New article preprint for Quantic

Last May 7th the members of Quantic Carlos Bravo Prieto, Diego García Martín and José Ignacio Latorre published an arXiv preprint named Quantum Singular Value Decomposer.

In this article we propose a hybrid classical-quantum algorithm that produces the Singular Value Decomposition of a bipartite pure state. The proposed algorithm (Quantum Singular Value Decomposer or QSVD) forces a diagonal form of the state by demanding exact output coincidence.

By training the unitaries to force that subtle diagonalization (the more layers the more precision), we recover the singular values from the probabilities of obtaining the computational-basis vectors after measurement. It follows that entropies can be estimated

A peculiar spinoff of the QSVD circuit is the possibility of performing a SWAP operation between parties A and B without using any gate that connects both subsystems. We just have to apply the adjoints of the unitaries in both parties by classical communication of the parameters.

 

We consider a further spinoff. We can use the QVSD and CNOTs as a quantum encoder of information of the original state onto one of its parties. This idea can be reversed and used to create random states with a precise entanglement structure.

 

New article preprint: Quantum circuits for maximally entangled states

Last April 16, Alba Cervera-Lierta, José Ignacio Latorre and Dardo Goyeneche published an arXiv preprint titled “Quantum circuits for maximally entangled states”

One of the main goals of this article is to propose simple quantum circuits (short depth and basic gates) that can be used to test and compare current quantum computers.

Quantum computers should be able to generate and hold highly entangled states. Otherwise, we have very sophisticated classical techniques (such as tensor networks) that can simulate efficiently slightly entangled states.

Following this idea, they proposed to construct circuits that generate Absolutely Maximally Entangled (AME) states. AME states are those pure states which maximally entangle all their bipartitions. A simple way to construct an AME state is by using graph states, that is, states that can be constructed from a graph. Each graph vertex corresponds with the operation F|0> (F = Fourier gate) and each edge is a CZ gate. For example, this circuit generates the AME(5,2) (5 qudits of dimension 2, that is, 5 qubits). For qubits, the operation F|0> is just H|0>.

The existence of AME states for any number of parties and any local dimension is an open problem. For more information, check Felix Huber table for a summary of known AME states:

For qubits, there only exist AME states for n=2 (Bell state), 3 (GHZ state), 5 and 6. This fact totally constraints the number of circuits that we can construct in current quantum computers… So they propose to “simulate” AME states of d>2 using qubits by implementing the mapping

|0> –> |00>,
|1> –> |01>,
|2> –> |10>,

With this mapping, one has “to adjust” the Fourier gates and the generalized CZ gates to multiqubit states. The explicit circuits and details about this mapping can be found in the main paper.

As a final remark, they also find an interesting property of these circuits. It turns out that AME (graph) state circuits majorize, that is, after applying each CZ gate (step), the entanglement of all bipartitions increases or remains equal, never decreases (entanglement measured with entropy S or eigenvalues of the reduced density matrix). In a sense, these circuits maximally entangle all their bipartitions in a very optimal way.

Can we use this property to find and construct highly entangled states, new AME states or simplify current quantum circuits? We will see.

Finally, they implement an AME(5,2) state in a current quantum computer: 3 H gates and 5 CZ gates. The results are not very encouraging… But one should take into account that this is a very hard test for a quantum computer, to force it to maximally entangle all its parts!

First experimental PhD student!

The Quantic team has a new addition: David López Núñez. He is going to be the first experimental PhD student of the Quantic group. He obtained his Bachelor Degree in Physics at Universitat de Barcelona. There, he also studied a Master’s Degree in Advanced Physics. He now moved towards experiments and is currently pursuing a PhD on quantum computing with superconducting circuits.

Welcome David!

New publication by Alba Cervera-Lierta and José Ignacio Latorre

Quantic PhD student Alba Cervera-Lierta and our P.I. José Ignacio Latorre have published a new article on Journal of Physics A: Mathematical and Theoretical.

The article title is “Multipartite entanglement in spin chains and the hyperdeterminant” and the reference is J. Phys. A: Math. Theor. 51 505301 (2018) (arXiv: [quant-ph] 1802.02596).

In this work, they study the multipartite entanglement in spin chains, in particular in the Ising model, XXZ model and Haldane-Shastry model.

As a figure of merit to quantify multipartite entanglement they use the Cayley hyperdeterminant, which is a polynomial constructed with the components of the wave function which is invariant under local unitary transformation. For n=2 and n=3, the hyperdeterminant coincides with the concurrence and the tangle respectively, well known figures of merit for multipartite entanglement. For n=4, Hyperdeterminant is a polynomial of degree 24 that can be written in terms of more simple polynomials, S and T, of degree 8 and 12 respectively.

They observe that these polynomials are able to capture the phase transitions present in the models studied as well as a subclass of quadripartite entanglement present in the eigenstates.

Besides spin chains, they also study the quadripartite entanglement of random states, ground states of random matrix Hamiltonians in the Wigner-Syson Gaussian ensambles and the quadripartite entangled states defined by Vestraete et al in 2002.

This figure shows the hyperdeterminant for the ground state and second excited state of a n=4 Ising spin chain as a function of the transverse magnetic field λ. For an infinite chain, this model has a phase transition at λ=1. As can be seen, the hyperdeterminant peaks close to this phase transition.

Seth Lloyd (MIT) visited us

A few days ago we were very honored to receive one of the top names in the world in Quantum Information such as Prof. Seth Lloyd from the Massachusetts Institute of Technology. Prof. Lloyd gave a seminar at the Physics Department at UB where he described his recent progress in Quantum Machine Learning, a field where he has been focusing lately, being one of the most promising to achieve quantum advantages in real-life applications in a not-so-distant future.

Prof. Seth Lloyd has been one of the pioneers of the quantum information field for his theoretical work in quantum simulation and quantum computation, aside from being very close to experimentalists, as shown by his record of joint works in NMR, superconducting qubits, and photonics, among other experimental areas of quantum information. In recent years his group has also entered the surprising area of Quantum Biology, where work on quantum description of processes such as photosynthesis has been published with a very high impact.

The visit could not end with a tour at Mare Nostrum.

Researchers’ night 2018

Pol Forn-Díaz and Alba Cervera-Lierta have participated in European Researchers’ Night 2018 by giving a talk at Cosmocaixa, Barcelona.

They gave a microtalk which consisted on 8 minutes talk about some scientific topic explained to a general audience. First, Alba presented what is a quantum computer and what are its aplications: to study new chemical reactions, to solve optimization problems or to simulate quantum systems. Second, Pol explained how it works and what is the appearence of its building blocks, qubits. In particular, he showed how is our quantum processor made of superconducting qubits.

 

Quantic team members are very active in scientific outreach activities. Follow us on twitter to stay informed about future events!

 

Tim Menke from MIT visits us

Last week we had a distinguished guest for the whole week. Tim Menke from the MIT group of Engineering Quantum Systems visited us through the MIT-La Caixa Foundation project which Dr. Forn-Díaz has together with Prof. Will Oliver from MIT to develop new circuits for quantum annealing and allow students and PIs to spend short periods of time at MIT/BSC.

Tim’s work is focusing on reverse-engineering circuits by theoretically sampling circuits with different properties and selecting the ones that display a response close to the desired one. Then those circuits can be fabricated and tested in an experiment. Tim also performs measurements in the quantum annealing project within MIT.

Tim has helped us a lot in the lab work to get the qubit control electronics and software up and running. Thanks for the visit Tim!