Author(s): Nicolas Loizeau and Alexei Grinbaum

Classical communication capacity of a channel can be enhanced either through a device called a “quantum switch” or by putting the channel in a quantum superposition. The gains in the two cases, although different, have their origin in the use of a quantum resource, but is it the same resource? Here ...

[Phys. Rev. A 101, 012340] Published Fri Jan 24, 2020

Author(s): Theerapat Tansuwannont, Christopher Chamberland, and Debbie Leung

Flag qubits have recently been proposed in syndrome extraction circuits to detect high-weight errors arising from fewer faults. The use of flag qubits allows the construction of fault-tolerant protocols with the fewest number of ancillas known to date. In this work, we prove some critical properties...

[Phys. Rev. A 101, 012342] Published Fri Jan 24, 2020

Artificial atom qubits in diamond have emerged as leading candidates for a range of solid-state quantum systems, from quantum sensors to repeater nodes in memory-enhanced quantum communication. Inversion-symmetric group IV vacancy centers, comprised of Si, Ge, Sn and Pb dopants, hold particular promise as their neutrally charged electronic configuration results in a ground-state spin triplet, enabling long spin coherence above cryogenic temperatures. However, despite the tremendous interest in these defects, a theoretical understanding of the electronic and spin structure of these centers remains elusive. In this context, we predict the ground- and excited-state properties of the neutral group IV color centers from first principles. We capture the product Jahn-Teller effect found in the excited state manifold to second order in electron-phonon coupling, and present a non-perturbative treatment of the effect of spin-orbit coupling. Importantly, we find that spin-orbit splitting is strongly quenched due to the dominant Jahn-Teller effect, with the lowest optically-active $^3E_u$ state weakly split into $m_s$-resolved states. The predicted complex vibronic spectra of the neutral group IV color centers are essential for their experimental identification and have key implications for use of these systems in quantum information science.

Onsager's relations allow one to express the second law of thermodynamics in terms of the underlying associated currents. These relations, however, are usually valid only close to equilibrium. Using a quantum phase space formulation of the second law, we show that open bosonic Gaussian systems also obey a set of Onsager relations, valid arbitrarily far from equilibrium. These relations, however, are found to be given by a more complex non-linear function, which reduces to the usual quadratic form close to equilibrium. This non-linearity implies that far from equilibrium, there exists a fundamental asymmetry between entropy flow from system to bath and vice-versa. The ramifications of this for applications in driven-dissipative quantum optical setups are also discussed.

Cryogenic buffer gas cells have been a workhorse for the cooling of molecules in the last decades. The straightforward sympathetic cooling principle makes them applicable to a huge variety of different species. Notwithstanding this success, detailed simulations of buffer gas cells are rare, and have never been compared to experimental data in the regime of low to intermediate buffer gas densities. Here, we present a numerical approach based on a trajectory analysis, with molecules performing a random walk in the cell due to collisions with a homogeneous buffer gas. This method can reproduce experimental flux and velocity distributions of molecules emerging from the buffer gas cell for varying buffer gas densities. This includes the strong decrease in molecule output from the cell for increasing buffer gas density and the so-called boosting effect, when molecules are accelerated by buffer-gas atoms after leaving the cell. The simulations provide various insights which could substantially improve buffer-gas cell design.

We investigate theoretically the application of Sawtooth Wave Adiabatic Passage (SWAP) within a 1D magneto-optical trap (MOT). As opposed to related methods that have been previously discussed, our approach utilizes repeated cycles of stimulated absorption and emission processes to achieve both trapping and cooling, thereby reducing the adverse effects that arise from photon scattering. Specifically, we demonstrate this method's ability to cool, slow and trap particles with fewer spontaneously emitted photons, higher forces and in less time when compared to a traditional MOT scheme that utilizes the same narrow linewidth transition. We calculate the phase space compression that is achievable and characterize the resulting system equilibrium cloud size and temperature.

The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional structure of the unitary. Given a quantum circuit with no path from input system $A$ to output system $B$, system $A$ cannot influence system $B$. Conversely, given a unitary $U$ with a no-influence relation from input $A$ to output $B$, it follows from [B. Schumacher and M. D. Westmoreland, Quantum Information Processing 4 no. 1, (Feb, 2005)] that there exists a circuit decomposition of $U$ with no path from $A$ to $B$. However, as we argue, there are unitaries for which there does not exist a circuit decomposition that makes all causal constraints evident simultaneously. To address this, we introduce a new formalism of `extended circuit diagrams', which goes beyond what is expressible with quantum circuits, with the core new feature being the ability to represent direct sum structures in addition to sequential and tensor product composition. A causally faithful extended circuit decomposition, representing a unitary $U$, is then one for which there is a path from an input $A$ to an output $B$ if and only if there actually is influence from $A$ to $B$ in $U$. We derive causally faithful extended circuit decompositions for a large class of unitaries, where in each case, the decomposition is implied by the unitary's respective causal structure. We hypothesize that every finite-dimensional unitary transformation has a causally faithful extended circuit decomposition.

We describe -- in a didactical and detailed way -- the so-called Lee model (which shares similarities with the Jaynes-Cummings and Friedrichs models) as a tool to study unstable quantum states/particles. This Lee model is based on Quantum Mechanics (QM) but possesses some of the features of Quantum Field Theory (QFT). The decay process can be studied in great detail and typical QFT quantities such as propagator, one-loop resummation, and Feynman rules can be introduced. Deviations from the exponential decay law as well as the Quantum Zeno effects can be studied within this framework. The survival probability amplitude as a Fourier transform of the energy distribution, the normalization of the latter, and the Breit-Wigner limit can be obtained in a rigorous mathematical approach.

The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U$(1)$] and discrete chiral ($Z_2$) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U$(1)$ part.

In the ${\rm AdS}_3/{\rm CFT}_2$ setup we elucidate how gauge invariant boundary patterns of entanglement of the CFT vacuum are encoded into the bulk via the coefficient dynamics of an $A_{N-3}$, $N\geq 4$ cluster algebra. In the static case this dynamics of encoding manifests itself in kinematic space, which is a copy of de Sitter space ${\rm dS}_2$, in a particularly instructive manner. For a choice of partition of the boundary into $N$ regions the patterns of entanglement, associated with conditional mutual informations of overlapping regions, are related to triangulations of geodesic $N$-gons. Such triangulations are then mapped to causal patterns in kinematic space. For a fixed $N$ the space of all causal patterns is related to the associahedron ${\mathcal K}^{N-3}$ an object well-known from previous studies on scattering amplitudes. On this space of causal patterns cluster dynamics acts by a recursion provided by a Zamolodchikov's $Y$-system of type $(A_{N-3},A_1)$. We observe that the space of causal patterns is equipped with a partial order, and is isomorphic to the Tamari lattice. The mutation of causal patterns can be encapsulated by a walk of $N-3$ particles interacting in a peculiar manner in the past light cone of a point of ${\rm dS}_2$.

An efficient error reconciliation scheme is important for post-processing of quantum key distribution (QKD). Recently, a multi-matrix low-density parity-check codes based reconciliation algorithm which can provide remarkable perspectives for high efficiency information reconciliation was proposed. This paper concerns the improvement of reconciliation performance. Multi-matrix algorithm is implemented and optimized on the graphics processing unit (GPU) to obtain high reconciliation throughput. Experimental results indicate that GPU-based algorithm can highly improve reconciliation throughput to an average 85.67 Mbps and a maximum 102.084 Mbps with typical code rate and efficiency. This is the best performance of reconciliation on GPU platform to our knowledge.

In this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which we call approximate tensorization of the relative entropy, can be expressed as a lower bound for the sum of relative entropies between a given density and its respective projections onto two intersecting von Neumann algebras in terms of the relative entropy between the same density and its projection onto an algebra in the intersection, up to multiplicative and additive constants. In particular, our inequality reduces to the so-called quasi-factorization of the entropy for commuting algebras, which is a key step in modern proofs of the logarithmic Sobolev inequality for classical lattice spin systems. We also provide estimates on the constants in terms of conditions of clustering of correlations in the setting of quantum lattice spin systems. Along the way, we show the equivalence between conditional expectations arising from Petz recovery maps and those of general Davies semigroups.

Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high fidelity. Here we propose a simple quantum error-correcting code for the detected amplitude damping channel. The code requires only two qubits. We implement the encoding, the channel, and the recovery on an optical platform, the IBM Q System, and a nuclear magnetic resonance system. For all of these systems, the error correction advantage appears when the damping rate exceeds some threshold. We compare the features of these quantum information processing systems used and demonstrate the advantage of quantum error correction on current quantum computing platforms.

Optical Bloch Equations (OBE) describe the coherent exchange of energy between a quantum emitter and a quasi-resonant field in the presence of a thermal reservoir. Despite it is an ubiquitous process in quantum technologies, a thermodynamical analysis is still missing. We hereby provide such an analysis. Our approach is based on a partial secular approximation applied on the dynamical equations of the full atom-bath system. We identify two regimes of parameters respectively leading to the OBE or the Floquet Master Equations (FME) and the consistent expressions the first and the second law of thermodynamics. In the regime where OBE are valid, we single out quantum signatures in the heat flows and in the entropy production, related to the creation of coherences by the driving field and their erasure by the bath. Our findings contribute to bridge an open gap between quantum thermodynamics and quantum optics.

In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open boundaries, and translational symmetry to simulate any local target Hamiltonian---i.e. to reproduce the whole of the target system within its low-energy subspace to arbitrarily-high precision. Since this implies the capability to simulate non-translationally-invariant many-body systems with translationally-invariant couplings, any effect such as characteristics commonly associated to systems with external disorder, e.g. many-body localization, can also occur within the low-energy Hilbert space sector of translationally-invariant systems. Then we sketch a variant of the universal lattice construction optimized for simulating translationally-invariant target Hamiltonians. Finally we prove that qubit Hamiltonians consisting of Heisenberg or XY interactions of varying interaction strengths restricted to the edges of a connected translationally-invariant graph embedded in $\mathbb{R}^D$ are universal, and can efficiently simulate any geometrically local Hamiltonian in $\mathbb{R}^D$.

The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by Schwinger-Keldysh formalism, we propose the contour-integral formulation of the work statistics. Based on this contour integral, we show how to do the perturbation expansion of the characteristic function of work (CFW) and obtain the approximate expression of the CFW to the second order of the work parameter for an arbitrary system under a perturbative protocol. We also demonstrate the validity of fluctuation theorems by utilizing the Kubo-Martin-Schwinger condition. Finally, we use noninteracting identical particles in a forced harmonic potential as an example to demonstrate the powerfulness of our approach.

Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem. We benchmark their performance as well as that of the commonly-used greedy search on physically relevant tensor networks. Where computationally feasible, we also compare them with the optimal contraction sequence obtained by an exhaustive search. We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.

Measurement-device-independent quantum key distribution (MDI-QKD) can remove all detection side-channels from quantum communication systems. The security proofs require, however, that certain assumptions on the sources are satisfied. This includes, for instance, the requirement that there is no information leakage from the transmitters of the senders, which unfortunately is very difficult to guarantee in practice. In this paper we relax this unrealistic assumption by presenting a general formalism to prove the security of MDI-QKD with leaky sources. With this formalism, we analyze the finite-key security of two prominent MDI-QKD schemes - a symmetric three-intensity decoy-state MDI-QKD protocol and a four-intensity decoy-state MDI-QKD protocol - and determine their robustness against information leakage from both the intensity modulator and the phase modulator of the transmitters. Our work shows that MDI-QKD is feasible within a reasonable time frame of signal transmission given that the sources are sufficiently isolated. Thus, it provides an essential reference for experimentalists to ensure the security of experimental implementations of MDI-QKD in the presence of information leakage.

For quantum systems with a total dimension greater than six, the positive partial transposition (PPT) criterion is sufficient but not necessary to decide the non-separability of quantum states. Here, we present an Automated Machine Learning approach to classify random states of two qutrits as separable or entangled using enough data to perform a quantum state tomography, without any direct measurement of its entanglement. We could successfully apply our framework even when the Peres-Horodecki criterion fails. In addition, we could also estimate the Generalized Robustness of Entanglement with regression techniques and use it to validate our classifiers.

One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event, and there is no way to distinguish between them, interference occurs. It is usually assumed that distinguishing information in the preparation, evolution or measurement of a system is sufficient to destroy interference. For example, determining which slit a particle takes in Young's double slit experiment or using distinguishable photons in the two-photon Hong-Ou-Mandel effect allow discrimination of the paths leading to detection events, so in both cases interference vanishes. Remarkably for more than three independent quantum particles, distinguishability of the prepared states is not a sufficient condition for multiparticle interference to disappear. Here we experimentally demonstrate this for four photons prepared in pairwise distinguishable states, thus fundamentally challenging intuition of multiparticle interference.