Ernesto Galvao | UFF - Universidade Federal Fluminense (original) (raw)

Papers by Ernesto Galvao

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, nondestructive measur... more Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, nondestructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+T gate set and having t T gates can be compiled into a PBC on t qubits. Here we propose practical ways of implementing PBC as adaptive quantum circuits, and provide code to do the required classical side-processing. Our first scheme reduces the number of quantum gates to O(t2) (from a previous O(t3/ log t) scaling) at the cost of one extra auxiliary qubit, with a possible reduction of the depth to O(t log t), at the cost of t additional auxiliary qubits (second scheme). We compile examples of random and hidden-shift quantum circuits into adaptive PBC circuits. We also simulate hybrid quantum computation, where a classical computer effectively extends the working memory of a small quantum computer by k virtual qubits, at a cost exponential in k. Our results demonstrate the practical advantage of PBC techniqu...

We study the class of discrete Wigner functions proposed by Gibbons et al. [Phys. Rev. A 70, 0621... more We study the class of discrete Wigner functions proposed by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to describe quantum states using a discrete phase-space based on finite fields. We find the extrema of such functions for small Hilbert space dimensions, and present a quantum information application: a construction of quantum random access codes. These are constructed using the complete set of phase-space point operators to find encoding states and to obtain the codes' average success rates for Hilbert space dimensions 2,3,4,5,7 and 8.

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner f... more Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by one of us [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.

In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W... more In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in all definitions of W in this class. For d<6 I show C_d is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.

Nicolò Spagnolo, Daniel J. Brod, Ernesto F. Galvão, 4 and Fabio Sciarrino Dipartimento di Fisica,... more Nicolò Spagnolo, Daniel J. Brod, Ernesto F. Galvão, 4 and Fabio Sciarrino Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy Instituto de F́ısica, Universidade Federal Fluminense, Niterói, RJ, 24210-340, Brazil International Iberian Nanotechnology Laboratory (INL), Ave. Mestre Jose Veiga, 4715-330, Braga, Portugal Instituto de Fisica, Universidade Federal Fluminense, Niterói, RJ, 24210-340, Brazil

The geometrical arrangement of a set of quantum states can be completely characterized using rela... more The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written as traces of products of density matrices. We describe how to measure Bargmann invariants using suitable generalizations of the SWAP test. This allows for a complete and robust characterization of the projective-unitary invariant properties of any set of pure or mixed states. As applications, we describe basis-independent tests for linear independence, coherence, and imaginarity. We also show that Bargmann invariants can be used to characterize multi-photon indistinguishability.

Physical Review Research, 2021

Quantum coherence marks a deviation from classical physics, and has been studied as a resource fo... more Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation. Finding reliable and effective methods for assessing its presence is then highly desirable. Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis. Here we experimentally measure a novel type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way. Our experiment uses a single interferometric setup to simultaneously measure the three pairwise overlaps among three single-photon states via Hong-Ou-Mandel tests. Besides coherence witnesses, we show the measurements also serve as a Hilbert-space dimension witness. Our results attest to the effectiveness of pooling many two-state comparison tests to ascertain various relational properties of a set of quantum states.

arXiv: Quantum Physics, 2019

Suppose we have NNN quantum systems in unknown states left∣psiirightrangle\left|\psi_i \right\rangleleft∣psiirightrangle, but know the ... more Suppose we have NNN quantum systems in unknown states left∣psiirightrangle\left|\psi_i \right\rangleleft∣psiirightrangle, but know the value of some pairwise overlaps left∣langlepsik∣psilrangleright∣2\left| \langle \psi_k |\psi_l\rangle \right|^2left∣langlepsik∣psilrangleright∣2. What can we say about the values of the unknown overlaps? We provide a complete answer to this problem for 3 pure states and two given overlaps, and a way to obtain bounds for the general case. We discuss how the answer contrasts from that of a classical model, and describe two applications: dimension witnesses, and characterisation of multi-photon indistinguishability.

2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), 2017

Recently, interference of multi-particle states has raised a strong interest in the scientific co... more Recently, interference of multi-particle states has raised a strong interest in the scientific community, since it is believed to be at the very heart of post-classical computation. In this context, Boson Sampling [1] devices exploit multi-photon interference effects to provide evidence of a superior quantum computational power with current state-of-the-art technology. Thus, the capability to correctly certify the presence of multi-particle interference and find optimal platforms, becomes a crucial task because is expected to find numerous applications in photonic quantum information as a diagnostic tool for quantum optical devices.

We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under... more We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under the effect of Hamiltonians quadratic in creation and annihilation operators, commonly referred to as linear optics. These anyonic models are obtained from deformations of the standard bosonic or fermionic commutation relations via the introduction of a non-trivial exchange phase between different lattice sites. We study the effects of the anyonic exchange phase on the usual bosonic and fermionic bunching behaviors. We show how to exploit the inherent Aharonov-Bohm effect exhibited by these particles to build a deterministic, entangling two-qubit gate and prove quantum computational universality in these systems. We define coherent states for bosonic anyons and study their behavior under two-mode linear-optical devices. In particular we prove that, for a particular value of the exchange factor, an anyonic mirror can generate cat states, an important resource in quantum information proces...

Multiphoton interference represents one of the key features in photonic platforms for quantum com... more Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.

New Journal of Physics, 2020

Photon indistinguishability plays a fundamental role in information processing, with applications... more Photon indistinguishability plays a fundamental role in information processing, with applications such as linear-optical quantum computation and metrology. It is then necessary to develop appropriate tools to quantify the amount of this resource in a multiparticle scenario. Here we report a four-photon experiment in a linear-optical interferometer designed to simultaneously estimate the degree of indistinguishability between three pairs of photons. The interferometer design dispenses with the need of heralding for parametric down-conversion sources, resulting in an efficient and reliable optical scheme. We then use a recently proposed theoretical framework to quantify four-photon indistinguishability, as well as to obtain bounds on three unmeasured two-photon overlaps. Our findings are in high agreement with the theory, and represent a new resource-effective technique for the characterization of multiphoton interference.

Physical Review A, 2019

Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficien... more Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear optical model which allows for universal quantum computation.

New Journal of Physics, 2018

Photonic interference is a key quantum resource for optical quantum computation, and in particula... more Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling devices. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively suppresses certain sets of events, as in the original Hong-Ou-Mandel effect. Recently, it was shown that some classical and semi-classical models could be ruled out by identifying such suppressions in Fourier interferometers. Here we propose a suppression law suitable for random-input experiments in multimode Sylvester interferometers, and verify it experimentally using 4-and 8-mode integrated interferometers. The observed suppression occurs for a much larger fraction of input-output combinations than what is observed in Fourier interferometers of the same size, and could be relevant to certification of boson sampling machines and other experiments relying on bosonic interference, such as quantum simulation and quantum metrology.

Science Bulletin, 2018

Particle indistinguishability is at the heart of quantum statistics that regulates fundamental ph... more Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Our approach employs the total variation distance to find those transformations that minimize the error probability in discriminating the behaviors of distinguishable and indistinguishable photons. In particular, we show that so-called Sylvester interferometers are near-optimal for this task. By using Bayesian tests and inference, we numerically show that Sylvester transformations largely outperform most Haar-random unitaries in terms of sample size required. Furthermore, we experimentally demonstrate the efficacy of the transformation using an efficient 3D integrated circuits in the single-and multiple-source cases. We then discuss the extension of this approach to a larger number of photons and modes. These results open the way to the application of Sylvester interferometers for optimal assessment of multiphoton interference experiments.

Science Advances, 2015

A novel experiment supports quantum computation using photonic circuits to greatly increase quant... more A novel experiment supports quantum computation using photonic circuits to greatly increase quantum device speed.

International Journal of Quantum Information, 2014

The Boson sampling problem consists in sampling from the output probability distribution of a bos... more The Boson sampling problem consists in sampling from the output probability distribution of a bosonic Fock state, after it evolves through a linear interferometer. There is strong evidence that Boson sampling is computationally hard for classical computers, while it can be solved naturally by bosons. This has led it to draw increasing attention as a possible way to provide experimental evidence for the quantum computational supremacy. Nevertheless, the very complexity of the problem makes it hard to exclude the hypothesis that the experimental data are sampled from a different probability distribution. By exploiting integrated quantum photonics, we have carried out a set of three-photon Boson sampling experiments and analyzed the results using a Bayesian approach, showing that it represents a valid alternative to currently used methods. We adopt this approach to provide evidence that the experimental data correspond to genuine three-photon interference, validating the results agains...

Frontiers in Ultrafast Optics: Biomedical, Scientific, and Industrial Applications XIV, 2014

ABSTRACT Integrated photonic circuits with many input and output modes are essential in applicati... more ABSTRACT Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, nondestructive measur... more Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, nondestructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+T gate set and having t T gates can be compiled into a PBC on t qubits. Here we propose practical ways of implementing PBC as adaptive quantum circuits, and provide code to do the required classical side-processing. Our first scheme reduces the number of quantum gates to O(t2) (from a previous O(t3/ log t) scaling) at the cost of one extra auxiliary qubit, with a possible reduction of the depth to O(t log t), at the cost of t additional auxiliary qubits (second scheme). We compile examples of random and hidden-shift quantum circuits into adaptive PBC circuits. We also simulate hybrid quantum computation, where a classical computer effectively extends the working memory of a small quantum computer by k virtual qubits, at a cost exponential in k. Our results demonstrate the practical advantage of PBC techniqu...

We study the class of discrete Wigner functions proposed by Gibbons et al. [Phys. Rev. A 70, 0621... more We study the class of discrete Wigner functions proposed by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to describe quantum states using a discrete phase-space based on finite fields. We find the extrema of such functions for small Hilbert space dimensions, and present a quantum information application: a construction of quantum random access codes. These are constructed using the complete set of phase-space point operators to find encoding states and to obtain the codes' average success rates for Hilbert space dimensions 2,3,4,5,7 and 8.

Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner f... more Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by one of us [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.

In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W... more In [Phys. Rev. A 70, 062101 (2004)] Gibbons et al. defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize a set C_d of states having non-negative W simultaneously in all definitions of W in this class. For d<6 I show C_d is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.

Nicolò Spagnolo, Daniel J. Brod, Ernesto F. Galvão, 4 and Fabio Sciarrino Dipartimento di Fisica,... more Nicolò Spagnolo, Daniel J. Brod, Ernesto F. Galvão, 4 and Fabio Sciarrino Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy Instituto de F́ısica, Universidade Federal Fluminense, Niterói, RJ, 24210-340, Brazil International Iberian Nanotechnology Laboratory (INL), Ave. Mestre Jose Veiga, 4715-330, Braga, Portugal Instituto de Fisica, Universidade Federal Fluminense, Niterói, RJ, 24210-340, Brazil

The geometrical arrangement of a set of quantum states can be completely characterized using rela... more The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written as traces of products of density matrices. We describe how to measure Bargmann invariants using suitable generalizations of the SWAP test. This allows for a complete and robust characterization of the projective-unitary invariant properties of any set of pure or mixed states. As applications, we describe basis-independent tests for linear independence, coherence, and imaginarity. We also show that Bargmann invariants can be used to characterize multi-photon indistinguishability.

Physical Review Research, 2021

Quantum coherence marks a deviation from classical physics, and has been studied as a resource fo... more Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation. Finding reliable and effective methods for assessing its presence is then highly desirable. Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis. Here we experimentally measure a novel type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way. Our experiment uses a single interferometric setup to simultaneously measure the three pairwise overlaps among three single-photon states via Hong-Ou-Mandel tests. Besides coherence witnesses, we show the measurements also serve as a Hilbert-space dimension witness. Our results attest to the effectiveness of pooling many two-state comparison tests to ascertain various relational properties of a set of quantum states.

arXiv: Quantum Physics, 2019

Suppose we have NNN quantum systems in unknown states left∣psiirightrangle\left|\psi_i \right\rangleleft∣psiirightrangle, but know the ... more Suppose we have NNN quantum systems in unknown states left∣psiirightrangle\left|\psi_i \right\rangleleft∣psiirightrangle, but know the value of some pairwise overlaps left∣langlepsik∣psilrangleright∣2\left| \langle \psi_k |\psi_l\rangle \right|^2left∣langlepsik∣psilrangleright∣2. What can we say about the values of the unknown overlaps? We provide a complete answer to this problem for 3 pure states and two given overlaps, and a way to obtain bounds for the general case. We discuss how the answer contrasts from that of a classical model, and describe two applications: dimension witnesses, and characterisation of multi-photon indistinguishability.

2017 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), 2017

Recently, interference of multi-particle states has raised a strong interest in the scientific co... more Recently, interference of multi-particle states has raised a strong interest in the scientific community, since it is believed to be at the very heart of post-classical computation. In this context, Boson Sampling [1] devices exploit multi-photon interference effects to provide evidence of a superior quantum computational power with current state-of-the-art technology. Thus, the capability to correctly certify the presence of multi-particle interference and find optimal platforms, becomes a crucial task because is expected to find numerous applications in photonic quantum information as a diagnostic tool for quantum optical devices.

We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under... more We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under the effect of Hamiltonians quadratic in creation and annihilation operators, commonly referred to as linear optics. These anyonic models are obtained from deformations of the standard bosonic or fermionic commutation relations via the introduction of a non-trivial exchange phase between different lattice sites. We study the effects of the anyonic exchange phase on the usual bosonic and fermionic bunching behaviors. We show how to exploit the inherent Aharonov-Bohm effect exhibited by these particles to build a deterministic, entangling two-qubit gate and prove quantum computational universality in these systems. We define coherent states for bosonic anyons and study their behavior under two-mode linear-optical devices. In particular we prove that, for a particular value of the exchange factor, an anyonic mirror can generate cat states, an important resource in quantum information proces...

Multiphoton interference represents one of the key features in photonic platforms for quantum com... more Multiphoton interference represents one of the key features in photonic platforms for quantum communication, quantum simulation, quantum computing and quantum sensing. Starting from the first two-photon experiment by Hong-Ou-Mandel [1], it has been shown that multiphoton interference lies at the heart of computational complexity in linear optical interferometers, the most notable example being provided by the Boson Sampling model [2]. This model corresponds to sampling from the evolution of n indistinguishable photons in a multimode linear network, and has been shown to be hard to simulate classicaly thus representing a promising route to experimentally reach the quantum advantage regime. It has been shown, however, that genuine multiparticle interference is necessary for high computational complexity. Hence, appropriate methods for detection of such feature should be developed since the complexity of problem prevents the application of trivial methods.

New Journal of Physics, 2020

Photon indistinguishability plays a fundamental role in information processing, with applications... more Photon indistinguishability plays a fundamental role in information processing, with applications such as linear-optical quantum computation and metrology. It is then necessary to develop appropriate tools to quantify the amount of this resource in a multiparticle scenario. Here we report a four-photon experiment in a linear-optical interferometer designed to simultaneously estimate the degree of indistinguishability between three pairs of photons. The interferometer design dispenses with the need of heralding for parametric down-conversion sources, resulting in an efficient and reliable optical scheme. We then use a recently proposed theoretical framework to quantify four-photon indistinguishability, as well as to obtain bounds on three unmeasured two-photon overlaps. Our findings are in high agreement with the theory, and represent a new resource-effective technique for the characterization of multiphoton interference.

Physical Review A, 2019

Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficien... more Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear optical model which allows for universal quantum computation.

New Journal of Physics, 2018

Photonic interference is a key quantum resource for optical quantum computation, and in particula... more Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling devices. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively suppresses certain sets of events, as in the original Hong-Ou-Mandel effect. Recently, it was shown that some classical and semi-classical models could be ruled out by identifying such suppressions in Fourier interferometers. Here we propose a suppression law suitable for random-input experiments in multimode Sylvester interferometers, and verify it experimentally using 4-and 8-mode integrated interferometers. The observed suppression occurs for a much larger fraction of input-output combinations than what is observed in Fourier interferometers of the same size, and could be relevant to certification of boson sampling machines and other experiments relying on bosonic interference, such as quantum simulation and quantum metrology.

Science Bulletin, 2018

Particle indistinguishability is at the heart of quantum statistics that regulates fundamental ph... more Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Our approach employs the total variation distance to find those transformations that minimize the error probability in discriminating the behaviors of distinguishable and indistinguishable photons. In particular, we show that so-called Sylvester interferometers are near-optimal for this task. By using Bayesian tests and inference, we numerically show that Sylvester transformations largely outperform most Haar-random unitaries in terms of sample size required. Furthermore, we experimentally demonstrate the efficacy of the transformation using an efficient 3D integrated circuits in the single-and multiple-source cases. We then discuss the extension of this approach to a larger number of photons and modes. These results open the way to the application of Sylvester interferometers for optimal assessment of multiphoton interference experiments.

Science Advances, 2015

A novel experiment supports quantum computation using photonic circuits to greatly increase quant... more A novel experiment supports quantum computation using photonic circuits to greatly increase quantum device speed.

International Journal of Quantum Information, 2014

The Boson sampling problem consists in sampling from the output probability distribution of a bos... more The Boson sampling problem consists in sampling from the output probability distribution of a bosonic Fock state, after it evolves through a linear interferometer. There is strong evidence that Boson sampling is computationally hard for classical computers, while it can be solved naturally by bosons. This has led it to draw increasing attention as a possible way to provide experimental evidence for the quantum computational supremacy. Nevertheless, the very complexity of the problem makes it hard to exclude the hypothesis that the experimental data are sampled from a different probability distribution. By exploiting integrated quantum photonics, we have carried out a set of three-photon Boson sampling experiments and analyzed the results using a Bayesian approach, showing that it represents a valid alternative to currently used methods. We adopt this approach to provide evidence that the experimental data correspond to genuine three-photon interference, validating the results agains...

Frontiers in Ultrafast Optics: Biomedical, Scientific, and Industrial Applications XIV, 2014

ABSTRACT Integrated photonic circuits with many input and output modes are essential in applicati... more ABSTRACT Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.