## Physics

### Letters for Andrei: QBism and the Unfinished Nature of Nature. (arXiv:2109.08153v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

From the Text: How shall I tribute Andrei Khrennikov in this volume? With an email collection of course! But with what theme? It ought to be something big. One of the troubles of QBism's ontological program is that it is so sideways to the ways most run-of-the-mill philosophers of physics think, they don't even have the tools to parse its sentences. They simply can't see it as having to do with ontology at all. Maybe there is no remedy for this except to wait for the generation to die away. But QBism can and must move forward. Here we select some emails that might inspire a young researcher to throw in on the QBist ontological project, to help develop it on its own terms. The road to a proper, detailed QBist ontology is sure to be a hard one, but one has to start somewhere.

Categories: Journals, Physics

### Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks. (arXiv:2109.08158v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as non-stabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding/encoding circuit. To highlight the framework's range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a 3d stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the 2d Bacon-Shor code after "dualizing" its tensor network encoding map.

Categories: Journals, Physics

### Quantum message-passing algorithm for optimal and efficient decoding. (arXiv:2109.08170v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

Recently, one of us proposed a quantum algorithm called belief propagation with quantum messages (BPQM) for decoding classical data encoded using a binary linear code with tree Tanner graph that is transmitted over a pure-state CQ channel [Renes, NJP 19 072001 (2017)]. This algorithm presents a genuine quantum counterpart to decoding based on classical belief propagation, which has found wide success in classical coding theory when used in conjunction with LDPC or Turbo codes. More recently Rengaswamy et al. [npj Quantum Information 7 97 (2021)] numerically observed that, for a small example code, BPQM implements the optimal decoder for determining the entire input codeword. Here we significantly expand the understanding, formalism, and applicability of the BPQM algorithm with the following contributions. First, we prove analytically that BPQM realizes optimal decoding for any binary linear code with tree Tanner graph. We also provide the first formal description of the BPQM algorithm in full detail and without any ambiguity. In so doing, we identify a key flaw overlooked in the original algorithm and subsequent works which implies quantum circuit realizations will be exponentially large in the code size. Although BPQM passes quantum messages, other information required by the algorithm is processed globally. We remedy this problem by formulating a truly message-passing algorithm which approximates BPQM and has circuit complexity $\mathcal{O}(\text{poly } n, \text{polylog } \frac{1}{\epsilon})$, where $n$ is the code length and $\epsilon$ is the approximation error. Finally, we also propose a novel method for extending BPQM to factor graphs containing cycles by making use of approximate cloning. We show some promising numerical results that indicate that BPQM on factor graphs with cycles can significantly outperform the best possible classical decoder.

Categories: Journals, Physics

### Direct solution of multiple excitations in a matrix product state with block Lanczos. (arXiv:2109.08181v1 [cond-mat.str-el])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted density matrix renormalization group method that acts on a bundled matrix product state, holding many excitations. The use of a block or banded Lanczos algorithm allows for the simultaneous, variational optimization of the bundle of excitations. The method is demonstrated on a Heisenberg model and other cases of interest. A large of number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain.

Categories: Journals, Physics

### Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality. (arXiv:2109.08202v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

This work analyses the performance of quantum circuits and general processes to transform $k$ uses of an arbitrary unitary operation $U$ into another unitary operation $f(U)$. When the desired function $f$ a homomorphism, i.e., $f(UV)=f(U)f(V)$, it is known that optimal average fidelity is attainable by parallel circuits and indefinite causality does not provide any advantage. Here we show that the situation changes dramatically when considering anti-homomorphisms, i.e., $f(UV)=f(V)f(U)$. In particular, we prove that when $f$ is an anti-homomorphism, sequential circuits could exponentially outperform parallel ones and processes with indefinite causal order could outperform sequential ones. We presented explicit constructions on how to obtain such advantages for the unitary inversion task $f(U)=U^{-1}$ and the unitary transposition task $f(U)=U^T$. We also stablish a one-to-one connection between the problem of unitary estimation and parallel unitary transposition, allowing one to easily translate results from one field to the other. Finally, we apply our results to several concrete problem instances and present a method based on computer-assisted proofs to show optimality.

Categories: Journals, Physics

### Utilizing machine learning to improve the precision of fluorescence imaging of cavity-generated spin squeezed states. (arXiv:2109.08221v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

We present a supervised learning model to calibrate the photon collection rate during the fluorescence imaging of cold atoms. The linear regression model finds the collection rate at each location on the sensor such that the atomic population difference equals that of a highly precise optical cavity measurement. This 192 variable regression results in a measurement variance 27% smaller than our previous single variable regression calibration. The measurement variance is now in agreement with the theoretical limit due to other known noise sources. This model efficiently trains in less than a minute on a standard personal computer's CPU, and requires less than 10 minutes of data collection. Furthermore, the model is applicable across a large changes in population difference and across data collected on different days.

Categories: Journals, Physics

### Parameter estimation in an anisotropic expanding spacetime. (arXiv:2109.08252v1 [gr-qc])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

In this work, we investigate how the anisotropy affects the cosmological parameters estimation. Here the anisotropy is incorporated as a small gravitational disturbance. We calculate the Fisher information for both cosmological parameters $\epsilon$ (expansion volume) and $\rho$ (expansion rate), and we show that the anisotropy introduces oscillations in the Fisher information spectrum. This implies that the estimation of the cosmological parameters is sensible to the direction of the momentum $k$ of particles. In addition, we observe that for small values of the momentum $k$ there is a substantial difference between the Fisher information spectrum for the minimum and conformal couplings.

Categories: Journals, Physics

### Super-resolution microscopy of optical fields using tweezer-trapped single atoms. (arXiv:2109.08314v1 [physics.atom-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

We realize a scanning probe microscope using single trapped $^{87}$Rb atoms to measure optical fields with sub-wavelength spatial resolution. Our microscope operates by detecting fluorescence from a single atom driven by near-resonant light and determining the ac Stark shift of an atomic transition from other local optical fields via the change in the fluorescence rate. We benchmark the microscope by measuring two standing-wave Gaussian modes of a Fabry-P\'{e}rot resonator with optical wavelengths of 1560 nm and 780 nm. We attain a spatial resolution of 300 nm, which is super-resolving compared to the limit set by the 780 nm wavelength of the detected light. Sensitivity to short length-scale features is enhanced by adapting the sensor to measure optical forces.

Categories: Journals, Physics

### Observation of non-Hermitian many-body skin effects in Hilbert space. (arXiv:2109.08334v1 [cond-mat.mes-hall])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

Non-Hermiticity greatly expands existing physical laws beyond the Hermitian framework, revealing various novel phenomena with unique properties. Up to now, most exotic nonHermitian effects, such as exceptional points and non-Hermitian skin effects, are discovered in single-particle systems. The interplay between non-Hermitian and manybody correlation is expected to be a more fascinating but much less explored area. Due to the complexity of the problem, current researches in this field mainly stay at the theoretical level. The experimental observation of predicted non-Hermitian manybody phases is still a great challenging. Here, we report the first experimental simulation of strongly correlated non-Hermitian many-body system, and reveal a new type of nonHermitian many-body skin states toward effective boundaries in Hilbert space. Such an interaction-induced non-Hermitian many-body skin effect represents the aggregation of bosonic clusters with non-identical occupations in the periodic lattice. In particular, by mapping eigen-states of three correlated bosons to modes of the designed threedimensional electric circuit, non-Hermitian many-body skin effects in Hilbert space is verified by measuring the spatial impedance response. Our finding not only discloses a new physical effect in the non-Hermitian many-body system, but also suggests a flexible platform to further investigate other non-Hermitian correlated phases in experiments.

Categories: Journals, Physics

### Experimental observation of anomalous supralinear response of single-photon detectors. (arXiv:2109.08347v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

The linearity of single-photon detectors allows accurate optical measurements at low light levels and using non-classical light in spectroscopy, biomedical imaging, optical communication, and sensing. However, in practice the response of single-photon detectors can exhibit intriguing nonlinear effects that may influence the performed measurements. Here, we demonstrate a direct single-source method for absolute measurement of nonlinearity of single-photon detectors with unprecedented accuracy. We discover a surprising supralinear behavior of single-photon avalanche diodes and show that it cannot be explained using known theoretical models. We also fully characterize sub- and supra-linear operation regimes of superconducting nanowire single-photon detectors and uncover the supralinearity under faint continuous illumination. The results identify new detector anomalies that supersede existing knowledge of nonlinear effects at the single-photon level. These effects are of particular importance to cutting-edge applications of single-photon detectors in quantum metrology.

Categories: Journals, Physics

### Observation of coherent perfect absorption at an exceptional point. (arXiv:2109.08353v1 [physics.optics])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

The past few years have witnessed growing interests in exceptional points (EPs) in various domains, including photonics, acoustics and electronics. However, EPs have mainly been realized based on the degeneracy of resonances of physical systems; distinct degeneracies occur relating to the absorption properties of waves, with distinct physical manifestations. Here we demonstrate this physically different kind of exceptional point, by engineering degeneracies in the absorption spectrum of optical microcavities with dissipation. We experimentally distinguish the conditions to realize a resonant EP and an absorbing EP. Furthermore, when the optical loss is optimized to achieve perfect absorption at such an EP, we observe an anomalously broadened lineshape in the absorption spectra, as predicted by theory. The distinct scattering properties enabled by this type of EP creates new opportunities for both the fundamental study and applications of non-Hermitian singularities.

Categories: Journals, Physics

### Less is more: more scattering leading to less resistance. (arXiv:2109.08390v1 [cond-mat.str-el])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

We study breaking of integrability by a finite density of dilute impurities, specifically the emerging diffusive transport. Provided the distance between impurities (localized perturbations) is large one would expect that the scattering rates are additive and therefore the resistivity is proportional to the number of impurities (so-called Matthiessen's rule). We show that this is in general not the case. If transport is anomalous in the original integrable system without impurities, diffusion constant in the non-integrable system gets a nontrivial power-law dependence on the impurity density, with the power being determined by the dynamical scaling exponent of anomalous transport. We also find a regime in which, counterintuitively, adding more impurities to an already diffusive system increases transport rather than decreasing it.

Categories: Journals, Physics

### Landauer's Principle in Qubit-Cavity Quantum Field Theory Interaction in Vaccum and Thermal States. (arXiv:2109.08391v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

Landauer's principle has seen a boom of interest in the last few years due to the growing interest in quantum information sciences. However, its relevance and validity in the contexts of quantum field theory (QFT) remain surprisingly unexplored. In this Letter, we consider Landauer's principle in qubit-cavity QFT interaction perturbatively, in which the initial state of the cavity QFT is chosen to be vacuum or thermal state. In the vacuum case, the QFT always absorbs heat and jumps to excited states. For the qubit at rest, its entropy decreases; whereas if the qubit accelerates, it may also gain energy and increases its entropy due to Unruh effect. For the thermal state, the QFT can both absorb and release heat, depending on its temperature and the initial state of the qubit, and the higher order perturbations can excite/de-excite the initial state to higher/lower state. Landauer's principle is valid in all the cases we consider. We hope that this study could pave a way for future explorations of Landauer's principle in QFT and gravity theories.

Categories: Journals, Physics

### Quantum hardware calculations of periodic systems: hydrogen chain and iron crystals. (arXiv:2109.08401v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

Running quantum algorithms on real hardware is essential for understanding their strengths and limitations, especially in the noisy intermediate scale quantum (NISQ) era. Herein we focus on the practical aspect of quantum computational calculations of solid-state crystalline materials based on theory developed in our group by using real quantum hardware with noise mitigation techniques. We select two periodic systems with different level of complexity for these calculations. One of them is the distorted hydrogen chain as an example of very simple systems, and the other one is iron crystal in the BCC and FCC phases as it is considered to be inaccessible by using classical computational wavefunction methods. The ground state energies are evaluated based on the translational quantum subspace expansion (TransQSE) method for the hydrogen chain, and periodic boundary condition adapted VQE for our iron models. In addition to the usual state preparation and measurement noise mitigation, we apply a novel noise mitigation technique, which performs post-selection of shot counts based on $Z_{2}$ and $U_{1}$ symmetry verification. By applying these techniques for the simplest 2 qubit iron model systems, the energies obtained by the hardware calculations agree with those of the state-vector simulations within $\sim$5 kJ/mol. Although the quantum computational resources used for those experiments are still limited, the systematic resource reduction applied to obtain our simplified models will give us a way to scale up by rolling approximations back as quantum hardware matures.

Categories: Journals, Physics

### Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains. (arXiv:2109.08408v1 [cond-mat.dis-nn])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

We analyze the finite-size scaling of the average gap-ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin-chain with quasi-periodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of Berezinskii-Kosterlitz-Thouless (BKT) transition, the same as in the case of uniformly disordered systems as advocated in recent studies. Moreover, we observe that the critical disorder strength shows a clear sub-linear drift with the system-size as compared to the linear drift seen in random disordered models, suggesting that the finite-size effects in the MBL transition for the QP systems are less severe than that in the random disordered scenario. Moreover, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of on-site magnetizations that can be traced back to the strong correlations present in the QP potential.

Categories: Journals, Physics

### Improving short-term stability in optical lattice clocks by quantum non-demolition measurements. (arXiv:2109.08418v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

We propose a multi-measurement estimation protocol for Quantum-Non-Demolition (QND) measurements in a Rabi clock interferometer. The method is well suited for current state-of-the-art optical lattice clocks with QND measurement capabilities. The protocol exploits the correlations between multiple non-destructive measurements of the initially prepared coherent spin state. A suitable Gaussian estimator for the clock laser detuning is presented, and an analytic expression for the sensitivity of the protocol is derived. We use this analytic expression to optimise the protocol using available experimental parameters, achieving an improvement of $9.1$dB with respect to the standard quantum limit (SQL) in terms of clock stability. We also discuss the measurement back-action effects of our protocol into the atomic state.

Categories: Journals, Physics

### Using gradient-based algorithms to determine ground state energies on a quantum computer. (arXiv:2109.08420v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is optimized to obtain the ground state energy. In our work, we investigate the variational Hamiltonian Ansatz (VHA), where the trial state is given by a non-interacting reference state modified by unitary rotations using generators that are part of the Hamiltonian describing the system. The lowest energy is obtained by optimizing the angles of those unitary rotations. A standard procedure to optimize the variational parameters is to use gradient-based algorithms. However, shot noise and the intrinsic noise of the quantum device affect the evaluation of the required gradients. We studied how different methods for obtaining the gradient, specifically the finite-difference and the parameter-shift rule, are affected by shot noise and noise of the quantum computer. To this end, we simulated a simple quantum circuit, as well as the 2-site and 6-site Hubbard model.

Categories: Journals, Physics

### Exact dynamics of non-additive environments in non-Markovian open quantum systems. (arXiv:2109.08442v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

When a quantum system couples strongly to multiple baths then it is generally no longer possible to describe the resulting system dynamics by simply adding the individual effects of each bath. However, capturing such multi-bath system dynamics has up to now required approximations that can obscure some of the non-additive effects. Here we present a numerically-exact and efficient technique for tackling this problem that builds on the time-evolving matrix product operator (TEMPO) representation. We test the method by applying it to a simple model system that exhibits non-additive behaviour: a two-level dipole coupled to both a vibrational and an optical bath. Although not directly coupled, there is an effective interaction between the baths mediated by the system that can lead to population inversion in the matter system when the vibrational coupling is strong. We benchmark and validate multi-bath TEMPO against two approximate methods - one based on a polaron transformation, the other on an identification of a reaction coordinate - before exploring the regime of simultaneously strong vibrational and optical coupling where the approximate techniques break down. Here we uncover a new regime where the quantum Zeno effect leads to a fully mixed state of the electronic system.

Categories: Journals, Physics

### Quantum Newton's method for solving system of nonlinear algebraic equations. (arXiv:2109.08470v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving $N$-dimensional system of nonlinear equations based on Newton's method. In QNM, we solve the system of linear equations in each iteration of Newton's method with quantum linear system solver. We use a specific quantum data structure and $l_{\infty}$ tomography with sample error $\epsilon_s$ to implement the classical-quantum data conversion process between the two iterations of QNM, thereby constructing the whole process of QNM. The complexity of QNM in each iteration is $O(\log^4N/\epsilon_s^2)$. Through numerical simulation, we find that when $\epsilon_s>>1/\sqrt{N}$, QNM is still effective, so the complexity of QNM is sublinear with $N$, which provides quantum advantage compared with the optimal classical algorithm.

Categories: Journals, Physics

### Broadband photon pair generation from a single lithium niobate microcube. (arXiv:2109.08489v1 [quant-ph])

arXiv.org: Quantum Physics - Mon, 2021-09-20 20:45

Nonclassical light sources are highly sought after as they are an integral part of quantum communication and quantum computation devices. Typical sources rely on bulk crystals that are not compact and have limited bandwidth due to phase-matching conditions. In this work, we demonstrate the generation of photon pairs from a free-standing lithium niobate microcube at the telecommunication wavelength through the spontaneous parametric down-conversion process. The maximum photon pair generation rate obtained from a single microcube with the size of ~4 microns is ~80 Hz, resulting in an efficiency of ~1.2 GHz/Wm per unit volume, which is an order of magnitude higher than the efficiency of photon-pair generation in bulky nonlinear crystals. The microcubes are synthesized through a solvothermal method, offering the possibility for scalable devices via bottom-up assembly. Our work constitutes an important step forward in the realization of compact nonclassical light sources with broadband tunability for various applications in quantum communication, quantum computing, and quantum metrology.

Categories: Journals, Physics