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- Nikolas Breuckmann (Bristol University)
- "Quantum Complexity and error correction"
Abstract We will discuss some recent results on the complexity of quantum many-body systems that rely on tools from quantum fault-tolerance. In particular, we will discuss the resolution of the cNLTS and NLTS conjectures via good classical and quantum LDPC codes and speculate about the role of quantum fault tolerance in tackling the qPCP conjecture.
- Bartlomiej Czech (Tsinghua University, Beijing)
- "Everything Everywhere All at Once: Holographic Entropy Inequalities, the Topology of Error Correction, Black Holes, Cubohemioctahedron, and (maybe) the Toric Code"
Abstract An important class of quantum states are those whose entanglement entropies can be computed by minimal cuts through some bulk structure---a holographic spacetime or a random tensor network. Such states obey linear constraints on their entanglement entropies, which are known as holographic entropy inequalities. I present two new infinite families of holographic entropy inequalities. The entropies featured in these inequalities are best visualized on graphs whose incidence relations reflect subsystem inclusion. These graphs turn out to be tessellations of the torus and the real projective plane. The non-contractible cycles on these manifolds play an indispensable role in proving the inequalities, which shows that they hold for essentially topological reasons. Physically, the inequalities represent constraints on holographic error correcting codes and, in some cases, the entropy of two-sided black holes. If time allows it, I will sketch bonus applications, which involve a non-planar polytope called "cubohemioctahedron" and (more speculatively) the toric code.
- Isaac Kim (University of California, Davis)
- "Complementarity and the unitarity of the black hole S-matrix"
Abstract Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity.
- Martin Kliesch (Hamburg University of Technology)
- "Guaranteed efficient energy estimation of quantum many-body Hamiltonians"
Abstract Energy estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottleneck for variational quantum algorithms.
- Tomotaka Kuwahara (Riken)
- "Optimal light cone and digital quantum simulation of interacting bosons"
Abstract This research addresses fundamental questions in many-body physics related to the propagation of information and the establishment of light cones. It begins by discussing causality, a central principle in many-body physics that restricts information propagation to within a "light cone." The famous Lieb-Robinson bound is introduced, characterizing the effective light cone and playing a crucial role in various quantum simulation algorithms and entanglement studies. However, these concepts have limitations, particularly in systems with long-range interactions and unbounded local energy. This work focuses on resolving these limitations. We start by mentioning prior results in characterizing the speed of boson particle transport and information propagation. Still, challenges remained in proving the speed limit for arbitrary initial states and identifying optimal light cones for non-steady initial states with low boson density. We present solutions to these problems in general setups, applicable to time-dependent Bose-Hubbard-type Hamiltonians in any dimension from non-steady initial states. Our result highlights the qualitative difference between bosons and other models in higher dimensions in terms of the information propagation. As the practical significance of these findings, we demonstrate an efficiency-guaranteed digital quantum simulation of interacting bosons, particularly in estimating gate complexity. In this talk, I offer a comprehensive understanding of information propagation and light cones in quantum boson systems, addressing long-standing challenges and providing practical insights for quantum simulations.
- Francois Le Gall (Nagoya University)
- "Theoretical Foundations of Quantum Advantage for Quantum Algorithms"
Abstract In this talk I will describe recent developments on establishing theoretical foundations of quantum advantage in quantum algorithms. I will start by presenting well-known quantum algorithms such as quantum algorithms for solving linear systems of equations (the HHL algorithm) or simulating chemical reactions (quantum phase estimation). I will then present recent results that establish the theoretical foundations of quantum advantage for these algorithms, as well as recent works that successfully "dequantize" them in some special cases. I will conclude by mentioning challenges and open problems.
- Michal Oszmaniec (Center for Theoretical Physics PAS Warsaw, and NASK)
- "Saturation and recurrence of complexity in random quantum dynamics"
Abstract Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of AdS black holes. In this context Brown and Susskind conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly-exponential times. In this work we prove the saturation and recurrence of the complexity of quantum states and unitaries in a model of chaotic time-evolution based on random quantum circuits, in which a local random unitary transformation is applied to the system at every time step. Importantly, our findings hold for quite general random circuit models, irrespective of the gate set and geometry of qubit interactions. Our results advance an understanding of the long-time behaviour of chaotic quantum systems and could shed light on the physics of black hole interiors. From a technical perspective our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs. The talk will be based on: arXiv:2205.09734
- Daniel Ranard (Massachusetts Institute of Technology)
- "Classification of 2D gapped phases with strict area law"
Abstract From the quantum information perspective, gapped quantum phases of matter may be understood as equivalence classes of ground states under constant-depth circuits. In 2D, the these phases have rich structure, and it is believed they are classified by certain tensor categories. We prove a version of this conjecture in a simplified setting, by assuming a strict area law.
- Shinsei Ryu (Princeton University)
- "Going beyond two – multipartite entanglement and higher Berry phase --"
Abstract One of the most fundamental concepts in quantum mechanics is the inner product defined for two quantum states – it represents the transition probability between them. The inner product is also intimately connected to quantum entanglement -- Bell-type bipartite entanglement in which two parties are perfectly correlated. In this talk, using multipartite quantum entanglement, we generalize the inner product for more than two quantum states. Such "multi-inner products" have many applications in quantum many-body physics. Specifically, we will discuss two applications for critical and gapped quantum systems in one spatial dimension.
- Jun Suzuki (The University of Electro-Communications)
- "Introduction to Optimal Design of Experiments (DeoE) and its Applications to Quantum Estimation"
Abstract In this talk, I will give a short introduction to optimal design of experiments (DoE), which is a branch of mathematical statistics. The theory of optimal DoE enables finding an optimal strategy to extract the maximum information about a statistical model.First, I will formulate quantum estimation problems based on DoE. Next, some of useful concepts from statistics are explained to analyze quantum system. I then provide analytical construction of optimal desings for several well-known optimality criteria in a qubit system.
- Lisa Yang (Massachusetts Institute of Technology)
- "Complexity of Learning Pseudorandom Dynamics: the Unpredictability of Black Holes & the Necessity of Event Horizons"
- Michał Banacki (International Centre for Theory of Quantum Technologies, University of Gdańsk)
- "Security based on quantum extremality - from no-signaling assemblages to channel steering with information leakage"
Abstract The idea of extremality considered within convex analysis can be seen as an important tool providing security of various protocols typical for quantum information theory. However, in the usual multiparty Bell scenario, described by the notion of local, quantum, and no-signaling correlations, it is impossible to provide quantum realization of non-local, and yet extreme points within the set of all no-signaling behaviours. Motivated by that considerations we analyze multipartite steering scenarios (with generalized no-signaling constraints) described mathematically by collections of subnormalized states - i.e. so-called assemblages. We define the notion of inflexibility and in particular, we use it to show that the central question concerning the possibility of quantum realization of extreme and non-local no-signaling assemblages admits a positive answer  (in contrast with Bell scenarios). This result provides a path to post-quantum security of quantum (semi)-Device-Independent cryptographic protocols and a tool for the detection of (genuine) entanglement. Moreover, we extend our reasoning to provide a cryptographic key secure against no-signaling adversaries with the presence of information leakage between the parties (and a finite number of settings). In particular, we introduce a specific bipartite channel steering scenario with quantum realization, in which an adversary attack of the eavesdropper modeled by possible convex decomposition of a process shared by the parties is not possible . Finally, we prove that the security holds even if we relax the steering scenario to the situation when the measurement has been performed on the trusted system .  Ravishankar Ramanathan, Michał Banacki, Ricard Ravell Rodríguez, Paweł Horodecki, Single trusted qubit is necessary and sufficient for quantum realization of extremal no-signaling correlations, npj Quantum Information, 8, 119 (2022)  Michał Banacki, Ravishankar Ramanathan, Paweł Horodecki, Multipartite channel assemblages, arXiv:2205.05033
- Adam Burchardt (QuSoft, University of Amsterdam)
- "Thirty-six entangled officers of Euler"
Abstract The negative solution to the famous problem of 36 officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers are entangled, and construct orthogonal quantum Latin squares of this size. As a consequence, we find an example of the long-elusive Absolutely Maximally Entangled state AME(4,6) of four subsystems with six levels each, equivalently a 2-unitary matrix of size 36, which maximizes the entangling power among all bipartite unitary gates of this dimension, or a perfect tensor with four indices, each running from one to six. During the talk, I will briefly present the problem of multipartite entanglement, and its relation to classical and quantum combinatorial designs.
- Michele Dall'Arno (Department of Computer Science, Toyohashi University of Technology)
- "On the role of designs in the data-driven approach to quantum statistical inference"
Abstract Designs, and in particular symmetric, informationally complete (SIC) structures, play an important role in the quantum tomographic reconstruction process and, by extension, in certain interpretations of quantum theory focusing on such a process. This fact is due to the symmetry of the reconstruction formula that designs lead to. However, it is also known that the same tomographic task, albeit with a less symmetric formula, can be accomplished by any informationally complete (non necessarily symmetric) structure. Here we show that, if the tomographic task is replaced by a data-driven inferential approach, the reconstruction, while possible with designs, cannot by accomplished anymore by an arbitrary informationally complete structure. Hence, we propose the data-driven inference as the arena in which the role of designs naturally emerges. Our inferential approach is based on a minimality principle according to which, among all the possible inferences consistent with the data, the weakest should be preferred, in the sense of majorization theory and statistical comparison.
- Andrew Darmawan (Yukawa Institute for Theoretical Physics, Kyoto University)
- "Tensor-network methods for developing practical quantum error-correcting codes"
Abstract In this talk I will discuss how numerical tensor-network techniques can be used to study the effect of realistic types of noise on quantum error-correction procedures. I will focus on one particularly harmful type of noise in quantum computers called qubit leakage, in which a qubit is excited to a level outside of the qubit subspace. I describe how the effect of leakage noise in quantum error correcting codes, as well as methods for eliminating it, can be studied with tensor-network methods.
- Nick Hunter-Jones (UT Austin)
- "Unitary designs from spectral gaps on any graph"
- Kansei Inamura (Institute for Solid State Physics, University of Tokyo)
- "Fusion surface models: 2+1d lattice models from fusion 2-categories"
Abstract We will discuss a systematic way to construct (2+1)-dimensional lattice models with generalized symmetries described by fusion 2-categories. These models are (2+1)-dimensional analogues of the 1+1d anyon chain models and are dubbed fusion surface models. We obtain these models by utilizing the "sandwich construction," i.e., putting a 4d topological field theory on a slab with a topological boundary condition imposed on one side and a dynamical boundary condition on the other. The fusion 2-category symmetry of the model is determined by a choice of the 4d topological field theory and its topological boundary condition. Examples of fusion 2-categories include modular tensor categories that describe the symmetries generated by anyons. Therefore, the fusion surface models may serve as candidates for lattice models realizing chiral topological orders.
- Zhian Jia (Centre for Quantum Technologies, National University of Singapore)
- "Boundary and domain wall theory of Hopf quantum double lattice"
Abstract During this talk, I will delve into the fascinating topic of the Hopf quantum double model, which serves as a remarkable two-dimensional non-chiral topologically ordered phase of matter. I will thoroughly explain how the comodule algebra determines the gapped boundary theory, and provide a comprehensive lattice construction for the gapped boundary. Additionally, I will discuss anyon condensation in detail. I will also demonstrate how the domain wall theory is determined by a bicomodule algebra, using the folding trick. Moreover, I will discuss its algebraic theory and lattice construction. Finally, I will explore the generalization of the Hopf quantum double model to the weak Hopf case and duality of the model.
- Tsung-Cheng Peter Lu (Perimeter Institute for Theoretical Physics)
- "Mixed-state long-range order and criticality from measurement and feedback"
Abstract I will introduce a general framework for using local measurements, local unitaries, and non-local classical communication to construct quantum channels which can efficiently prepare mixed states with long-range quantum order or quantum criticality. As an illustration, symmetry-protected topological (SPT) phases can be universally converted into mixed-states with long-range entanglement, which can undergo phase transitions with quantum critical correlations and a logarithmic scaling of the entanglement negativity, despite coexisting with volume-law entropy. Furthermore, based on fermion occupation number measurements and feedback, I will show how to convert Chern insulators into a mixed state with critical quantum correlations in the bulk, hence providing a non-trivial example where mixed-state quantum criticality can emerge from a gapped state of matter in constant depth.
- Pasquale Marra (University of Tokyo)
- "Majorana modes in 2D topological superconductors with inhomogeneous order: A possible platform for quantum computing and quantum gravity"
Abstract Majorana modes have gained significant interest due to their potential applications in topological quantum computing and effectively realizing exotic quantum phases. Two-dimensional topological superconductors and proximitized semiconducting nanowires are the most extensively studied condensed-matter systems for realizing Majorana modes, each having advantages and limitations. Here we describe an alternative platform: a two-dimensional topological superconductor with inhomogeneous superconducting order parameter, where Majorana modes are predicted to localize at the ends of "topologically-nontrivial stripes". In particular, we describe possible braiding and fusion protocols to highlight the relevance of this platform in the context of topological quantum computation. Furthermore, we will describe how this platform can realize emergent quantum-mechanical symmetry in certain regimes. Finally, we will give an outlook on realizing more exotic quantum states such as Yang-Lee anyons with non-unitary and non-abelian braiding statistics, the Sachdev-Ye-Kitaev model, and synthetic horizons within this platform.
- Yosuke Mitsuhashi (The University of Tokyo)
- "Clifford Group and Unitary Designs under Symmetry"
Abstract The Clifford group on qubits is well known to be a unitary 3-design. We have generalized this statement into symmetric cases by extending the notion of unitary design. Concretely, we have proved that a symmetric Clifford group is a symmetric unitary 3-design if and only if the symmetry constraint is described by some Pauli subgroup. For Pauli subgroup symmetries, we have found a complete and unique construction of symmetric Clifford groups by simple quantum gates. For the overall understanding, we have also considered physically relevant U(1) and SU(2) symmetry constraints, which cannot be described by Pauli subgroups, and have proved that the symmetric Clifford group is a symmetric unitary 1-design but not a 2-design under those symmetries. This work will open a new perspective into quantum information processing such as randomized benchmarking, and pave a way to further explore many-body systems such as measurement-induced phase transitions.
- Mio Murao (Graduate School of Scinece, The University of Tokyo)
- "Higher-order quantum operations of blackbox unitaries"
Abstract Supermaps are higher-order transformations taking maps as input. Quantum mechanically implementable supermaps are called quantum supermaps and their general properties are formulated by the framework of quantum networks and quantum combs proposed by Chiribella et al. We consider the implementability of supermaps in quantum mechanics when the input maps are unitaries given as blackboxes and the unitary blackboxes can be used multiple but finite times to explore fundamental quantum properties exhibited in higher-order transformations possibly utilized for quantum computation. We regard such direct implementations of supermaps for blackbox quantum operations with multiple uses of the blackboxes as “higher-order quantum operations”. We investigate how the causal structure and spacetime symmetry of these unitary blackboxes affects their performance in implementing higher-order quantum operations. We analyze several tasks, inversion, complex conjugation, and transposition of blackbox unitaries and controllization of divisible blackbox unitaries based on controllization of quntum combs.
- Tomasz Młynik (Institute of Theoretical Physics and Astrophysics, University of Gdańsk)
- "Transformation of an unknown unitary operation: complex conjugation"
Abstract Let U be an arbitrary unitary operator representing an arbitrary d-dimensional unitary quantum operation. Our work presents optimal quantum circuits for transforming a number k of calls of U into its complex conjugate U*. Our circuit admits a parallel implementation and is proven to be optimal for any number of uses k and dimension d with average fidelity coinciding with the worst-case fidelity showing that average fidelity is a relevant figure of merit. The average fidelity is given by a relation that only depends on global parameters k and d. This extends previous works which considered the scenario of a single call (k=1) of the operation U, and the special case of k = d-1 calls. In our solution, we strongly rely on methods coming from group representation theory and semi-definite programming (SDP).
- Aswin Parayil Mana (C.N Yang Institute for Theoretical Physics, Stony Brook University)
- "Fractons, strange correlates and dualities from measuring cluster states"
Abstract In quantum information theory, it is often useful to express the partition function of spin systems as an overlap between the so-called cluster state and an appropriate product state. In the context of topological phases of matter, related formulation have appeared as so-called strange correlators, which relate certain statistical partition functions to string-net wave functions in a topological order. In this presentation, we will introduce a similar relation between subsystem symmetric spin systems and fracton orders. We will obtain classical partition functions of spin systems from measuring cluster states used to prepare the ground states of fracton orders.
- Dimitrios Patramanis (University of Warsaw)
- "The Krylov Panopticon"
Abstract In recent years the notion of computational complexity has become the object of intensive study for physicists despite the fact that it is a concept originating from computer science. So why is the physics community so interested in this particular topic and what can we hope to learn from it? In my talk I will briefly address these questions in a general context and then proceed to discuss the measure called Krylov complexity in particular. This measure, although one of many, has become very popular because of its wide range of applicability and computability. I will elaborate on these qualities by reviewing its construction and highlighting certain aspects that in principle make it an interesting probe for any quantum system. Hence, it can be likened to a panopticon from which one can gain access to information about systems ranging from condensed matter to exotic QFTs and possibly holography. Finally, I will present some of the latest advancements and discuss how they shape our current understanding of Krylov complexity and its place in the “zoo” of complexity measures.
- Leon Sander (FAU Erlangen-Nürnberg)
- "QCNN as Phase Detection Circuit on the Toric Code"
Abstract Understanding macroscopic behaviour of quantum materials is an interesting challenge in the field of quantum technologies. This macroscopic behavior can be evaluated by examining quantum phases. Consequently, recognising the phase of a given input state is an important problem, which is often solved by measuring the corresponding order parameter. However, previous work by Cong et al. and Hermann et al. suggests quantum convolutional neural networks (QCNN) are an alternative method of phase detection that can also improve sampling efficiency near the phase boundary compared to direct measurements. We construct a QCNN designed to act as a phase recognition circuit that determines whether incoherent noise of a certain strength is sufficient to induce a phase transition in the toric code. The error correcting toric code is an interesting model for this study as it promises to reveal connections between quantum information and quantum phase transitions.
- Harshank Shrotriya (Centre for Quantum Technologies, NU Singapore)
- "Nonlocality of Deep Thermalization"
Abstract We study the role of global system topology in governing deep thermalization, the relaxation of a local subsystem towards a maximally-entropic, uniform distribution of post-measurement states, upon observing the complementary subsystem in a local basis. Concretely, we focus on a class of (1+1)d systems exhibiting `maximally-chaotic' dynamics, and consider how the rate of the formation of such a universal wavefunction distribution depends on boundary conditions of the system. We find that deep thermalization is achieved exponentially quickly in the presence of either periodic or open boundary conditions; however, the rate at which this occurs is twice as fast for the former than for the latter. These results are attained analytically using the calculus of integration over unitary groups, and supported by extensive numerical simulations. Our findings highlight the nonlocal nature of deep thermalization, and clearly illustrates that the physics underlying this phenomenon goes beyond that of standard quantum thermalization, which only depends on the net build-up of entanglement between a subsystem and its complement.
- Michal Studzinski (Institute of Theoretical Physics and Astrophysics, University of Gdańsk)
- "When the symmetric group meets partial transposition: new tools for studying quantum systems"
Abstract In this talk we give an overview of the recent developments in representation theory of the symmetric group and its deformation by partial transposition. Motivated by the famous Schur-Weyl duality we construct irreducible matrix basis for the deformed algebra allowing for reducing the complexity of analytical and numerical computations for various problems appearing not only in the quantum information theory. We show that developed tools have universal character in the sense that tey allow us for effective studies of many complex systems since the considered deformed symmetries appear naturally in many aspects of physics, applied and pure mathematics. From the point of view of physics we explain how considered symmetries arise in many-body physics, quantum teleportation, theory of higher-order operations or particular aspects of gravity theories. We show by presenting particular examples how our tools lead from general complicated statement to final closed expression for quantities under interest. From the side of the applied and pure mathematics, we explain how our results meets complexity reduction in semi-definite programming and novel approach to the representation theory of the symmetric group called the Vershik-Okounkov approach.
- Vincent P. Su (Berkeley Center for Theoretical Physics, UC Berkeley)
- "Learning to Play with Quantum Legos - Reinforcement Learning for QECC Design"
Abstract Recently, the quantum lego framework was introduced where smaller codes can be used to construct larger codes in a modular fashion. Rich behavior can emerge in instances such as the HaPPY code, which is built from many copies of the [[5,1,3]] code, and the Toric code, which can be built from many copies of a [[4,2,2]] self-dual CSS code. In this work, we present results on novel code design by teaching a machine to design codes within the quantum lego framework.
- Hiroki Sukeno (C.N. Yang Institute for Theoretical Physics, Stony Brook University)
- "Lattice gauge theories from measuring entangled states"
Abstract Lattice gauge theory has been a cardinal formulation in theoretical physics with its relevancy ranging from quantum information science, high energy physics, and condensed matter physics. In this presentation, I will first talk about a quantum simulation scheme  for lattice gauge theories motivated by Measurement-Based Quantum Computation . We consider preparing a so-called resource state whose entanglement structure is tailored to reflect the spacetime structure of the gauge theory. We then consider measuring qubits in the resource state in a certain adaptive manner, and we demonstrate that it drives the Hamiltonian quantum simulation of the lattice gauge theory at the boundary of the resource state. I will elucidate that the entanglement structure in the resource state gives rise to symmetry-protected topological orders with respect to higher-form symmetries. Then, I will discuss applications/connections of the idea above to other problems in high energy/condensed matter physics.  R. Raussendorf and H. J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86, 5188 (2001)  H. Sukeno and T. Okuda, Measurement-based quantum simulation of Abelian lattice gauge theories, arXiv:2210.10908
- Ryotaro Suzuki (Free University of Berlin)
- "Quantum complexity phase transitions in monitored random circuits"
Abstract Recently, the dynamics of quantum systems that involve both unitary evolution and quantum measurements have attracted attention due to the exotic phenomenon of measurement-induced phase transitions. At the same time, quantum complexity emerged as a key quantity for understanding phenomena in quantum computation, quantum many-body dynamics, and black hole physics. In this talk, we consider the dynamics of the quantum state complexity in monitored random circuits, where n qubits evolve according to a random unitary circuit and are individually measured with a fixed probability at each time step. We rigorously show that the evolution of the exact quantum state complexity undergoes a phase transition when changing the measurement rate. Below a critical measurement rate, the complexity grows at least linearly in time until saturating to the maximum value exponentially in n. Above, the complexity does not grow more than polynomial in n. In the proof, we use percolation theory to exhibit paths along which an exponentially long quantum computation can be run below the critical rate, and to identify events where the state complexity is reset to zero above the critical rate. We lower bound the exact state complexity in the former regime using recently developed techniques based on algebraic geometry.
- Kento Tsubouchi (The University of Tokyo)
- "Cost-optimal quantum error mitigation based on universal cost bound"
Abstract We present two lower bounds on the sampling cost of quantum error mitigation (QEM) and cost-optimal QEM method that achieves these lower bounds. Our first bound applies to generic layered quantum circuits under a wide class of Markovian noise: we showed that the sampling cost required to construct an unbiased estimator of an observable grows exponentially with the circuit depth. In particular, under the global depolarizing noise, we find that the bound can be asymptotically saturated by simply rescaling the measurement results. Our second bound shows that for random circuits with local noise, where each gate is drawn from unitary 2-design, the cost also grows exponentially with the qubit count. Through numerical simulations, we extend this result to more general random circuits. Even if the circuit has only linear connectivity, such as the brick-wall structure, we observe that each noise channel converges to the global depolarizing channel, with its strength growing exponentially with the qubit count.This not only implies the exponential growth of cost both with the depth and qubit count, but also validates the rescaling technique for sufficiently deep quantum circuits. Our results contribute to the understanding of the physical limitations of quantum error mitigation and provide a new criterion for evaluating the performance of quantum error mitigation techniques.
- Yixu Wang (Institute for Advanced Studies, Tsinghua University)
- "Quantum Error Thresholds and von Neumann Algebra Types"
Abstract In this project we use tools of von Neumann algebras, especially the types of algebras to discuss the threshold problem. The fault tolerant threshold of quantum error correction codes has deep connections to other aspects of theoretical physics. From condensed matter point of view, the threshold problem can be transformed to a phase transition problem in a random bond Ising model. From gravity side, recently researchers point out that the phase transition state from a thermal AdS to a black hole, exactly corresponds to the transition from below to above fault tolerant threshold. In this work, we try to determine the von Neuman algebra types of several models below and above its fault tolerant threshold, mainly focusing on the qubit toric code and GKP toric code model. This would characterize different error corrections in terms of their algebra type change below and above the threshold.
- Masataka Watanabe (University of Amsterdam & Yukawa Institute for Theoretical Physics, Kyoto University)
- "Quantum quench and the split property"
Abstract I will give a concrete physical procedure which obtains the split property of von Neumann algebras of quantum field theories, used in defining the reduced density matrix and in computing the entanglement entropy.
- Yijia Xu (Joint Center for Quantum Information and Computer Science, University of Maryland)
- "Equivalence between fermion-to-qubit mappings in two spatial dimensions"
Abstract We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization in Chen et al. [Ann. Phys. (N. Y) 393, 234 (2018)], whose gauge constraints project onto the subspace of the toric code with emergent fermions. Starting from the exact bosonization and applying Clifford finite-depth generalized local unitary transformation, we can achieve all possible fermion-to-qubit mappings (up to the re-pairing of Majorana fermions). In particular, we discover a new supercompact encoding using 1.25 qubits per fermion on the square lattice. We prove the existence of finite-depth quantum circuits to obtain fermion-to-qubit mappings with qubit-fermion ratios r=1+1/2kfor positive integers k, utilizing the trivialness of quantum cellular automata in two spatial dimensions. Also, we provide direct constructions of fermion-to-qubit mappings with ratios arbitrarily close to 1. When the ratio reaches 1, the fermion-to-qubit mapping reduces to the one-dimensional Jordan-Wigner transformation along a certain path in the two-dimensional lattice. Finally, we explicitly demonstrate that the Bravyi-Kitaev superfast simulation, the Verstraete-Cirac auxiliary method, Kitaev’s exactly solved model, the Majorana loop stabilizer codes, and the compact fermion-to-qubit mapping can all be obtained from the exact bosonization.
- Masahito Yamazaki (Kavli IPMU)
- Satoshi Yoshida (The University of Tokyo)
- "Universal, deterministic, and exact protocol to reverse qubit-unitary and qubit-encoding isometry operations"
Abstract In this work, we report a deterministic and exact protocol to reverse any unknown qubit-unitary and qubit-encoding isometry operations. We present the semidefinite programming (SDP) to search the Choi matrix representing a quantum circuit reversing any unitary operation. We derive a quantum circuit transforming four calls of any qubit-unitary operation into its inverse operation by imposing the SU(2)×SU(2) symmetry on the Choi matrix. This protocol only applies only for qubit-unitary operations, but we extend this protocol to any qubit-encoding isometry operations. For that, we derive a subroutine to transform a unitary inversion protocol to an isometry inversion protocol by constructing a quantum circuit transforming finite sequential calls of any isometry operation into random unitary operations.
- Beata Zjawin (International Centre for Theory of Quantum Technologies, University of Gdańsk)
- "Quantifying EPR: the resource theory of nonclassicality of common-cause assemblages"
Abstract We develop a resource theory for assemblages in a variety of different Einstein-Podolsky-Rosen (EPR) scenarios. We take the set of free operations to be Local Operations and Shared Randomness (LOSR), reflecting the view that such scenarios have a common-cause causal structure. The types of correlations we study include those in bipartite and multipartite EPR scenarios, as well as generalizations in which Bob is allowed to have classical or quantum inputs and outputs (i.e., channel, Bob-with-input, and measurement-device-independent EPR scenarios). As our main technical contribution, we show that resource conversion under LOSR operations can be evaluated with a single instance of a semidefinite program, making the problem numerically tractable. Moreover, we derive new EPR resource monotones and study the structure of the pre-order of assemblages. We study conversions between both quantum and post-quantum resources. The most significant conceptual advantage of our LOSR approach is that it unifies the study of nonclassicality of assemblages with the study of nonclassicality of arbitrary processes in common-cause (e.g., Bell) scenarios.
- Juan Diego Arias Espinoza (Institute of Theoretical Physics, University of Amsterdam)
- "Information Scrambling and the Correspondence of Entanglement- and Operator Dynamics in Systems with Nonlocal Interactions"
Abstract How fast quantum information scrambles such that it becomes inaccessible by local probes turns out to be central to various fields. Motivated by recent works on spin systems with nonlocal interactions, we study information scrambling in different variants of the Ising model. Our work reveals that nonlocal interactions can induce operator dynamics not precisely captured by out-of-time-order correlators (OTOCs). In particular, the operator size exhibits a slowdown in systems with generic powerlaw interactions despite a highly nonlinear lightcone. A recently proposed microscopic model for fast scrambling does not show this slowdown, which uncovers a distinct analogy between a local operator under unitary evolution and the entanglement entropy following a quantum quench. Our work gives new insights on scrambling properties of systems in reach of current quantum simulation platforms and complements results on possibly observing features of quantum gravity in the laboratory.
- Gonzalo Alfredo Carvacho Vera (Università degli studi di Roma "La Sapienza")
- "Daylight entanglement-based quantum key distribution with a quantum dot source"
Abstract Entanglement-based quantum key distribution can enable secure communication in trusted node-free networks and over long distances. Although implementations exist both in fiber and in free space, the latter approach is often considered challenging due to environmental factors. Here, we implement a quantum communication protocol during daytime for the first time using a quantum dot source. This technology presents advantages in terms of narrower spectral bandwidth -- beneficial for filtering out sunlight -- and negligible multiphoton emission at peak brightness. We demonstrate continuous operation over the course of three and a half days, across an urban 270-m-long free-space optical link, under different light and weather conditions.
- Michele Dall'Arno (Department of Computer Science, Toyohashi University of Technology)
- "Quantum Guesswork: a combinatorial instance of quantum hypothesis testing"
Abstract We consider a game-theoretical scenario involving two parties, say Alice and Bob. At each round, Alice chooses a quantum state from a given ensemble, known to both parties, and sends it to Bob. Bob is allowed to perform any quantum operation on the state and to query Alice multiple times, one state at a time, until he correctly guesses the state. The game is repeated many times, and Bob's aim is to minimize the average number of queries needed. This problem, known as quantum guesswork, can be reframed as an instance of quantum hypothesis testing, and has therefore long been conjectured not to admit analytical solutions except for the cases in which the hypothesis testing problem is solvable, that is, for binary and symmetric ensembles. Here, we disprove such a belief by deriving conditions under which the guesswork problem can be recast as a combinatorial problem, that is, an optimization over a finite set, and therefore can be solved analytically by exhaustive search. We further show that such conditions are verified by any qubit ensemble, thus conclusively settling the problem in dimension two, and we show that in that case the guesswork is equivalent to a combinatorial problem known as quadratic assignment problem (QAP). Finally, we introduce the (infinite) class of so-called benevolent qubit ensembles, which includes symmetric, informationally complete (SIC) and mutually unbiased basis (MUBs) ensembles, and we explicitly solve the corresponding QAP for such a class.
- Rathindra Nath Das (Julius-Maximilians-Universität Würzburg)
- "Exploring Krylov State Complexity and Quantum Chaos in Pseudo-Integrable Quantum Billiards"
Abstract In light of recent advancements made towards quantifying quantum chaos in dynamical systems, and motivated by the search for viable definitions of complexity in quantum field theory and holography, we revisit pseudo-integrable quantum billiards and examine the recently proposed measure of Krylov state complexity known as spread complexity. In particular, we investigate the growth of Krylov state complexity in the system of triangular billiard systems with both rational and irrational angles, which we take to be the boundary of two-dimensional infinite potential boxes. While classically, these billiards exhibit zero Lyapunov exponent, quantum mechanically they display exponential growth of out-of-time-order-correlations (OTOC) and Krylov complexity. We further investigate higher moments of Krylov state complexity as well as new universality classes among them. Normally, the level spacing statistics follow Gaussian orthogonal ensemble statistics, but deviations caused by scarring and superscarring mechanisms occur. We check the effect of these mechanisms on the growth of complexity and quantum chaos in such billiards in general. This work has future directions of using new quantum chaos quantifiers to establish a quantum mechanical ergodic hierarchy, and may point towards new holography duals of complexity.
- Thiago L. M. Guedes (Forschungszentrum Jülich)
- "Measurement-free local quantum error correction in 1D systems"
Abstract Quantum computers, the apex devices for entanglement manipulation, should be a game-changer in the study of complex problems, ranging from condensed matter to quantum gravity. The pursuit of such systems, however, has faced serious challenges due to quantum errors. On the one hand, encoding logical quantum states into many-body ensembles of qubits/qudits constrains the performances of active error-correction protocols due to the need for observer-assisted collection of syndromes (whose measurement times scale with the system size). On the other hand, passive error correcting protocols, although free from measurements, often show lower performances compared to active counterparts. It is unavoidable to infer that an active error-correction protocol independent from observers and whose correction times do not scale with the system size (i.e., local) would pave the way to the achievement of optimal performances, but current error-correcting approaches have yet to fulfil all those criteria, and to date it has remained unclear whether this is possible at all. We propose a local and syndrome/observer-free mechanism for active error correction in 1D systems. Furthermore, we study the decay time of logical states of varied physical sizes under several levels of noise, showing under which conditions our protocol can outperform the repetition code. This approach should pioneer the development of faster and fully automated error-correcting techniques, as well as quantum simulations in future quantum computers.
- Nicolas Medina Sanchez (University of Vienna)
- "Information-theoretic foundations of Quantum statistics"
Abstract One of the main consequences of the indistinguishability of particles in quantum theory is the existence of only two types of particles, bosons and fermions. They are determined by the exchange symmetry of the corresponding multiparticle wave functions. The symmetrization postulate states that those wave functions are symmetric under exchange for bosons and antisymmetric for the fermionic case. However, the operational meaning of the exchange symmetry is not clear, given that exchanging identical particles among a specific type of degrees of freedom is naturally not well-defined as a physical dynamical operation given the informational impossibility of labeling . A specific case arises when these degrees of freedom are understood as positions in physical space. Then, the exchange symmetry can be simulated by adiabatic displacement of particles. It is known that in this scenario is possible to proof the symmetrization postulate when the displacements occur in configuration spaces of dimension greater or equal than 3 . Unfortunately, the reasoning of that proof requires coupling quantum theory with the geometry of the configuration space, an object that is not described by quantum theory, even though we know that the existence of bosons and fermions is a purely quantum phenomenom that in principle should not require adding elements exterior to what quantum mechanics can describe. In this work we study an approach to the symmetrization postulate from an operational point of view. Assuming only the validity of quantum theory and an interpretation of locality among the degrees of freedom of interest, we can *almost* reproduce the Fock space structure for quantum particles, getting in general two broad families of particles: bosonic-like and fermionic-like. These families contain new types of statistics consistent with quantum theory, apart from standard bosons and fermions, where the difference consists on an intrinsic degeneracy controlled by a discrete parameter. These new statistics are different than parastatistics  and can be used to treat problems in particle theory, cosmology and condensed matter physics that will be briefly discussed additionally to give a novel perspective about the origin of bosons and fermions.  P. Goyal. Informational Approach to Identical Particles in Quantum Theory, Jun 2014  J. M. Leinaas and J. Myrheim. On the theory of identical particles, Jan 1977  H.S. Green. A generalized method of field quantization, Phys. Rev. 90, 270–273 (1953)
- Nicola Pranzini (University of Helsinki)
- "Born rule extension for non-replicable systems and its consequences for Unruh-DeWitt detectors"
Abstract The Born rule describes the probability of obtaining an outcome when measuring an observable of a quantum system. As it can only be tested by measuring many copies of the system under consideration, it cannot hold strictly for non-replicable systems. For these systems, we give a procedure to predict the future statistics of measurement outcomes through Repeated Measurements (RM). We prove that if the statistics of the results acquired via RM is sufficiently similar to that obtained by the Born rule, the latter can be used effectively. We apply our framework to a repeatedly measured Unruh-DeWitt detector interacting with a massless scalar quantum field, which is an example of a system (detector) interacting with an uncontrollable environment (field) for which using RM is necessary. Analysing what an observer learns from the RM outcomes, we find a regime where history-dependent RM probabilities are close to the Born ones. Consequently, the latter can be used for all practical purposes. Finally, we study numerically inertial and accelerated detectors showing that an observer can see the Unruh effect via RM.
- Maria Quadeer (Nanyang Technological University, Singapore)
- "Random and pretty-good measurements for Bayesian state estimation"
Abstract We study Haar random orthonormal bases and Pretty-good measurements as measurement choices for Bayesian state estimation, and wish to obtain comparisons between single-copy Bayesian updates' algorithm for both of these measurement settings.
- Gonçalo Quinta (Institute of Telecommunications)
- "The Quantum Information of Virtual Particles"
Abstract We show that virtual particles, despite being unobservable, can be described by quantum operators which can be interpreted under certain conditions as valid quantum states with interesting connections to quantum information. For virtual fermions, we prove that such states can be regarded as 2-qubit thermal states and study their entanglement. For spin-1 virtual bosons and virtual pairs of fermions, we find them to be associated to 4-qubit operators containing all the details of the interactions. Finally, we study how renormalization affects these results. These findings represent new connections between quantum field theory, quantum information and quantum thermodynamics.
- Sarah Racz (University of Texas at Austin)
- "Scrambling in quantum cellular automata"
Abstract Scrambling is the delocalization of quantum information over a many-body system and underlies all quantum-chaotic dynamics. We employ discrete quantum cellular automata as classically simulable toy models of scrambling. We observe that these automata break ergodicity, i.e. they exhibit quantum scarring. We also find that the time-scale of scrambling rises with the local Hilbert-space dimension and obeys a specific combinatorial pattern. We then show that scarring is mostly suppressed in a semiclassical limit, demonstrating that semiclassical-chaotic systems are more ergodic.
- Tamás Vértesi (Institute for Nuclear Research)
- "Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant"
Abstract We address the problem of testing the quantumness of two-dimensional systems in the prepare-and-measure (PM) scenario, using a large number of preparations and a large number of measurement settings, with binary outcome measurements. In this scenario, we introduce constants, which we relate to the Grothendieck constant of order 3. We relate them to the white noise resistance of the prepared qubits and to the critical detection efficiency of the measurements performed. Large-scale numerical tools are used to bound the constants. This allows us to obtain new bounds on the minimum detection efficiency that a setup with 70 preparations and 70 measurement settings can tolerate.
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