From Asymptotic Freedom to θ Vacua: Qubit Embeddings of the O(3) Nonlinear σ Model
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Faster Tensor Network Decoding for Topological Quantum Codes
We present a fast and Bayes-optimal-approximating tensor network decoder for planar quantum LDPC codes based on the tensor renormalization group algorithm, originally proposed by Levin, and Nave. By precomputing the renormalization group flow for the null syndrome, we need only recompute tensor contractions in the causal cone of the measured syndrome at the time of decoding. This allows us to achieve an overall runtime complexity of ($pnχ^6$) where p is the depolarizing noise rate, and χ is the cutoff value used to control singular value decomposition approximations used in the algorithm. We apply our decoder to the surface code in the code capacity noise model and compare its performance to the original matrix product state (MPS) tensor network decoder introduced by Bravyi, Suchara, and Vargo. The MPS decoder has a p-independent runtime complexity of $\mathcal{O}(nχ^3)$ resulting in significantly slower decoding times compared to our algorithm in the low-p regime.
97 MATHEMATICS AND COMPUTING↗
MBE HgCdTe heterostructure detectors
HgCdTe has been the mainstay for medium (3 to 5 micron) and long (10 to 14 micron) wavelength infrared detectors in recent years. Conventional growth and processing techniques are continuing to improve the material. However, the additional ability to tailor composition and placement of doped layers on the tens of angstroms scale using molecular beam epitaxy (MBE) provides the opportunity for new device physics and concepts to be utilized. MBE-based device structures to be discussed here can be grouped into two categories: tailored conventional structures and quantum structures. The tailored conventional structures are improvements on familiar devices, but make use of the ability to create layers of varying composition, and thus band gap, at will. The heterostructure junction can be positioned independently of doping p-n junctions. This allows the small band gap region in which the absorption occurs to be separated from a larger band gap region in which the electric field is large and where unwanted tunneling can occur. Data from hybrid MBE/liquid phase epitaxy (LPE)/bulk structures are given. Quantum structures include the HgTe-CdTe superlattice, in which the band gap and transport can be controlled by alternating thin layers (tens of angstroms thick) of HgTe and CdTe. The superlattice has been shown to exhibit behavior which is non-alloy like, including very high hole mobilities, two-dimensional structure in the absorption coefficient, resonant tunneling, and anisotropic transport.
Schulman, Joel N.↗
Clifford orbits from cayley graph quotients
We describe the structure of the $n$-qubit Clifford group $\mathcal{C}_n$ via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we introduce a quotient procedure. Quotienting the Cayley graph by the stabilizer subgroup of a state gives a reduced graph which depicts the state's Clifford orbit. Using this protocol for $\mathcal{C}_2$, we reproduce and generalize the reachability graphs. Since the procedure is state-independent, we extend our study to non-stabilizer states, including the W and Dicke states. Furthermore, our new construction provides a more precise understanding of state evolution under Clifford circuit action.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
On the universality of S n -equivariant k -body gates
The importance of symmetries has recently been recognized in quantum machine learning from the simple motto: if a task exhibits a symmetry (given by a group $\mathfrak{G}$), the learning model should respect said symmetry. This can be instantiated via $\mathfrak{G}$-equivariant quantum neural networks (QNNs), i.e. parametrized quantum circuits whose gates are generated by operators commuting with a given representation of $\mathfrak{G}$. In practice, however, there might be additional restrictions to the types of gates one can use, such as being able to act on at most k qubits. In this work we study how the interplay between symmetry and k-bodyness in the QNN generators affect its expressiveness for the special case of $\mathfrak{G}=S_n$, the symmetric group. Our results show that if the QNN is generated by one- and two-body Sn-equivariant gates, the QNN is semi-universal but not universal. That is, the QNN can generate any arbitrary special unitary matrix in the invariant subspaces, but has no control over the relative phases between them. Then, we show that in order to reach universality one needs to include n-body generators (if n is even) or ($n-1$)-body generators (if n is odd). As such, our results brings us a step closer to better understanding the capabilities and limitations of equivariant QNNs.
97 MATHEMATICS AND COMPUTING↗
Quantum reference frames from top-down crossed products
All physical observations are made relative to a reference frame, which is a system in its own right. If the system of interest admits a group symmetry, the reference frame observing it must transform commensurately under the group to ensure the covariance of the combined system. We point out that the crossed product is a way to realize quantum reference frames from the bottom-up; adjoining a quantum reference frame and imposing constraints generates a crossed product algebra. We provide a top-down specification of crossed product algebras and show that one cannot obtain inequivalent quantum reference frames using this approach. As a remedy, we define an abstract algebra associated to the system and symmetry group built out of relational crossed product algebras associated with different choices of quantum reference frames. We term this object the G -framed algebra, and show how potentially inequivalent frames are realized within this object. We comment on this algebra’s analog of the classical Gribov problem in gauge theory, its importance in gravity where we show that it is relevant for semiclassical de Sitter and potentially beyond the semiclassical limit, and its utility for understanding the frame dependence of physical notions like observables, density states, and entropies. Published by the American Physical Society 2024
Astronomy & Astrophysics↗
Detection of topology via entanglement oscillations
In this work, we introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an “entanglement gap,” showing that it is generally applicable to pure and disordered quantum systems. Using exact diagonalization and the strong disorder renormalization group method, we demonstrate that this approach gives results in agreement with the use of traditional topological invariants, especially in cases where topological order is known to persist in the presence of off-diagonal bond disorder. The entanglement gap is then used to analyze classes of quantum systems with alternating bond types, allowing us to construct their topological phase diagrams. The validity of these phase diagrams is verified in limiting cases of dominant bond types, where the solution is known.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Engineered MXene quantum dots for micro-supercapacitors with excellent capacitive behaviors
Micro-supercapacitors (MSCs) have drawn tremendous attention as promising candidates to power miniaturized portable/wearable electronics, but they still suffer from unsatisfactory electrochemical performance (e.g., insufficient energy density, mediocre rate capability), thus impeding their widespread applications. Here, a synergistic surface and structure engineering strategy achieved by downsizing to quantum dot scale, doping of heteroatoms, and introducing defects and functional groups is proposed to regulate the physicochemical properties of Ti 3 C 2 T x MXene. Encouragingly, the resulting MSCs based on defect-rich nitrogen-doped Ti 3 C 2 T x quantum dots (QDs) possess excellent electrochemical performance as demonstrated by large operating voltage (3.0 V in ionic liquid and 1.0 V in aqueous electrolyte), perfect rectangular CV shape even at 1000 V·s -1 , high volumetric capacitance of 33.1 F·cm -3 , and superior cycling stability after 10000 cycles. By employing experimental characterizations and density functional theory calculations, the remarkable performance of the MSCs is mainly due to the special chemical states as well as the unique surface and structural features of Ti 3 C 2 T x QDs, which offer abundant active sites, shorten ion diffusion pathways, promote ion/electron transports, and provide enhanced capacitance. Finally, this work provides a new strategy for the design of high-performance MSCs and a reference for the applications of MXene QDs in other energy-related fields.
42 ENGINEERING↗
Super Photon Counters
The perfect photon detector would measure the arrival time, the energy, the polarization, and the position of every arriving quantum, but that is easier said than done. Two groups have now succeeded in doing time-resolved spectroscopy on the Crab Nebula pulsar, measuring everything but the polarization, with reports from Romani et al. at Stanford and from Perryman et al. at ESTEC. Both groups use superconducting detectors to gain the necessary speed and sensitivity. The photon can heat the electrons in a superconductor biased in the middle of its resistive transition, or break bound superconducting electron-hole pairs, which can then be collected. Three years ago, Peacock et al. reported that they had detected single optical photons with a superconducting tunnel junction (STJ), and Paresce wrote a News and Views article. A tunnel junction uses two pieces of conductive material, separated by a tiny gap of insulating material or even vacuum. If the gap is thin enough, electrons can tunnel across anyway, and if the conductors are superconductors, the junction displays very useful quantum mechanical properties and electrical nonlinearities. Amplifiers, detectors, oscillators, and computer circuits can all be made from them. Their special advantage is that they operate at very low temperatures, dissipate very little power, operate very fast, and are very small.
Mather, John↗
Effective Field Theory of Random Quantum Circuits
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Accuracy of quantum sensors measuring yield photon flux and photosynthetic photon flux
Photosynthesis is fundamentally driven by photon flux rather than energy flux, but not all absorbed photons yield equal amounts of photosynthesis. Thus, two measures of photosynthetically active radiation have emerged: photosynthetic photon flux (PPF), which values all photons from 400 to 700 nm equally, and yield photon flux (YPF), which weights photons in the range from 360 to 760 nm according to plant photosynthetic response. We selected seven common radiation sources and measured YPF and PPF from each source with a spectroradiometer. We then compared these measurements with measurements from three quantum sensors designed to measure YPF, and from six quantum sensors designed to measure PPF. There were few differences among sensors within a group (usually <5%), but YPF values from sensors were consistently lower (3% to 20%) than YPF values calculated from spectroradiometric measurements. Quantum sensor measurements of PPF also were consistently lower than PPF values calculated from spectroradiometric measurements, but the differences were <7% for all sources, except red-light-emitting diodes. The sensors were most accurate for broad-band sources and least accurate for narrow-band sources. According to spectroradiometric measurements, YPF sensors were significantly less accurate (>9% difference) than PPF sensors under metal halide, high-pressure sodium, and low-pressure sodium lamps. Both sensor types were inaccurate (>18% error) under red-light-emitting diodes. Because both YPF and PPF sensors are imperfect integrators, and because spectroradiometers can measure photosynthetically active radiation much more accurately, researchers should consider developing calibration factors from spectroradiometric data for some specific radiation sources to improve the accuracy of integrating sensors.
NASA Center KSC↗
Bounding entanglement entropy with Clifford double cosets
Following on our previous work studying the orbits of quantum states under Clifford circuits via reachability graphs, we introduce contracted graphs whose vertices represent classes of quantum states with the same entropy vector. These contracted graphs represent the double cosets of the Clifford group, where the left cosets are built from the stabilizer subgroup of the starting state and the right cosets are built from the entropy-preserving operators. We study contracted graphs for stabilizer states, as well as 𝑊 states and Dicke states, discussing how the diameter of a state's contracted graph constrains the entropic diversity of its two-qubit Clifford orbit. We derive an upper bound on the number of entropy vectors that can be generated using any 𝑛-qubit Clifford circuit, for any quantum state. Here, we speculate on the holographic implications for the relative proximity of gravitational duals of states within the same Clifford orbit. Although we concentrate on how entropy evolves under the Clifford group, our double-coset formalism, and thus the contracted graph picture, is extendable to generic gate sets and generic state properties.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Global quantum phase diagram and non-Abelian chiral spin liquid in a spin- 3 2 square-lattice antiferromagnet
Since strong quantum fluctuations are essential for the emergence of quantum spin liquids, there have been extensive exploration and identification of spin liquid candidates in spin-$\frac{1}{2}$ systems, while such activities are rare in higher spin systems. Here we report an example of non-Abelian chiral spin liquid emerging in a spin-$\frac{3}{2}$ Heisenberg model on a square lattice. By tuning Heisenberg exchange interaction and scalar chirality interaction, we map out a quantum phase diagram enclosing three conventional magnetic orders and a chiral spin liquid based on density-matrix renormalization group studies. The nature of the spin liquid is identified as a long-sought bosonic version of the Read-Rezayi state that supports non-Abelian Fibonacci anyonic statistics, identified by the ground state entanglement spectrum. Significantly, we establish that the non-Abelian chiral spin liquid emerges through the enlarged local degrees of freedom and enhanced quantum fluctuations near the classical phase boundaries of competing magnetic orders. Finally, our numerical discovery of an exotic quantum spin liquid in a spin-$\frac{3}{2}$ system suggests a route for discovering fractionalized quantum phases in frustrated higher spin magnetic compounds.
2-dimensional systems↗
Island Shape Instabilities and Surfactant-Like Effects in the Growth of InGaAs/GaAs Quantum Dots
InGaAs/GaAs island formation during vapor phase epitaxy showed diverging behaviors when varying group V partial pressures (PP). Differences include changes in critical thicknesses for the onset of the Stranski-Krastanow (S-K) transformation, surface coverages, ratios between coherent and incoherent islands, and dissimilar morphologies upon annealing.
Quantum↗
Holographic codes and bulk RG flows
We consider the coarse-graining of holographic quantum error correcting codes under a generalized notion of bulk renormalization-group flow. In particular, we study the renormalization under this flow of the $A/4G$ term in the Faulkner-Lewkowycz-Maldacena formula and in its Rényi generalization. This provides a general quantum code perspective on the arguments of Susskind and Uglum. Specifically, given a 'UV' code with two-sided recovery and appropriately flat entanglement spectrum together with a set of 'seed' states in the UV code, we explicitly construct an 'IR' code with corresponding properties which contains the given seed states and is of minimal size in a sense we describe.
FOS: Physical sciences↗
Quantum Barkhausen noise induced by domain wall cotunneling
Most macroscopic magnetic phenomena (including magnetic hysteresis) are typically understood classically. Here, we examine the dynamics of a uniaxial rare-earth ferromagnet deep within the quantum regime, so that domain wall motion, and the associated hysteresis, is initiated by quantum nucleation, which then grows into large-scale domain wall motion, which is observable as an unusual form of Barkhausen noise. We observe noncritical behavior in the resulting avalanche dynamics that only can be explained by going beyond traditional renormalization group methods or classical domain wall models. We find that this “quantum Barkhausen noise” exhibits two distinct mechanisms for domain wall movement, each of which is quantum-mechanical, but with very different dependences on an external magnetic field applied transverse to the spin (Ising) axis. These observations can be understood in terms of the correlated motion of pairs of domain walls, nucleated by cotunneling of plaquettes (sections of domain wall), with plaquette pairs correlated by dipolar interactions; this correlation is suppressed by the transverse field. Similar macroscopic correlations may be expected to appear in the hysteresis of other systems with long-range interactions.
Science & Technology - Other Topics↗
Classical symmetries and the Quantum Approximate Optimization Algorithm
Here, we study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.
97 MATHEMATICS AND COMPUTING↗
Quantum propagation in single mode fiber
This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.
Joneckis, Lance G.↗