Exact ground states of strongly interacting spin systems are normally highly entangled and complex. Yet at particular finite values of the applied magnetic field such systems may exhibit a completely separable exact ground state, i.e. a simple product state where each spin points along a specific direction. Such remarkable phenomenon is known as ground state factorization.

Here we show the existence of an exceptionally degenerate set of completely separable ground states in XXZ systems immersed in a nonuniform field, arising at a remarkable quantum critical point where all magnetization plateaus merge. These points can emerge in arrays of any size, spin and dimension for a wide range of nonuniform field configurations, and exhibit other special critical properties like long range pair entanglement in their immediate vicinity.

The XXZ model is an archetypal quantum spin system which has helped to understand interacting many-body systems and their quantum phase transitions, and which has recently received renewed attention due the possibility of its finite size simulation with state-of-the-art technologies and its potential for implementing quantum information processing tasks. Among other possibilities, present results open the way to design exactly separable ground states in such system through a finite controlled field, which can be used as initial states for quantum protocols.

You can find the paper here:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.220605

And on the arXiv:

https://arxiv.org/abs/1708.00565

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All image credits go to Zach Weinersmith’s Saturday Morning Breakfast Cereal @SMBC

If sharing this image goes against any copyrights, please let me know!

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*Now the shepherds met together, according to custom, that they might send their monthly report about the flocks to the king; into their assembly he came having the ring on his finger, and as he was sitting among them he chanced to turn the collect of the ring inside his hand, when instantly he became invisible to the rest of the company and they began to speak of him as if he were no longer present. He was astonished at this, and again touching the ring he turned the collet outwards and reappeared; he made several trials of the ring, and always with the same result-when he turned the collet inwards he became invisible, when outwards he reappeared. *

*Whereupon he contrived to be chosen one of the messengers who were sent to the court; where as soon as he arrived he seduced the queen, and with her help conspired against the king and slew him, and took the kingdom.*

– The Ring of Gyges, Plato [1]

What would you do in the place of Gyges upon finding a ring that would turn you invisible? Would you use it for a greater good? Or for your own personal benefit? What can we expect from humans to do with power over others?

These are some of the questions about human nature arising from Plato’s thought experiment in the Republic, and they remains as valid today as they were 2,400 years ago. The ring of Gyges has been used as a paradigmatic example when discussing ethics and it can be the perfect starting point towards a discussion about the ethics of quantum computation.

Although it is still not clear what the full extent of the power of quantum computers might be, there are some very particular examples of quantum algorithms that can largely outperform their classical counterparts. One of them is Peter Shor’s factorization algorithm [2], which can factorize any number exponentially faster than any classical algorithm on a classical computer.

Factorizing a number entails the determination of all prime numbers which multiply together to result in the original number. For instance:

The possibility to factorize large numbers efficiently might seem as a handy mathematics trick your nerdy friend might want to pull out as a closing number for his one man show, but its implications are far more complex. One of the most widely used cryptography systems is the RSA public key crystosystem, which is used to encrypt your emails, your bank transactions and your credit cards numbers via the internet. The security of the messages encoded via this encryption method relies on the fact that factorizing a large number is an extremely difficult task to accomplish using your everyday computers. This means that given a sufficiently large quantum computer (i.e., with enough qubits), you could easily break the RSA public key crystosystem and decipher the contents of its message.

I’m hopping that by now you are starting to realize as I do that a quantum computer is just as powerful as the ring of Gyges, and that we should start discussing the ethical challenges that this new era of quantum information processing is producing.

It baffles me that so little is being said about the ethics of quantum computers, while the so-called “threat” of quantum computing has been so widely broadcasted [3-6]. Almost every major nation in the world acknowledges that we could be heading towards a major internet security crisis if a hacker gets its hands on a quantum computer. Most of those governments have joined Google, D-Wave, Microsoft, IBM, Toshiba, any many other private companies in the race towards a quantum computer but *no one* has raised the issue of *ethi**cs* so far.

It is quite obvious that whoever wins the “race” and has the ability to harness the power of quantum computers will hold an incredible advantage over those who don’t have access to these new technologies. The issue of cryptography is only one of many that arise when considering that a scalable quantum computer might be developed in the nearby future. How do we handle the intellectual property of scientific discoveries? What could happen if a government acquires a quantum computer and has the ability to decipher private messages? What if a company manages to construct one? Who could they sell it to? Won’t their profits margins bias their decisions? Wont’ they use their ring of Gyges for their own personal benefit?

As a physicist working in the field of quantum information and quantum computation I believe that these are some questions that need to be addressed not only in the scientific community, but along with private companies and nation governments. I know that with so much at stake it is a sensitive subject, but fortunately quantum computers are still in their infancy and we still have time to raise the issue.

If you see what I see, if you feel as I feel, and if you would seek as I seek, then I ask you to stand beside me.

[1] Plato, the Republic, Book II, 358d—361d.

[2] Peter W. Shor, *Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer*

[3] NSA Says It “Must Act Now” Against the Quantum Computing Threat

[4] NSA memorandum

[5] Australia: Govt Prepares for Quantum Computing Threat to Encryption

[6] Prepare for Threat of Quantum Computing to Encrypted Data, Canadian Conference Told

[7] Here, There and Everywhere, Quantum technology is beginning to come into its own

All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.

Why we should be talking about the ethics of quantum computation by Marco Vinicio Sebastian Cerezo de la Roca is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Based on a work at https://entangledphysics.com/.

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Nothing that is done in one system can instantaneously affect the density matrix of another isolated system, although it can affect the state vector.

Nobel Laureate Steven Weinberg, [1]

[1] “Quantum mechanics without state vectors”, Steven Weinberg, Phys. Rev. A **90**, 042102 (2014).

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One of the most important consequences of the existence of *entanglement* in quantum mechanics is related to the *quantity of information* necessary to describe the state of a quantum system. In a classical system, the number of parameters needed to characterize its state is equal to the sum of the degrees of freedom of each of its components. However, for a quantum system, the number of parameters needed to describe its state grows *exponentially* with the number of constituents. And this makes the task of simulating a quantum system a very difficult one even for systems with few constituents, the computational resources needed for the simulation quickly become unreachable using computational techniques based on classical computers.

In 1982 Nobel laureate Richard Feynman conjectured that these limitations could be overcome using computers based on quantum systems. Based on this conjecture, physicists started exploiting the potential of quantum mechanics to develop new quantum computers (**universal quantum simulators**) capable of simulating quantum systems.

Nowadays there are several quantum systems than can be used as hardware for quantum simulators: trapped ions, cold atoms in optical lattices, liquid and solid-state NMR, photons, quantum dots, superconducting circuits, and NV centres. [1]

Go to the Dictionary of Quantum Information and Quantum Computation.

All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.

The More You Know: Quantum Simulator by Marco Vinicio Sebastian Cerezo de la Roca is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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Although my first thought was to use a generic drawing software the results were not at all satisfying. Thus I proceeded to take the next logical step: an online search for a Quantum Circuit drawing tool. In this article I review two particularly interesting tools I found.

I first came across this website by programmer Davy Wybiral, which is an *online based* **Quantum Circuit Simulator**. It’s interface is very clean and the circuit can be easily and intuitively created by simply selecting the quantum gates and placing them in the circuit. This website produces results such as the following

Additionally, as its name indicates, this website can also perform a simulation of the quantum circuit. For instance, the previous circuit generates the Greenberger-Horne-Zeilinger (GHZ) state

, (1)

and its simulation yields

0.70710678+0.00000000i|000>50.0000%0.70710678 + 0.00000000i|111>50.0000%,

which coincides with Eq. (1).

Although the circuits created with this website are quite nice, there are some operations that are not available and thus cannot be drawn (like measurements). I recommend this website for anyone who needs to quickly draw a Quantum Circuit and who does not know how to use .

A deeper search led me to many downloadable softwares, but in particular it led me to Michael Nielsen’s blog where he recommends this LaTeX package for drawing Quantum Circuits. As cited in their website this tool is

[…] a simple text-format language for describing acyclic quantum circuits composed from single qubit, multiply controlled single-qubit gates, multiple-qubit, and multiple-qubit controlled multiple-qubit gates.

Figures of quantum circuits in the book “Quantum Computation and Quantum Information,” by Nielsen and Chuang, were produced using an earlier version of this package.

Needless to say, after a couple of minutes reviewing their *17 examples*, I was in love with this tool. Once you get the hang of it it’s pretty simple to use and the results are just amazing!

I would *strongly recommend* MIT LaTeX package to anyone who knows how to use and who needs to draw Quantum Circuits on a regular basis.

Although I’m sure there are software out there available for people without programming or experiencie I didn’t try them all out. If any of you has any recommendations I’d be glad to review them!

All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.

Tools for Drawing Quantum Circuits by Marco Vinicio Sebastian Cerezo de la Roca is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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The data in a Quantum Circuit is usually encoded in a -qubit state (other Quantum Circuit models can use -level quantum systems instead of these -level systems) which is set to a known vale, i.e. . Thus, for every qubit in the circuit a horizontal rail, a *wire*, is drawn to represent its evolution, time flows from left to right.

Additionally, a Quantum Circuit is built from elementary quantum gates (unitary operations) acting on a fixed number of qubits. Since Quantum Circuits are read from left to right, leftmost gates act first.

Then, a description of the Quantum System consists of

**Input**: A controlled input -qubit state.**Evolution**: Prescribed sequence of Unitary Single-qubit and Two-qubit logic quantum gates which give the evolution of the initial quantum state.**Output**: Readout (measurement) of the state of the qubits.

Go to the Dictionary of Quantum Information and Quantum Computation.

Quantum Circuits where drawn using this LaTeX package.

All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.

The More You Know: Quantum Circuit por Marco Vinicio Sebastian Cerezo de la Roca se distribuye bajo una Licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional.

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In the *computational basis* the four maximally entangled Bell states are expressed as

,

.

To understand the correlations present in these states consider the Bell state . If a measurement is performed on the first qubit the result may be 0 or 1, after which the two qubit state collapses to or respectively. Then, a measurement on the second qubit *must* result in 0 or 1, yielding the same result as the measurement on the first one. That is, the outcomes of the measurements are *correlated*.

John Bell proved that the correlations present in EPR pairs* cannot be accounted for by any classical theory*. See this article for more.

Go to the Dictionary of Quantum Information and Quantum Computation.

All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.

The More You Know: Bell States/EPR Pairs por Marco Vinicio Sebastian Cerezo de la Roca se distribuye bajo una Licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional.

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,

where and are complex number such that . Since an overall phase has no observable effects, or can be chosen as real numbers and can written as

,

where and . The parameters and define a point on the sphere called the Bloch Sphere (Fig. 1).

The points in the *surface* of the sphere represent *pure* states of the qubit, with as the North pole and as the South pole, and the equator states of the form . Additionally any *mixed state* of a qubit can be represented as a point *inside* the sphere, with maximally mixed states at the center of the Bloch Sphere.

This representation is useful in Quantum Computation to visualize the effect of single qubit gates.

Go to the Dictionary of Quantum Information and Quantum Computation.

All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.

The More You Know: Bloch Sphere por Marco Vinicio Sebastian Cerezo de la Roca se distribuye bajo una Licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional.

Image credits here.

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A classical bit can be in one of two different states: 0 or 1, whereas a Qubit can be in the quantum states , but also in any *superposition* of these two. That is, the state of a Qubit will be of the form

,

where and are complex number satisfying

.

The states and form the so-called *computational basis* . Then, as a mathematical concept, a Qubit is a vector normalized to length 1 in a complex vector field.

Just as it’s classical analogue, a Qubit can have many physical realizations: The polarization of a photon, the spin of an electron or a nucleus, the localization of a charge, among other two-state quantum systems.

Go to the Dictionary of Quantum Information and Quantum Computation.

All text copyright © Marco Vinicio Sebastian Cerezo de la Roca.

The More You Know: Qubit by Marco Vinicio Sebastian Cerezo de la Roca is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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