Session M35: General Quantum Information I

Hierarchical graph states of k-uniform and absolutely maximally entangled states

It is important to characterize the entanglement properties of multipartite quantum states such as graph states, k-uniform, and Absolutely-Maximally-Entangled (AME) states. By merging these concepts we provide a remarkable relationship between geometry of graph states and entanglement of the corresponding states.

The k-uniform states are a particular type of highly entangled states, all of their reductions to k parties are maximally-mixed. A special case of this set are AME states that are maximally entangled along any splitting of parties into two groups. Moreover, the graph states are another set of well-entangled quantum states defined based on a graph, are also a class of stabilizer states.

We present a hierarchical procedure that leads us to study the geometric structure of k-uniform and AME states in the graph states representation. First, we introduce the most generalized method of constructing k-uniform and AME states from classical-error-correcting codes. Next, we introduce hierarchical graph states that construct the highly entangled states by iterating a certain geometric structure in graph state representation. We also show at each level of iteration the states that are all k-uniform cannot be converted into each other by SLOCC (stochastic local operations and classical communication).   

Quantum Information Processing with Finite-State Information Transducers

A quantum information source with a finite-state memory emits sequences of qudits that can be classically-correlated or entangled. These sequences are characterized by properties such as the von Neumann entropy rate and quantum excess entropy, calculated via the convergence of qudit block entropy to its asymptotic form. These quantities also serve as bounds on the classical information properties of observed sequences when using fixed-basis measurements. We show that qudit sequences serve as information reservoirs for quantum transducers that perform information-processing tasks and determine associated thermodynamic costs for operations such as erasure and synchronizing to the internal state of a given source via an adaptive measurement protocol.   

Quantum non-Markovianity and information back-flow in quantum teleportation

Quantum non-Markovianity (QNM) is a phenomenon associated to the information back-flow from the environment to the dynamical system, i.e., dynamical systems evolving through quantum channels with memory effects. In this work, we establish a connection between QNM and the protocol of quantum teleportation (QT). In particular, we consider the quantum computation-based QT of discrete-variable states [Brassard et al., Phys. D 120, 43 (1998)] and the all-optical QT of continuous-variable states [Ralph, Opt. Lett. 24, 348 (1999)] to show how information from the input state (system) moves to the environment and subsequently returns back to create the output state (which is ideally identical to the input state). Given that in QT protocols entanglement is utilized as a resource, a connection between entanglement and QNM is also drawn. Finally, the interesting role that QNM plays in quantum information protocols is discussed, given that QT protocols form the basis of various tasks in quantum communication and computation.   

Memory Structure in Measured Stochastic Processes of Quantum States

A time series of qubits, when measured by a classical observer, generically result in highly complex observed classical time series. The measurement can both increase or decrease the inherent randomness of the observed classical stochastic process with respect to the underlying stochastic process of qubits. Even when the underlying stochastic process of qubits can be predicted with a finite memory resources, the act of measuring it will generically result in a classical stochastic process that requires infinite memory resources to predict. We discuss the causes for this divergence in memory requirements and present a method to quantify the rate of this divergence, the statistical complexity dimension of the measured process. This represents a quantifier for the structure of the measured classical process, and smoothly varies with the choice of measurement.   

The grasshopper problem

A grasshopper lands at a random point on a planar lawn of area one. It then makes one jump of fixed distance d in a random direction. What shape should the lawn be to maximize the chance that the grasshopper remains on the lawn after jumping? This easily stated yet hard to solve mathematical problem has intriguing connections to quantum information and statistical physics. A generalized version on the sphere provides insight into a new class of Bell inequalities. In this setup two parties measure spins about randomly chosen axes and obtain correlations for pairs of axes separated by a fixed angle. A discrete version can be modeled by a spin system, representing a new class of statistical models with fixed-range interactions, where the range d can be large. We show that, perhaps surprisingly, there is no d > 0 for which a disc shaped lawn is optimal. If the jump distance is smaller than the radius of the unit disc, the optimal lawn resembles a cogwheel, with transitions to more complex, disconnected shapes at larger d. We will discuss several classes of optimal lawn shapes on the plane and on the sphere with focus on their connection to Bell inequalities that involve random measurement choices.   

Exploring the practicability of quantum linear solvers for QCFD simulations.

Quantum computing (QC) as we know today, has begun to proliferate its presence in many scientific disciplines. With every advancement in quantum algorithms and error correction, QC challenges its classical counterpart. However, for QC to emerge as an indispensable tool for practical applications, the exigency is not just for novel protocols that process quantum information but also for extracting it wisely in classical formats that cater to the solution of practical problems. Here we draw attention to potential methods of conducting fluid mechanics research using QC, which we call Quantum Computation of Fluid Dynamics (QCFD). In this light, we evaluate an end-to-end performance demonstration of modified Harrow-Hassidim-Lloyd (HHL) type algorithms to study problems such as the flow in a pipe and the 1D Burgers equation. For this, we also introduce here a new, high performance QC simulator, specific to fluid-dynamics, which we call "QuOn", designed to simulate most standard quantum algorithms. We shall present results using both QuOn and the IBMQ - Qiskit tools.   

Provable quantum computational advantage with the cyclic cluster state

We propose two Bell-type nonlocal games that can be used to prove quantum computational advantage in a hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a subset of its Pauli stabilizers on a quantum computer is compared to that of classical Boolean circuits with the same gate connectivity. Using a circuit-based trapped-ion quantum computer, we prepare and measure a six-qubit cyclic cluster state with an overall fidelity of 60.6% and 66.4%, before and after correcting measurement-readout errors, respectively. Our experimental results indicate that while this fidelity readily passes conventional (or depth-0) Bell bounds for local hidden variable models, it is on the cusp of demonstrating quantum advantage against depth-1 classical circuits. Our games offer a practical and scalable set of quantitative benchmarks for quantum computers in the pre-fault-tolerant regime as the number of qubits available increases.   

The quantum condition space and a classification of quantum circuits with qubit functional configurations

In this work we first propose to exploit the fundamental properties of quantum physics to evaluate the probability of events with projection measurements. Next, to study what events can be specified by quantum methods, we introduce the concept of the condition space, which is found to be the dual space of the classical outcome space of bit strings. Just like the classical outcome space generates the quantum state space, the condition space generates the quantum condition space that offers a novel perspective of understanding quantum states with the duality picture. In addition, the quantum conditions have physical meanings and realizations of their own and thus may be studied for purposes beyond the original motivation of characterizing events for probability evaluation. An immediate application of the theory is to use the relation between the condition space and quantum circuits to systematically study how state vector entries are collectively modified by quantum gates: this leads to a classification of quantum circuits into types defined by qubit functional configurations.   

Long-time signatures of non-Markovianity in open quantum systems

Memory effects in open systems typically manifest on short timescales, as their contribution is overwhelmed by thermal dissipation over long times. Furthermore, standard metrics quantifying such non-Markovian evolution are tomographic in nature, making them impractical for experimental observation [1]. Given their versatility and ease of implementation, spectroscopic measurements present an attractive alternative to characterize such dynamics. In this talk, I will first discuss an approach based on a time-dependent master equation and apply it to the archetypal qubit-resonator system. We obtain an analytical expression for the qubit emission spectrum that captures persistent non-Markovian features in the steady state [2]. I will then introduce a new approach which allows such analysis to be done directly in the frequency domain, bypassing the cumbersome calculation of two-time correlators. Our results highlight the parameter regimes where deviations from Markovianity are most pronounced and how they may be tuned via the choice of interaction and resonator dynamics.   

Genuine Multipartite Network Nonlocality in Stabilizer Networks

Quantum entanglement shared across a multi-node network can be used to generate complicated forms of correlations through local measurements at each node. Some forms of nonlocality exhibited in these configurations are unique to networks and cannot be generated otherwise. We define genuine network k-nonlocality as correlations that can be generated using just (k-1)-partite sources of shared entanglement, but cannot be simulated with classical states. While it is known that genuine network nonlocality (GNN) can emerge in triangle networks, the necessary and sufficient conditions to obtain such correlations remain unspecified. In this work, we show that GNN fails to emerge in multi-qubit triangle networks with no inputs when the networks are limited to stabilizer operations, i.e. state preparations/measurements in the computational basis along with Clifford gates. We also present numerical evidence that GNN does not emerge in triangle networks with local input choices of dichotomic stabilizer measurements and independent EPR states shared between pairs of nodes. Hence, just as non-stabilizer operations are needed to achieve universal quantum computation, we show that non-stabilizer operations are also needed to achieve genuine network nonlocality in multi-qubit triangle networks.   

Tensor Networks for Plasma Dynamics

Matrix product states (MPS) are widely used as a computational tool in the quantum physics community. However, it is believed that MPS can also potentially exponentially reduce the cost of numerical simulations of classical systems. Indeed, a few works have already used MPS or equivalent methods to solve multi-dimensional systems described by partial differential equations, such as those of fluids or large molecules, and reported significant computational savings. Here, we investigate the use of MPS to simulate a first-principles, kinetic description of plasmas, based on the (electrostatic or electromagnetic) Vlasov equation. Furthermore, we attempt to provide some additional insight on the MPS representation of this system and when the representation is efficient, which in turn can identify how quantum computers may be able assist these numerical simulations.   

Quantification and manipulation of magic channels

In our work, we extend the resource theory of magic from the state domain to the channel domain by introducing and characterizing the set of superchannels that completely preserve the set of completely stabilizer preserving operations. We then extend the generalized robustness of magic and the min relative entropy of magic defined for states to the channel case and show that they bound the single-shot dynamical magic cost and distillation. Lastly, we give a classical simulation algorithm for simulating quantum circuits whose runtime is related to the generalized robustness of magic for channels. Our algorithm depends on some pre-defined precision, and if there is no bound on the desired precision then it achieves a constant runtime.   

Bloch sphere representation of geodesics and null phase curves of higher-dimensional state space

The geometrical representation of the state space of an n-level quantum system is essential in characterizing the system. One possible way to achieve that is to understand the structure of geodesics and null phase curves in the state space. The null phase curves are the paths along which there is no geometric phase accumulation, and geodesics give the shortest distance between any given two points and are special cases of null phase curves. The state-space for the 2-level system is the (Bloch) sphere, and geodesics are the great circles. However, finding geodesics is not trivial in higher-level systems. Here, in this work, we propose a consistent way to construct geodesics and a class of null phase curves in d-level systems using Majorana star representation which maps a pure quantum state of an n-level system to the symmetric subspace of n-1 2-level systems. This work can be instrumental in studying the topological phases in the systems with three or more band structures.   

Universal limitation of quantum information recovery: symmetry versus coherence

Quantum information is scrambled via chaotic time evolution in many-body systems. The recovery of initial information embedded locally in the system from the scrambled quantum state is a fundamental concern in many contexts. From a dynamical perspective, information recovery can measure dynamical instability in quantum chaos, fault-tolerant quantum computing, and the black hole information paradox. Here, we establish fundamental limitations on the information recovery that hold whenever the scrambling dynamics satisfy an arbitrary Lie group symmetry. We show universal relations between information recovery, symmetry, and quantum coherence, which apply to many physical situations. The relations predict that the behaviour of the Hayden-Preskill black hole model changes qualitatively under the assumption of the energy conservation law. Consequently, we can rigorously prove that under the energy conservation law, quantum black holes do not return an unignorable part of information until the black holes completely evaporate. Furthermore, the relations provide a unified view of the symmetry restrictions on quantum information processing, such as the approximate Eastin-Knill theorem and the Wigner-Araki-Yanase theorem for unitary gates.   

Optimal clock speed of qubit gate operations on open quantum systems

We report that an optimal speed of gate operations yields maximum fidelity for qubits in open quantum systems. We show that the fast qubit gate operations and achieving high fidelity are not two independent processes in the presence of drive-induced dissipation (DID). The speed of qubit gates cannot in principle be arbitrarily fast without compromising the fidelity of the gate operations. The fidelity is found to be a function of the DID and the relaxation terms arising from the qubit-environment coupling; as a result, it behaves nonmonotonically with the drive amplitude. We show that the competition between these two sources of decoherence, naturally leads to an optimum value of the drive amplitude. The fidelity of the qubit gate becomes maximum at this optimum value of the drive amplitude. To incorporate DID in the analysis, we used a previously reported fluctuation-regulated quantum master equation. The existence of the optimum drive amplitude implies that the qubit gate operations would have an optimal clock speed. For efficient implementation of quantum computation, precise knowledge of this clock speed is essential. In the presentation, we would also emphasize on the generic nature of the results achieved for the gate operations on single as well as multiple qubit systems.