNOT by

    \sigma_X(1)^{n(2)}

    and a Toffoli gate (= doubly controlled NOT) by

    \sigma_X(1)^{n(2)n(3)}

    where 1 labels the target qubit and 2,3 label control qubits. \sigma_X(1) is the X Pauli matrix applied to qubit 1. n(2) is the number operator (n=|1\rangle\langle 1|) applied to qubit 2. This notation is clear, compact, useful and unambiguous (A^B, a matrix A raised to a power B which is itself a matrix, can be defined rigorously). Most of the quantum computing literature uses other, less convenient alternatives to this notation.

September 6, 2011

Microwaving Trapped Ions

Filed under: Uncategorized — rrtucci @ 4:34 pm

The ion trap group at NIST has recently built an ion trap proto-QC that works at microwave frequencies (their old ones worked at optical frequencies and required costly lasers). Their new device is built on a chip and operates at room temperature. It only supports 2 qubits so far though. Pretty exciting and promising, don’t you think?

Check out Chad Orzel’s great blog post about this. It’s always instructive to hear an explanation of an experiment, given by a real experimentalist. Chad Orzel is a Prof of experimental AMO (atomic/molecular/optical) physics at Union College in Schenectady, NY.

My explanation: It’s like a humane version of focusing rays of sunlight on ants. In the humane version, we focus less deadly (?) cell-phone (radar, microwave oven) rays on trapped, yearning to be free, ions. (ions are charged inhabitants of Ionia, a part of ancient Greece.)

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