Three papers published

When it rains it pours. I had three papers published in the last week. One experimental paper and two papers about entanglement.

  1. Experimental violation of the Leggett–Garg inequality in a three-level system. A cool experimental project with IQC’s liquid state NMR group.    Check out the outreach article  about this experiment.
  2. Extrapolated quantum states, void states and a huge novel class of distillable entangled states. My first collaboration with Tal Mor and Michel Boyer and my first paper to appear in a bona fide CS journal (although the content is really mathematical physics). It took about 18 months to get the first referee reports.
  3. Entanglement and deterministic quantum computing with one qubit. This is a follow up to the paper above, although it appeared on arXiv  a few months earlier.

Towards quantum supremacy

 Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.

Asher Peres

Being a theorist, it is easy to forget that physics is an empirical science.  This is especially true for those of us working on quantum information. Quantum theory has been so thoroughly tested, that we have gotten into the habit of assuming our theoretical predictions must correspond to physical reality. If an experiment deviates from the theory, we look for technical flaws (and usually find them) before seeking an explanation outside the standard theory. Luckily, we have experimentalists who insist on testing our prediction.

Quantum computers are an extreme prediction of quantum theory. Those of us who expect to see working quantum computers at some point in the future, expect the theory to hold for fairly large systems undergoing complex dynamics.  This is a reasonable expectation but it is not trivial.  Our only way to convince ourselves that quantum theory holds at fairly large scales, is through experiment. Conversely, the most reasonable way to convince ourselves that the theory breaks down at some scale, is through experiment. Either way, the consequences are immense,  either we build quantum computers or we make the most significant scientific discovery in decades.

Unfortunately, building quantum computers is very difficult.

There are many different routes towards  quantum computers.  The long and difficult roads, are those gearing towards universal quantum computers, i.e those that are at least as powerful as any other quantum  computer. The (hopefully) shorter and less difficult roads are those aimed at specialized (or semi or sub-universal) quantum computers. These should outperform classical computers for some specialized tasks and allow a demonstration of quantum supremacy; empirical evidence that quantum mechanics does not break down at a fairly high level of complexity.

One of the difficulties in building quantum computers is optimizing the control sequences. In many cases we end up dealing with catch-22. In order to optimize the sequence we need to simulate the system; in order to simulate the system we need a quantum computer; in order to build a quantum computer we need to optimize the control sequence…..

Recently Jun Li and collaborators found a loophole. The optimization algorithm requires a simulation of the quantum system under the imperfect pulses. This type of simulation can be done efficiently on the same quantum processor. We can generate the imperfect pulse `perfectly’, on our processor and it can obviously simulate itself.   In-fact, the task of optimizing pulses seems like a perfect candidate for demonstrating quantum supremacy.

I was lucky to be in the right place at the right time and be part of the group that implemented this idea on a 12-qubit processor. We showed that at the 12-qubit level, this method can outperform a fairly standard computer. It is not a demonstration of quantum supremacy yet, but it seems like a promising road towards this task. It is also a promising way to optimize control pulses.

As a theorist, I cannot see a good reason why quantum computers will not be a reality, but it is always nice to know that physical reality matches my expectations at least at the 12-qubit level.

P.S – A similar paper appeared on arXiv a few days after ours.

  1. Towards quantum supremacy: enhancing quantum control by bootstrapping a quantum processor – arXiv:1701.01198
  2. In situ upgrade of quantum simulators to universal computers – arXiv:1701.01723
  3. Realization of a Quantum Simulator Based Oracle Machine for Solving Quantum Optimal Control Problem – arXiv:1608.00677

Quantum discord

After a long an eventful month that included a visit by Kavan Modi to IQC and my visit to Israel (I’m posting from Israel), it’s time I got back to writing something. This time I’ll say something about my work for the past four years (as promised). One of the main subjects of my research is quantum correlations, and their role in defining the difference between quantum and classical (not quantum) systems.
Imagine a piece of information shared between two people Alice and Bob. Now think of a way to quantify the correlations between them. One way to quantify correlations is to ask what can Alice know about Bob’s part of the information by looking at her own part.
For example lets say Alice and Bob are each given a queen from a chess board. Alice then looks at her queen and sees it is white. She now knows Bob’s queen must be black. Alice and Bob are strongly correlated, since Alice always knows Bob’s piece by looking at her own.
For the second example Alice and Bob are each given a queen, but this time from a Deck of cards. If Alice sees a red queen she can say that it is more likely that Bob has a black queen, but she has no certainty. Correlations are lower in this case then in the chess example.
There is another way to account for correlations. We can ask about difference between the information in Alice and Bob’s hands individually and the information in their hands together. In the chess example Alice and Bob can each get one of two types of queens: black or white Together they also have two options Black White or White Black.
It turns out that both options for quantifying correlations are the same. To see this in the example we need to quantify the information in bits. Since Bob has two options in his hand “black queen” or “white queen” he has one bit of information. The amount of information Alice can discover about Bob is precisely this one bit. So they have one bit of correlations. Alternatively we can say that Alice has one bit of information: “black queen” or “white queen”; Bob has one bit of information: “black queen” or “white queen” and together they also have one bit “black white” or “white black”. The difference (1+1)-1 is again 1 bit so there is one bit of correlations.
Since i’m avoiding maths you will have to take my word that both methods give the same result in all cases… in the classical world. In the quantum world things are a bit different.
There are two essential (and related) aspects of quantum theory that make these two ideas about how to to quantify correlations give different results. 1) Measurements affect the system. If Alice wants to know the color of her queen, she needs to make a measurement, this measurement can change the state of the system; and 2) Quantum systems can be correlated in a much stronger way then classical systems, a phenomenon known as entanglement.
Before discussing the first aspect in detail, I will say a bit about entanglement. Entanglement was a term coined by Schrodinger in his famous “cat” paper, this paper was inspired by the earlier “paradox” of Einstein Podolski and Rosen (EPR). They showed that quantum mechanics predicts a situation where a system shared by two parties is in a well defined state although locally it is not defined. A system is in a well defined state if making a measurement on this system will give some result with certainty. So if I give Alice and Bob an entangled system I can predict the result of a measurement made on the whole system, but I cannot predict the result of a measurement made by Alice and Bob separately.
Entanglement is the most remarkable prediction of quantum mechanics, and in one way of another it is the driving force behind most of the really cool quantum phenomena. From quantum computers to Schrodinger’s cat. Nevertheless entanglement does not account for all the non-classical features of the theory. At least not directly. When discussing correlations, measurements and their effects on the system play a crucial role in describing non-classicality. To explain quantum measurements we can imagine a quantum system as an arrow pointing to some direction, X, in the simplest case we can think of this problem in two dimensions.
A quantum measurement is a question regarding the direction of the arrow. Is the arrow pointing in direction A? This has one of two results either yes or no. The probability is given by the angle between the “actual” direction and the direction in question. The effect of the measurement is that the arrow will now point in the same direction as the result. If the answer is yes it will point in direction A if the answer is no, it will point in the opposite direction.

 

A quantum measurement will "collapse" the state X into A or Not A.

A quantum measurement will “collapse” the state X into A or Not A.

Ok so what does this have to do with correlations? Well lets go back to the two definitions for correlations. The first was “What information can Alice find about Bob by looking at her own system”. In the quantum case this is no a clear question, we need to also say what measurement Alice is making. Different measurements will reveal different information about Bob. The second definition for correlations is what is the difference between the information in Alice’s hands plus the information in Bob’s hands and the information in their joint system” This is not directly related to measurement, so clearly it is not the same as the first definition. The difference between these definitions in the quantum case is the quantum discord. It is a measure of the “quantumness” of correlations.
As it turns out discord can be found in many interesting quantum systems and paradigms, but it is not yet clear what this means…