In Cove a collection of qubits is represented by an instance of IQuantumRegister. The logical manipulation of qubits in a register is largely inspired by Python's list manipulating, or slicing as it is called. There are a variety of ways these qubits can be logically manipulated, the following illustration demonstrates a few:

In the above the numbers represent the index is represented by numbers, just like you would with an array. The letters A - D represent specific qubits. So you can see the SliceTo(2) operation obtains indexes 0 to 2, resulting in qubits A, B, C. The SliceSubset() operation slices the current indexes to an arbitrary set. In this case the qubit at index 2 (C) will become the first one and the qubit at index 1 (A) will become the second qubit in the new slice.

It is important to point out that each of the slicing operation returns a new instance of IQuantumRegister. This means that the slices can be independently manipulated. That being said, they all share the same qubits: so the manipulation of one slice may impact another. As an example if we perform a Not operation on qubit A, it will be Not'ed in every slice.

This allows for easy applications of operations. Take a CNot (controlled not) operation for example, this is an operation on two qubits. So if we take the original register of 4 qubits and want to perform the operation on qubits A and D we can just do something like this:

MyRegister.SliceSubset(new int[] {0, 3}).OperationCNot();

The OperationCNot() will also return the slice after the operation is performed. So this example shows how operations can be chained together to manipulate the register, then discarded if needed- leaving MyRegister as the original 4 qubits after the above line of code is executed.

## Thursday, December 24, 2009

## Friday, December 18, 2009

### D-Wave and Google

Google teaming up with D-Wave has been making a lot of noise lately. I wasn't originally going to write anything about it, until I came across a recent post by Scott Aaronson titled "Hopefully my last D-Wave post ever". I thought the way he wrote it was humorous- I liked the fictional interchange. I recommend reading both the post and comments.

I don't really have too much more to add other than to quote Carl Sagan: "extraordinary claims require extraordinary evidence" [1]. We're still waiting for the extraordinary evidence from D-Wave.

References

[1] C. Sagan, Billions & Billions: Thoughts on Life and Death at the Brink of the Millennium, 1 ed. New York, NY: Ballantine Books, 1997.

I don't really have too much more to add other than to quote Carl Sagan: "extraordinary claims require extraordinary evidence" [1]. We're still waiting for the extraordinary evidence from D-Wave.

References

[1] C. Sagan, Billions & Billions: Thoughts on Life and Death at the Brink of the Millennium, 1 ed. New York, NY: Ballantine Books, 1997.

## Tuesday, December 8, 2009

### Why we should program quantum computers with frameworks

I knew when I started my doctoral research at Colorado Tech that I wanted to do it in quantum computing. I work on software for a living, so I was thinking it would be good if I could combine the two somehow. It didn't take me long in my literature review to come across and settle on quantum computer programming as a research area as a way to blend on these two areas.

One thing really stood out to me at first: most of the existing proposals for quantum computers were languages designed for quantum computing. However, I think there are very strong reasons for creating frameworks on top of existing classical languages instead of creating new languages:

(I've written about this previously in my dissertation on Cove to a certain degree, this just makes it more explicit in a more condensed blog format.)

References

[1] T. J. Bergin, "A History of the History of Programming Languages," Communications. ACM, vol. 50, p. 5, May 2007 2007.

[2] P. W. Shor, "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer," SIAM Journal on Computing, vol. 26, p. 25, October 1997 1997.

[3] E. Knill, "Conventions for Quantum Pseudocode," Los Alamos National Laboratory LAUR-96-2724, 1996.

[4] H. C. Cunningham, L. Yi, and T. Pallavi, "Framework design using function generalization: a binary tree traversal case study," in Proceedings of the 44th annual Southeast regional conference Melbourne, Florida: ACM, 2006.

[5] B. Omer, "A Procedural Formalism for Quantum Computing," in Theoretical Physics. vol. Masters Vienna: Technical University of Viena, 1998, p. 93.

[6] S. Bettelli, "Towards an architecture for quantum programming," in Mathematics. vol. Ph.D. Trento, Italy: University of Trento, 2002, p. 115.

[7] S. Bettelli, T. Calarco, and L. Serafini, "Toward an architecture for quantum programming," The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics, vol. 25, p. 19, August 2003 2003.

One thing really stood out to me at first: most of the existing proposals for quantum computers were languages designed for quantum computing. However, I think there are very strong reasons for creating frameworks on top of existing classical languages instead of creating new languages:

- Over 8500 programming languages have been created [1], but in reality only a few see any sort of wide spread use. In my opinion, it is highly unlikely that we'll adopt new languages solely for the purpose of quantum computing.
- By creating a new language the designer(s) must tackle not only the quantum issues, which are hard enough, but all the classical ones as well. We've spent years on classical languages, the focus of quantum programming design efforts should be on quantum computation, not rehashing classical problems. Tackling the classical issues as well distracts from the goal at hand.
- Quantum computing is only typically utilized for part of the computation. Take Shor's algorithm for factoring [2] as an example: a quantum computer is utilized only for part of the algorithm, the rest is classical. Put that in the bigger picture of whatever software is doing the factoring and it becomes clear that quantum computing really does fit into Knill's QRAM model [3] where the quantum computer is a resource of the classical computer.
- Frameworks are meant to be extended, perhaps in ways the designer didn't envision. Frameworks are much easier to extend (through hot spots [4]) by their very nature than languages are. Extending the framework can lead to more elegant solutions and more readable code as opposed to trying the bend a language to accomplish something the designer didn't intend or want to allow.

(I've written about this previously in my dissertation on Cove to a certain degree, this just makes it more explicit in a more condensed blog format.)

References

[1] T. J. Bergin, "A History of the History of Programming Languages," Communications. ACM, vol. 50, p. 5, May 2007 2007.

[2] P. W. Shor, "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer," SIAM Journal on Computing, vol. 26, p. 25, October 1997 1997.

[3] E. Knill, "Conventions for Quantum Pseudocode," Los Alamos National Laboratory LAUR-96-2724, 1996.

[4] H. C. Cunningham, L. Yi, and T. Pallavi, "Framework design using function generalization: a binary tree traversal case study," in Proceedings of the 44th annual Southeast regional conference Melbourne, Florida: ACM, 2006.

[5] B. Omer, "A Procedural Formalism for Quantum Computing," in Theoretical Physics. vol. Masters Vienna: Technical University of Viena, 1998, p. 93.

[6] S. Bettelli, "Towards an architecture for quantum programming," in Mathematics. vol. Ph.D. Trento, Italy: University of Trento, 2002, p. 115.

[7] S. Bettelli, T. Calarco, and L. Serafini, "Toward an architecture for quantum programming," The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics, vol. 25, p. 19, August 2003 2003.

## Thursday, December 3, 2009

### GHz Manipulation of Quantum States of Electrons

## Wednesday, December 2, 2009

### Paper: Evolution of Quantum Systems by Diagrams of States

I came across this paper on arXiv, titled "Evolution of Quantum Systems by Diagrams of States" by Felloni, Leporati, and Strini. You can get the paper from arXiv here.

I've only skimmed it so far, but it is good to see this sort of thing. I suppose by the nature of things, quantum computation is very math intensive and we lack good visual representations of things. The only real two exceptions to this are quantum circuit diagrams and the Bloch Sphere. The circuit diagrams represent the application of operations to quantum registers (collections of qubits). As an example, here is the circuit diagram to construct a Sum operation from elementary operations:

The other big graphical representation we have is the Bloch Sphere. Basically this is a way of viewing the state of a single qubit on a sphere. In this the poles (of the z axis) represent |0> and |1>, and a point on the surface represents the state of the qubit. This is great for visualizing a single qubit, but doesn't scale beyond that. I wouldn't cite in a paper, but this blog is a more informal forum, so here's the link to Bloch Sphere on Wikipedia. Here's what a Bloch Sphere looks like though:

As I said, it is good to see a paper like this. The abstract the authors put together for the paper sums it up better than I would, so here it is:

I've only skimmed it so far, but it is good to see this sort of thing. I suppose by the nature of things, quantum computation is very math intensive and we lack good visual representations of things. The only real two exceptions to this are quantum circuit diagrams and the Bloch Sphere. The circuit diagrams represent the application of operations to quantum registers (collections of qubits). As an example, here is the circuit diagram to construct a Sum operation from elementary operations:

The other big graphical representation we have is the Bloch Sphere. Basically this is a way of viewing the state of a single qubit on a sphere. In this the poles (of the z axis) represent |0> and |1>, and a point on the surface represents the state of the qubit. This is great for visualizing a single qubit, but doesn't scale beyond that. I wouldn't cite in a paper, but this blog is a more informal forum, so here's the link to Bloch Sphere on Wikipedia. Here's what a Bloch Sphere looks like though:

As I said, it is good to see a paper like this. The abstract the authors put together for the paper sums it up better than I would, so here it is:

We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by quantum circuits. We present quantum diagrams of states for representations of quantum states by density matrices, partial trace operations, density matrix purification and time-evolution by Kraus operators. Following these representations, we describe by diagrams of states themost general transformations related to single qubit decoherence and errors.

Diagrams of states prove to be a useful approach to analyze quantum computations, by offering an intuitive graphic representation of the processing of quantum information. They also help in conceiving novel quantum computations, from describing the desired information processing to deriving the final implementation by quantum gate arrays.

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