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In quantum mechanics, physical states are represented by rays in Hilbert space, which is a vector space imbued by an inner product whose physical meaning arises as the overlap between a pure state (description of preparation) and a projective measurement. However, quantum mechanics in principle does not formally address the consequences of preparation and measurement being at different spacetime sites. Following concepts of PT symmetry, we introduce purity-preserving transport, which can be interpreted as a changing inner product. We show that such a change in inner product is consistent with standard quantum mechanics, and is observable in a tomographic sense. Mathematically, we show that changing the inner product can be realized by a quantum channel corresponding to a completely positive trace-nonincreasing map, and observing a changing inner product is equivalent to process tomography on this channel. Further, we show how to realize experimentally a changing inner product for a qubit Hilbert space in terms of a qutrit protocol by using only unitary dynamics.

Quantum 2020

Changing the Hilbert-space Inner Product

metric operator

non-hermitian quantum mechanics

pt symmetry

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The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.


Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. The broad themes covered by Quantum 2020 included:

Quantum communication;
Quantum computing and quantum simulation;
Quantum sensing, metrology and imaging;
Quantum information theory, software and algorithms;
Quantum foundations;
Quantum technology in industry.
The four-day event featured talks from world-renowned scientists, interactive poster sessions and two exciting panel discussions on the themes of Quantum Technology in Industry and Quantum Technology Programmes Around the World.


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Recent experimental advances allow one to engineer topological models in bosonic systems like photonic crystals, coupled microwave resonators, or optical lattices experiments, among other platforms [1]. In parallel, experimental progress is also being made to couple quantum emitters to such platforms in order to obtain (or simulate) light-matter Hamiltonians [2-4] with topological photons. The emergent behaviour and applications of such topological quantum optics models, however, remain mostly unexplored.


In this talk, I will discuss the emergence of unconventional quantum dynamics and interactions when quantum emitters are coupled to topological 1D waveguides [5] and 3D photonic Weyl environments [6]. We will show how the photon-mediated interactions induced by these topological photons give rise to the emergence of spin models with exotic and tunable long-range interactions, that can be used for quantum simulation purposes, e.g., to simulate quantum chemistry problems [7].



References
[1] Rev. Mod. Phys. 91, 015006 (2019)
[2] Nature 508, 241–244 (2014), Nature Communications 5, 3808 (2014), Rev. Mod. Phys. 87, 347 (2015), Science 359, 666 (Feb 2018)
[3] Nature Physics 13 (1), 48-52 (2017), Nature Communications, 9, 3706 (2018)
[4] Nature 559, 589–592 (2018)
[5] Science Advances 5, eaaw0297 (2019)
[6] arXiv:1903.07513
[7] Nature 574 , 215-218 (2019)

Quantum simulation of topological optics models

Fermionic statistics includes the parity superselection rule, having to do with the global Z_2 (parity) symmetry of fermionic Hamiltonians. In lattice theories, this symmetry can be gauged and made local, with "parity Gauss laws" relating the local fermionic parity on each site with the divergence of parity gauge fields around it. These local constraints allow one to transfer the statistics from the fermionic matter to the gauge field. Lattice gauge theories, whose gauge group contains a normal Z_2 subgroup, offer this possibility without introducing any extra ingredients. I will discuss a transformation we have recently derived, which maps lattice gauge theories with fermionic matter to equivalent theories with hard core bosonic matter. In the resulting models, the interaction of the matter with the gauge fields is slightly changed, but in a local way. Unlike in the Jordan-Wigner procedure, this mapping gives rise to no nonlocality, and can be performed in arbitrary space dimensions. Furthermore, it can be extended to models without any gauge field, by the introduction of an auxiliary, non-dynamical Z_2 field which will absorb the statistics.

Locally and Unitarily Mapping Lattice Fermions to Bosons in the Presence of a Gauge Field

A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. We give the conditions for a class of superposition state transformations by using the tools of resource theory of superposition. These conditions strictly depend on the scalar products of the basis states and reduce to the well-known majorization condition for quantum coherence in the limit of orthonormal basis. To further superposition-free transformations of d-dimensional systems, we provide superposition-free operators for a deterministic transformation of superposition states. The linear independence of a finite number of basis states requires a relation between the scalar products of these states. With this information in hand, we determine the maximal superposition states which are valid over a certain range of scalar products. Notably, we show that scalar products of the pure superposition-free states have a greater place in seeking maximally resourceful states for d > 2.

Resource theory of superposition: State transformations

The High Luminosity Large Hadron Collider (HL-LHC) is expected to reach a significant increase in complexity and scale of data. Hence, the task of reconstructing the trajectories is getting more and more complex due to the increasing number of simultaneous collisions, occupancy and scalability. Aiming to identify the particle paths, machine learning techniques such as graph neural networks are being explored in the HEP.TrkX project and its successor, the Exa.TrkX project. Both show promising results and reduce the combinatorial nature of the problem. Previous results of our team have demonstrated the successful attempt of including quantum computing concepts within graph neural networks that are able to reconstruct the particle track based on the hits of the detector. A higher overall accuracy is gained by representing the training data in a meaningful way within an embedded space. That has been included in the Exa.TrkX project by applying a classical MLP. Consequently, pairs of hits belonging to different trajectories are pushed apart while those belonging to the same ones stay close together. We explore the applicability of quantum circuits within the task of embedding using hybrid-classical neural network architectures and show preliminary results.

Exploring hybrid quantum-classical neural networks for particle tracking

Structured photons have attracted a lot of attention in quantum photonics ranging from fundamental studies to quantum information applications. In the latter, they often serve as powerful tools to realize high-dimensional quantum states beneficial to quantum information tasks such as cryptography or quantum simulations. While mature techniques exist for the generation and detection of structured photons, many applications are suffering from the absence of methods for performing complex unitary operations between transverse structured photons. We demonstrate that using recent advances in multi-plane mode-conversion techniques, it is possible to perform any unitary operation between different sets of transverse structures in a versatile, simple, and efficient manner. More importantly, we study different two-photon interferences such as coalesce and anti-coalescence between various orthogonal transverse structures. In contrast to previous studies, where two photons bunched into different paths depending on the spatial structures, the interference that we observed occurs along a single beamline. Finally, we show that the ability to perform bi-photon interferences using custom-tailored spatial structures enables the generation of spatial-mode NOON-states, which offer angular super-sensitivity.

Single-Path Two-photon Interferences Between Spatial Structures

While taking the complementary position of the well-known qubit architecture, Continuous Variable (CV) architecture offers an alternative perspective of quantum computing, which encodes quantum information in a continuous physical observable. Initial works have shown that it allows constructing a neural network similar to the structure of a classical fully connected layer by decomposing it into a combination of CV gates. Using this CV neural network (CVNN), we built a simple binary classifier to discriminate classical data encoded in quantum states. Especially, its performance has been evaluated through an application in High Energy Physics (HEP) to distinguish real data, which are the calorimeter outputs interpreted as pixelated images, from random fake data. Following the successful results obtained in the CV classifier test with reduced problem size, we introduce and analyze a new prototype of quantum Generative Adversarial Networks (qGAN) employed in CV quantum computing. Two CV qGAN models with a quantum and a classical discriminator have been tested to reproduce the same training set used in the previous classifier case, and their limitations are discussed.

Quantum Generative Adversarial Networks in Continuous Variable Architecture to Simulate High Energy Physics Detectors

Noise in quantum metrology reduces the sensitivity to which one can determine an unknown parameter in the evolution of a quantum state, such as time. Here, we consider a noiseless quantum system (the probe, or the clock) prepared in a pure state that encodes some time t, on which we apply an arbitrary noise channel. We show an uncertainty relation stating that the noisy probe’s sensitivity to time trades off exactly with the environment’s sensitivity to the energy of the noiseless probe. We obtain necessary and sufficient conditions for when zero sensitivity is lost after application of the noise channel. These conditions are analogous to the Knill-Laflamme quantum error correction conditions but they are easier to satisfy. I will mention applications to many-body quantum metrology, such as computing the sensitivity of many-body interacting probe states exposed to local amplitude-damping noise.

Bipartite energy-time uncertainty relation  and  quantum error correction for metrology with noise

Any realistic physical system is unavoidably coupled to some external degrees of freedom and should then be treated as an open system. That is why the open, reduced quantum dynamics plays an important role also in quantum technology applications. 
In the study of the dynamics of an open quantum system it is well known that alternative approximated descriptions are often useful. Here we show that also equivalent exact evolution equations can be introduced, investigating a newly introduced link between time local and time non-local master equations [1, 2]. Though these equations are in principle equivalent as their solutions are the same reduced density operator, the knowledge of both can be beneficial. Our approach, based on the damping basis representation, give some insights into the occurrence of different dephasing channels in time local and time non-local master equations and the non-Markovianity property of the exact and the approximated reduced dynamics.



[1] - N. Megier, A. Smirne, B. Vacchini, New J. Phys. 22: 083011, 2020

[2] - N. Megier, A. Smirne, B. Vacchini, Entropy 22(7): 796, 2020

Different descriptions of open quantum system dynamics - master equations

The standard quantum optics treatment of the squeezed light generation the material susceptibility is taken as a constant prefactor. This treatment is justified when the fields are far off-resonant with respect to matter. Resonant nonlinear spectroscopy investigates material properties, which requires an explicit treatment of the matter response via nonlinear susceptibilities.

We propose a set of nonlinear spectroscopic measurements with quantum light [1]. It involves a strong pump and a weak probe interacting with a solid state target to generate a conjugated beam via nondegenerate four-wave mixing. The third order nonlinear susceptibility can be measured by the noise spectra of the intensity difference of the squeezed beams.

We further discuss three spectroscopic
setups based on squeezed light: first, single four-wave mixing in a single crystal; second, cascading scheme involving two crystals; third, an SU(1, 1) interferometer based on two separate four-wave mixing processes. We further investigate the microscopic noise and optical losses in all three setups. Simulations are presented for silicon-vacancy color centers in diamond.

References:

Z. Yang, P. Saurabh, F. Schlawin, S. Mukamel, and K. E. Dorfman, Appl. Phys. Lett., 116, 244001 (2020).

Multidimensional spectroscopy with squeezed light

Error correcting codes with a universal set of transversal gates are the desiderata of realising quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, it also rules out codes which are covariant with respect to the action of transversal unitary operations forming continuous symmetries. In this work, starting from an arbitrary code, we construct approximate codes which are covariant with respect to local SU(d) symmetries using quantum reference frames. We show that our codes are capable of efficiently correcting different types of erasure errors. When only a small fraction of the n qudits upon which the code is built are erased, our covariant code has an error that scales as 1/n^2, which is reminiscent of the Heisenberg limit of quantum metrology. When every qudit has a chance of being erased, our covariant code has an error that scales as 1/n. We show that the error scaling is optimal in both cases. Our approach has implications for fault-tolerant quantum computing, reference frame error correction, and the AdS-CFT duality.

Changing the Hilbert-space Inner Product

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