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↗
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↗
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↗
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↗
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↗
Predicting Quantum Criticality in Single-Crystalline Ce 2 Ru 3 Ge 5
Strongly correlated f-electron systems are known to host exotic quantum states, such as quantum criticality, complex order parameters, and unconventional superconductivity. However, the appearance of these exotic states is difficult to predict, making the study of quantum critical behavior challenging, especially in ferromagnetic materials. Herein, we report a structure–property map for Ce 2 M 3 X 5 (M = transition metal; X = main group element) that aids in the targeted design of materials likely to exhibit quantum criticality. Guided by this map, we report on the synthesis of single-crystalline Ce 2 Ru 3 Ge 5 and provide, for the first time, magnetic susceptibility, heat capacity, resistivity, and magnetoresistance measurements on single crystals. Here, we observe a weak ferromagnetic-like response at 7.5 K, which is contrasted with the bulk ferromagnetic ordering that appears in polycrystalline samples. Non-Fermi liquid behavior is seen in the temperature dependent electrical resistivity and heat capacity of the single crystals, suggesting proximity to a ferromagnetic quantum critical point without chemical or physical pressure. Given the contrast with previous reports of polycrystals, these results lead us to propose that single crystalline Ce 2 Ru 3 Ge 5 is intrinsically tuned into the vicinity of a ferromagnetic quantum critical point.
36 MATERIALS SCIENCE↗
Bond-dependent anisotropy and magnon decay in cobalt-based Kitaev triangular antiferromagnet
Following tremendous success of the graphene-derived fundamental and applied research, the magnetic van der Waals materials that can be cleaved into monolayer two-dimensional atomic crystals have emerged as a new platform in the studies of low-dimensional physics and in the design of artificial heterostructures with novel properties. Because of that, the family of dihalides and trihalides of the 3d transition group receive a strong renewed interest. Together with our experimental collaborators, we have investigated the novel dynamical properties of one of such promising material CoI 2 , and demonstrated that spin excitations in it are prone to substantial breakdown and complex level repulsion, the important quantum effects whose theoretical understanding has been significantly advanced by our group in the last two decades. Both phenomena are dramatically revealed by experiments and verified by the theory in our joint study, published in Nature Physics. Altogether, our results pave the way toward a new research direction for the magnetic van der Waals materials.
36 MATERIALS SCIENCE↗
Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
We formulate a family of spin Topological Quantum Field Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf–Witten TQFTs. They are obtained by gauging G-equivariant invertible spin-TQFTs, or, in physics language, gauging the interacting fermionic Symmetry Protected Topological states (SPTs) with a finite group G symmetry. We use the fact that the torsion part of the classification is given by Pontryagin duals to spin-bordism groups of the classifying space BG. We also consider unoriented analogues, that is G-equivariant invertible pin ± -TQFTs (fermionic time-reversal-SPTs) and their gauging. We compute these groups for various examples of abelian G using Adams spectral sequence and describe all corresponding TQFTs via certain bordism invariants in 3, 4 and other dimensions. This gives explicit formulas for the partition functions of spin-TQFTs on closed manifolds with possible extended operators inserted. The results also provide explicit classification of ’t Hooft anomalies of fermionic QFTs with finite abelian group symmetries in one dimension lower. We construct new anomalous boundary spin-TQFTs (surface fermionic topological orders). Finally, we explore SPT and symmetry enriched topologically (SET) ordered states, and crystalline SPTs protected by space-group (e.g. translation Z) or point-group (e.g. reflection, inversion or rotation C m ) symmetries, via the layer-stacking construction.
97 MATHEMATICS AND COMPUTING↗
Transition Path Sampling Study of the Feruloyl Esterase Mechanism
Serine hydrolases cleave peptide and ester bonds and are ubiquitous in nature, with applications in biotechnology, in materials, and as drug targets. The serine hydrolase two-step mechanism employs a serine–histidine–aspartate/glutamate catalytic triad, where the histidine residue acts as a base to activate poor nucleophiles (a serine residue or a water molecule) and as an acid to allow the dissociation of poor leaving groups. This mechanism has been the subject of debate regarding how histidine shuttles the proton from the nucleophile to the leaving group. To elucidate the reaction mechanism of serine hydrolases, we employ quantum mechanics/molecular mechanics-based transition path sampling to obtain the reaction coordinate using the Aspergillus niger feruloyl esterase A (AnFaeA) as a model enzyme. The optimal reaction coordinates include terms involving nucleophilic attack on the carbonyl carbon and proton transfer to, and dissociation of, the leaving group. During the reaction, the histidine residue undergoes a reorientation on the time scale of hundreds of femtoseconds that supports the “moving histidine” mechanism, thus calling into question the “ring flip” mechanism. We find a concerted mechanism, where the transition state coincides with the tetrahedral intermediate with the histidine residue pointed between the nucleophile and the leaving group. Moreover, motions of the catalytic aspartate toward the histidine occur concertedly with proton abstraction by the catalytic histidine and help stabilize the transition state, thus partially explaining how serine hydrolases enable poor nucleophiles to attack the substrate carbonyl carbon. Rate calculations indicate that the second step (deacylation) is rate-determining, with a calculated rate constant of 66 s –1 . Altogether, these results reveal the pivotal role of active-site dynamics in the catalytic mechanism of AnFaeA, which is likely similar in other serine hydrolases.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Perturbative instability of nonergodic phases in non-Abelian quantum chains
An important challenge in the field of many-body quantum dynamics is to identify nonergodic states of matter beyond many-body localization (MBL). Strongly disordered spin chains with non-Abelian symmetry and chains of non-Abelian anyons are natural candidates, as they are incompatible with standard MBL. In such chains, real space renormalization group methods predict a partially localized, nonergodic regime known as a quantum critical glass (a critical variant of MBL). Here, this regime features a treelike hierarchy of integrals of motion and symmetric eigenstates with entanglement entropy that scales as a logarithmically enhanced area law. We argue that such tentative nonergodic states are perturbatively unstable using an analytic computation of the scaling of off-diagonal matrix elements and accessible level spacing of local perturbations. Our results indicate that strongly disordered chains with non-Abelian symmetry display either spontaneous symmetry breaking or ergodic thermal behavior at long times. We identify the relevant length and timescales for thermalization: Even if such chains eventually thermalize, they can exhibit nonergodic dynamics up to parametrically long timescales with a nonanalytic dependence on disorder strength.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗