New paper by Quantic members!

Diego García-Martín and José Ignacio Latorre recently published “The Prime state and its quantum relatives”, together with E. Ribas, S. Carrazza and G. Sierra.Congratulations! You can see this paper in arXiv ( and scirate (

The Prime state is the uniform superposition of all the computational-basis states corresponding to prime numbers. This state encodes, quantum mechanically, arithmetic properties of the primes. Moreover, it can be efficiently created on a quantum computer.

In this paper, it is shown that the Quantum Fourier Transform of this state provides direct access to Chebyshev-like biases in the distribution of primes. Also, the entanglement traits of the Prime state are studied. These reveal correlations between prime numbers. In particular, the reduced density matrix for natural bi-partitions is characterized by the Hardy-Littlewood constants.

A relation is found between the scaling of the von Neumann entropy and the Shannon entropy of half the density of square-free numbers. This relation also holds when considering qudit bases, showing this property is intrinsic to the primes. It also holds when considering states defined from prime numbers belonging to arithmetic progressions.



The entanglement of other quantum number-theoretical states is also studied.
An open-source library that diagonalizes matrices using floats of arbitrary precision has been developed for this paper. In summary, a novel approach to Number Theory using the tools of Quantum Information Theory.

Outreach in Quantic

Quantic group has collaborated in a new outreach article for the Journal “Compàs d’Amalgama” in the University of Barcelona. Carlos Bravo-Prieto, Diego García-Martín and Adrián Pérez-Salinas wrote “Computació i supremacia quàntica, per què tothom parla d’això?” (Quantum computing and supremacy, why does everybody talk about that?) You can all read it here (in Catalan)


New paper by the theory team: measuring the tangle

Measuring the tangle of three-qubit states, by A. Pérez-Salinas, C. Bravo-Prieto, D. García-Martín and J. I. Latorre


In this paper, the authors propose a method for transforming an unknown three-qubit state into its canonical form up to phases. This transformation can be achieved variationally and may be used to estimate the tangle. Simulations on this method have been performed.

The tangle is a three-qubit entanglement invariant that quantifies genuine tripartite entanglement. The state with maximum tangle is the GHZ state (and its local transformations). The distribution of tangle for random three-qubit states is depicted below.


The canonical form up to phases can be achieved when the number of measurements of three possible elements in the computational basis are zero. In this form, the tangle is easily measured. The canonical form can be cast by applying local unitaries on each qubit.


The tangle is affected by errors in the circuit. To mitigate these errors, a post-selection scheme can be applied after measuring the output state. This post-selection consists of discarding those results that should not appear in the canonical form.

First, the authors have analyzed the GHZ state. The estimation of the tangle with this method provides lower values as the errors (“t”) in the circuit increase. Post-selection mitigates the errors considerably.


This behavior has found to be a common tendency for many different random states. In the figure depicted below, each dot corresponds to a random three-qubit state.
With errors comparable to those in the state-of-the-art quantum hardware, the tangle presents a mean underestimation of ~30%. Post-selection lowers this result to ~17%.
Although the method herein presented does not provide any speed up respect to quantum tomography, it can be used as a module for other algorithms, such as a classifier.
UPDATE: This paper has been published in Entropy

Postdoctoral position available for the University of Barcelona

There is a new open post-doc position to work at the University of Barcelona with Dr. Luca Tagliacozzo and Dr. Sofyan Iblisdir. The announcement has been recently published

Dear colleagues,
Applications are invited for one or two postdoctoral positions in the field of Quantum Computation.
The successful candidate will work with Dr. Sofyan Iblisdir and Dr. Luca Tagliacozzo, at the
University of Barcelona (Spain) in quantum computation and related topics, from developing and
characterizing new quantum algorithms, to their classical simulation, to the characterization of noise
and imperfections in specific experimental implementations, to quantum machine learning. Beside
quantum computation, the group has strong expertise in the theory of many-body quantum systems
at and out of equilibrium, and in tensor networks techniques.
The positions are for a period of 1 year that will be possibly extended to 2 years depending
on performances and availability of funding. The positions should be filled as soon as possible.
Applicants are expected to have a doctoral degree in Physics, Computer Science, Mathematics, or a
related discipline before the starting date of the position, and have previous expertise in one (or
more) of the following areas: quantum computation, quantum information, tensor networks,
machine learning, quantum many-body systems, condensed matter physics, quantum field theory.
Applicants should have a strong interest in solving challenging problems, as well as a proven record
of research, including publication of original work in at least one of the above areas. Excellent
scientific writing ability and good communication skills are essential.
Applications should be sent to Dr. Sofyan Iblisdir and should include: 1) a motivation letter;
2) a curriculum vitae including a list of publications; 3) a research statement; 4) the name and email
of two references. All qualified applicants will receive equal consideration without regard to
appearance, beliefs, sex, sexual orientation, gender identity, national origin, disability or age. For
full consideration, applications should be submitted by the 10th of March 2020.

Please direct informal enquiries to:
Dr Sofyan Iblisdir: sofyan.iblisdir(at)
Dr Luca Tagliacozzo: luca.tagliacozzo(at)

New arXiv preprint by the theory team

Scaling of variational quantum circuit depth for condensed matter systems, by C. Bravo-Prieto, J. Lumbreras, L. Tagliacozzo and J.I. Latorre

In this paper, the authors have analyzed the performances of a finite depth quantum circuit in order to encode the ground state of local Hamiltonians. They have shown that as expected, the precision improves exponentially with the depth of the circuit in gapped phases.

In conformally invariant gapless phases, the precision improves very slowly up to a number of layers that increase linearly with the system size. They identify that regime with a finite-depth regime, where the depth of the circuit dictates the appearance of an effective correlation length. Beyond that number of layers, the precision improves again exponentially (finite-size regime).


They have provided an explanation of this phenomenon in terms of Lieb-Robinson bounds, and also compared the power of different variational ansatz in representing the ground state of critical systems. Finally, they believe that, in the context of critical systems, the actual entanglement entropy of the wave-function provides a proper measurement of the effective number of free parameters in the ansatz, the number that is ultimately responsible for the accuracy of the results.



New article by the theory team, now with more finance!

This is Quantic’s latest article “Quantum unary approach to option pricing“, by Sergi Ramos-Calderer, Adrián Pérez-Salinas, Diego García-Martín, Carlos Bravo-Prieto, Jorge Cortada, Jordi Planagumà, and José I. Latorre, available on the ArXiv.

This manuscript introduces a novel algorithm for European option pricing that uses the unary representation of the asset price. That is, each qubit maps into a single price of the underlying asset.

The amplitude distributor that uploads the expected price evolution to the qubit register and the circuit that encodes the estimated payoff into an ancilla are remarkably simple in the unary representation.

Schematic of qubit connectivity map to run the algorithm.

The amplitude distributor only requires first-neighbor interactions between qubits, therefore a simplified chip architecture is enough to run the algorithm.

Results of the algorithm running either unary and binary representations. Unary representation is clearly superior in this particular instance.

This scheme allows for a post-processing procedure that results in error mitigation for Noisy Intermediate-Scale Quantum devices. This algorithm is more robust to noise than their usual binary

Option pricing in this unary representation can therefore be beneficial for near-term quantum computers.

New article by the Theory Team!

This is Quantic’s latest article “Quantum observables for continuous control of the Quantum Approximate Optimization Algorithm via Reinforcement Learning”, by A. Garcia-Saez & J. Riu, available on the ArXiv.
The article presents a classical optimization strategy for the Quantum Approximation Optimization Algorithm (QAOA) using Reinforcement Learning (RL). The algorithm is tested for several instances of the MAXCUT problem.

In general, RL approaches consist of discrete-time agent-environment interactions. The agent is provided with partial/total observation of the environment and maximizes the reward by acting into it.

The QAOA is implemented such that, at each step of an episode of arbitrary but fixed length p, a pair of parameter-dependent unitary transformations are applied to a quantum state.
Gate sequence of the algorithm implemented.
The values of the parameters are selected by the Deep RL agent using as inputs to the Neural Network a set of measurements of the quantum state, which include the expected values of X and Z operators for each qubit as well as the clauses of the objective Hamiltonian individually.
At the end of each episode, the agent is rewarded with an amount equal to the expected value of the objective Hamiltonian in the final quantum state of the environment. Results for an instance of a 3-regular graph with 13 vertices are shown in the following graph:
Moreover, an incremental training strategy that allows the agent to reach larger p’>p episode lengths is successfully used for graphs with 21 qubits and p up to 25:

New experimental PhD student in Quantic!

This week, Fabian Zwiehoff from Germany has enrolled in our group as a new PhD student He did his studies at Karlsruhe Institute of Technology (KIT) and Technische Universität (TU) Berlin, and his Master’s project at ICFO on QKD. He will be working in the experimental team building superconducting quantum devices.

Welcome, Fabian!

Quantic at SONAR+D

Last summer, some members of Quantic were at Sonar+D, showing what a quantum computer looks like. It was a great experience, sharing some days with interesting people who exhibited their projects too. You can see here a little bit of the making of our quantum computer-toy.

We hope you enjoy it as much as we did!

People in this video: Pol Forn, Artur García, David López, Adrián Pérez

David López and his outreach

The Quantic member David lópez Núñez took part in the “Nit de Recerca Jove (European Researchers’ Night) 2019” hosted by CSIC, and gave a talk in his former High School in L’Hospitalet de Llobregat.

The title of the talks was: “Bricocuántica, ¿Cómo hacer un ordenador cuántico?” (Quantum DIY: how to make a quantum computer?)



It is always nice to get closer to new generations! Good job!