New paper by the Theory team

We present our last article “Data re-uploading for a universal quantum classifier”, by A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster and J. I. Latorre. It is available in arXiv:1907.02085 and SciRate

 

The main result of this work is to show that there is a trade-off between the number of qubits needed to perform classification and multiple data re-uploading.

The quantum classifier we built can be understood as a modification of a Neural Network. In feed-forward neural networks (NN), each data point is entered and processed in each neuron. If NN were affected by the no-cloning theorem, they couldn’t work as they do. To build a quantum classifier (QClass), we need to load classical data several times along the computation.

To upload and process data in the QClass, we use a general unitary gate. Each of these gates (called “layer L”) introduces the data points “x” and the processing parameters “phi” that should be adjusted by using some cost function.

We train a single-qubit QClass by dividing the Bloch Sphere into several regions, one for each class, and fine-tune the processing parameters to distribute each data point to its corresponding region. We choose these regions to be maximally orthogonal.

Then, we can define the cost function as the fidelity of the final state of the QClass and the corresponding “class state”. We propose two ways to do that, which can be found in the article. A single-qubit QClass can’t represent any quantum advantage, although, for its simplicity, could be a part of larger circuits. However, this QClass can be generalized to multi-qubit QClass, where the introduction of entanglement will improve the classification procedure. Once we have defined the QClass and the cost function, we need to use a classical minimization method to find the processing parameters. The QClass belongs to the family of parametrized quantum circuits, as the VQE or Qautoencoder. We have used the L-BFGS-B algorithm from scipy.

Benchmark: we have tested the single- and multi-qubit QClass composed by a different number of layers in several problems with different characteristics.

 

New Doctor at Quantic!

We are glad to announce that last June 21st the member of Quantic Alba Cervera-Lierta has become the first Quantic doctor. She defended her PhD thesis in front of Dr. Alejandro Perdomo-Ortiz (Zapata Computing Inc.), Dr. Ivano Tavernelli (IBM-Zürich) and Prof. Germán Sierra (IFT-CSIC).

The whole Quantic Group congratulates you. Your amazing perseverance as well as your dedication has at last paid off.

Congrats, Alba! There is a wonderful future ahead of you!

 

 

Experimental team moves to IFAE

Since May 1st 2019, the experimental team in Quantic led by Pol Forn-Díaz is now located at the High Energy Physics Institute (IFAE, Institut de Física d’Altes Energies), located at the UAB campus in Bellaterra, near Barcelona.

The move represents the first time IFAE gets involved in quantum computation, joining in this way BSC and UB within the QUANTIC family. IFAE has traditionally focused its research in particle detection, both at accelerators as well as those with cosmic origin. It also develops X-ray detection for medical purposes, neutrinos, and more recently gravitational waves. The electronics and mechanical workshops are world-class and will be extremely positive for the development of the experimental team at Quantic.

Pol Forn-Díaz has established the Quantum Computing Technology group at IFAE, being the PI of this new line of research. One of the other PIs at IFAE, Prof. Manel Martínez who led the creation of the MAGIC consortium and now leads the CTA project on gamma-ray astronomy, is joining the Quantic team, strengthening the experimental side significantly.

The rest of the experimental team in QUANTIC is also moving to IFAE. All IFAE members will retain the BSC affiliation through an institutional agreement signed between the two centers.

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.

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!