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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.

Quantum 2020

Covariant Quantum Error Correcting Codes via Reference Frames

quantum reference frames

transversal gates

quantum error correction

quantum metrology

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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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. 

technical paper

Quantum light mediated matter-matter interactions is a topic of interest. Started with the seminal works of Dicke or Hepp & Lieb nowadays nice physics and applications are found. Some examples are controlling superconductivity, chemical reactivity or novel phases of matter. In quantum technologies these light mediated interactions are also used to generate squeezing, q-gate construction or for building quantum simulators. 



In this talk, I will review what I call magnetic cavity QED where spins (rather than dipoles) are magnetically (rather than electrically) coupled to superconducting cavities, resonators or waveguides. Magnetic coupling, being weaker than electric, has been somehow ignored but, recently, several tricks to enlarge it has been proposed and experimentally reported [1]. This opens the possibility of using magnetic molecules as qubits and quantum light as mediators. During the talk, I will emphasize the differences and equivalences between electrical and magnetic systems and the experimental state of the art. Besides, within the theory and experimental situation I will explain some applications in squeezing generation[3], magnetic phases detection [4] and the realization of superradiance equilibrium phase transition within magnetic cavity QED[5].

[1] Jenkins...Dalton Trans.45,16682(2016). 



[2] Gimeno...ACS Nano,14,8707(2020)



[3] Macri...PRA101,053818(2020)



[4] Roca...(in preparation)



[5] Román-Roche...(in preparation)

Quantum magnetism driven by vacuum fields

Quantum sensors made of NV centers in diamond have generated tremendous interest over the past decade, owing to a unique combination of sensitivity and atomic-scale sampling volumes. Significant progress has been made in a growing number of applications ranging from material science, to navigation, to detection of single proteins. The technology is now at a tipping point where commercial instruments start to be available. One particular field that benefits from nano-scale images with high sensitivity is that of electronics and magnetic memories.

In this work we show imaging of antiferromagnetic spin textures with state-of-the-art accuracy using a commercial platform. We present two modes of operation allowing rapid convergence towards quantitative understanding of the magnetic textures at the surface of an antiferromagnet. We use BiFeO3 as a prototype example. Remarkably, the data reveal a “zigzag” shaped modulation on the periodic stray field, which are assigned to changing cycloid wave-vector directions due to the presence of ferroelectric domains. The used platform for real-space, nanoscale magnetic imaging offers access to non-trivial spin textures which would be largely inaccessible otherwise. The ability to perform quantitative and non-perturbative analysis of such materials is key to the development of advanced materials in the field of spintronics.

Using a commercial scanning single spin microscope to diagnose magnetic materials for next generation magnetic memories

If nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. In [Sci. Adv. 5, eaav8370] we have shown that generalized uncertainty relations, as well as a specific notion of locality, give rise to both familiar and new characterizations of quantum correlations. In particular, we have identified a condition, relativistic independence, which states that uncertainty relations are local in the sense that they cannot be influenced by other experimenters’ choices of measuring instruments. We proved that theories with nonlocal correlations stronger than the quantum ones do not satisfy this notion of locality, and therefore, they either violate the underlying generalized uncertainty relations or allow experimenters to nonlocally tamper with the uncertainty relations of their peers. In this talk I will discuss several implications of this work to multiplicative Bell inequalities, causality and networks. Finally, I will support the claim that locally consistent indeterminism should be understood as the enabler of most quantum phenomena (and possibly all of them).

Relativistic independence and the immense explanatory power of quantum uncertainty

Randomized benchmarking (RB) protocols represent an efficient tool to compare different qubit technologies and architectures. Despite traditional methods of characterizing gate fidelity that involve quantum process tomography, RB possesses some advantages in terms of the robustness against the state preparation and measurement (SPAM) errors, beyond the fact that it scales efficiently with the system size, requiring fewer resources. RB experiments have been performed in many different physical contexts for quantum technologies, ranging from superconducting qubits, trapped ions or semiconducting qubits, i.e. nitrogen-vacancy centers in diamond, quantum dots and donors (e.g. phosphorous) atoms in silicon. In this study, we simulated randomized benchmarking protocols in a semiconducting all-electrical three-electron double-quantum dot qubit, i.e. hybrid qubit, under different error models, that include quasi-static Gaussian and the more realistic 1/f noise model, for the input controls. The average error of specific quantum computational gates is extracted through interleaved randomized benchmarking obtained including Clifford gates between the gate of interest. Quantitative results are reported that on one hand allow to predict the fidelity when specific error parameters are included, on the other provide a complete picture of the hybrid qubit operations in view of realization of more complex circuits, such as quantum error correction circuits.

Randomized benchmarking protocols in the all-electrical quantum dot qubit with 1/f noise

The concept of topological phases is a powerful framework to characterize many-body systems beyond the paradigm of symmetry breaking. In addition to studying topological phases in condensed-matter systems, a large effort is underway to realize topological matter in quantum simulators. Various platforms have already succeeded in designing non-trivial topological single-particle modes [Ozawa2018,Cooper2018]; however, these modes have only been populated with non-interacting particles, where properties of the many-body states are solely determined by the single-particle modes. A current challenge is to introduce strongly interacting particles in these systems and search for emergent properties of the many-body states. 

Here, we use a quantum simulator based on atoms trapped in optical tweezers and excited to Rydberg levels [Browaeys2020] to realize a symmetry-protected topological (SPT) phase of interacting bosons in a 1D-lattice hosting non-trivial topological modes [deLéséleuc2019]. I will present signatures of the single-particle modes and of the many-body SPT phase obtained by half-filling the lattice with hard-core bosons. Especially, I will show that some perturbations affect single-particle modes, but not the many-body phase: in striking contrast from what occurs in non-interacting topological phases.

[Ozawa2018,Cooper2018] RMP 91, 015005 and 015006 (2018)
[Browaeys2020] Nat. Phys. 16, 132 (2020)
[deLéséleuc2019] Science 365, 775 (2019)


Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms

Open classical and quantum systems with effective parity-time (PT) symmetry have shown tremendous promise for advances in sensing, lasers and non-reciprocal devices. And yet, how such effective PT-symmetric non-Hermitian models emerge out of Hermitian quantum mechanics is not well understood. An active quantum PT-symmetric system, which requires a precisely controllable gain medium, is yet to be realized. Starting from a fully Hermitian microscopic Hamiltonian description, we show that a non-Hermitian Hamiltonian emerges naturally in an already state-of-the-art double-quantum-dot-circuit-QED (DQD-circuit-QED) set-up, which can be controllably tuned to an active PT-symmetric point. This effective Hamiltonian governs the dynamics of two coupled circuit-QED cavities with a voltage-biased DQD in one of them, which acts as the tunable gain medium. Our analysis also reveals the effect of quantum fluctuations on the PT-symmetric system. As simple applications of the PT-transition in this set-up, we show that loss-induced lasing and loss-induced trapping of photons can be observed in the coupled cavities. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system with a gain medium in quantum regime, as well as its potential applications for quantum technology.

Emergent PT symmetry in a double-quantum-dot circuit QED set-up

We present a fine-structure entanglement classification under stochastic local operation and classical communication (SLOCC) for multiqubit pure states. To this end, we employ specific algebraic-geometry tools that are SLOCC invariants, secant varieties, to show that for n-qubit systems there are ⌈2n/(n+1)⌉ entanglement families. By using another invariant, ℓ-multilinear ranks, each family can be further split into a finite number of subfamilies. Not only does this method facilitate the classification of multipartite entanglement, but it also turns out to be operationally meaningful as it quantifies entanglement as a resource.

Fine-Structure Classification of Multiqubit Entanglement by Algebraic Geometry

An excited electron can relax by emitting a photon. In a radiative Auger process, this optical decay leads to the simultaneous excitation of another particle (shake-up). On a single quantum emitter, radiative Auger has not been observed. Here, we report radiative Auger for trions in individual quantum dots. For the trion, just one electron is left after the optical recombination. The radiative Auger process promotes this Auger electron to a higher shell of the quantum dot, and the emitted photon is red-shifted. We show that the energy splitting between this red-shifted photon and the resonance fluorescence directly measures the single-particle splittings of the quantum dot [1], which is otherwise difficult to acquire. We prove the radiative Auger mechanism by measuring the photon statistics and the magnetic field dispersion of the emission. Going beyond the original work in the X-ray spectrum of atoms, we apply quantum optics techniques to the radiative Auger photons. We show how quantum optics gives access to the single-electron dynamics, notably the relaxation and tunneling rates. All these properties of radiative Auger can be exploited on other semiconductor nanostructures and quantum emitters in the solid-state.

[1] M. C. Löbl et al., Nat. Nanotechnol. 15, 558–562 (2020)

Radiative Auger process in the single-photon limit

We propose an efficient, scalable and deterministic scheme[1] to generate up to hundreds of indistinguishable photons over multiple channels, on demand. Our design relies on multiple single-photon sources, each coupled to a waveguide, and all of them interacting with a common cavity mode. The cavity synchronizes and triggers the simultaneous emission of one photon by each source, which are collected by the waveguides. For a state-of-the-art circuit QED implementation, this scheme supports the creation of single photons with purity, indistinguishability, and efficiency of $99\%$ at rates of $\sim $MHz. We also discuss conditions to create a device to produce 30-photon simultaneously with efficiency above $70\%$ at a rate of hundreds of kHz. This is several orders of magnitude more efficient than previous demultiplexed sources for boson sampling, and enables the realization of deterministic multi-photon sources and scalable quantum information processing with photons.

[1] Li, M., et al., arXiv:2009.02382 (2020).

Synchronization of single-photon sources via a cavity

The nonclassical properties of quantum states are of tremendous interest due to their potential applications in future technologies. It has recently been realized that the concept of a resource theory is a powerful approach to quantifying and understanding nonclassicality. To realize the potential of this approach, one must first find resource theoretic measures of nonclassicality that are operational, meaning that they also quantify the ability of quantum states to provide enhanced performance for specific tasks, such as precision sensing.

In this talk, I will discuss some interesting results we have achieved in this endeavor by presenting the first operational resource theoretic measure [1]. In addition to satisfying the requirements of a resource measure, I will show that our measure has the closest possible relationship to the quantum enhancement provided by a nonclassical state for measuring phase-space displacement: It is equal to this enhancement for pure states and has a tight upper bound on it for mixed states. I will further show that a lower bound on this measure can be obtained experimentally using a simple Mach-Zehnder interferometer.

[1] W. Ge, K. Jacobs, S. Asiri, M. Foss-Feig, and M. Suhail Zubairy Phys. Rev. Research 2, 023400 (2020)

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Covariant Quantum Error Correcting Codes via Reference Frames

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