arXiv subjects

Zoltán Zimborás

Publications and source records attributed to Zoltán Zimborás.

At least 73 records · Page 4Linked to original sources

arXiv2021

Photonic Quantum Policy Learning in OpenAI Gym

In recent years, near-term noisy intermediate scale quantum (NISQ) computing devices have become available. One of the most promising application areas to leverage such NISQ quantum computer prototypes is quantum machine learning. While quantum neural networks are widely studied for supervised learning, quantum reinforcement learning is still just an emerging field of this area. To solve a classical continuous control problem, we use a continuous-variable quantum machine learning approach. We introduce proximal policy optimization for photonic variational quantum agents and also study the effect of the data re-uploading. We present performance assessment via empirical study using Strawberry Fields, a photonic simulator Fock backend and a hybrid training framework connected to an OpenAI Gym environment and TensorFlow. For the restricted CartPole problem, the two variations of the photonic policy learning achieve comparable performance levels and a faster convergence than the baseline classical neural network of same number of trainable parameters.

quant-ph↗

arXiv2021

Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm

We introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using Diagonal Detector Overlapping Tomography -- a generalization of the recently introduced Quantum Overlapping Tomography to the problem of reconstruction of readout noise with restricted locality. The procedure allows to characterize $k$-local measurement cross-talk on $N$-qubit device using $O(k2^klog(N))$ circuits containing random combinations of X and identity gates. We perform experiments on 15 (23) qubits using IBM's (Rigetti's) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor $>22$ ($>5.5$) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.

quant-ph↗

arXiv2021

Concept of orbital entanglement and correlation in quantum chemistry

A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements of numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement previously seen. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.

quant-ph↗

arXiv2020

Central charges of aperiodic holographic tensor network models

Central to the AdS/CFT correspondence is a precise relationship between the curvature of an anti-de Sitter (AdS) spacetime and the central charge of the dual conformal field theory (CFT) on its boundary. Our work shows that such a relationship can also be established for tensor network models of AdS/CFT based on regular bulk geometries, leading to an analytical form of the maximal central charges exhibited by the boundary states. We identify a class of tensors based on Majorana dimer states that saturate these bounds in the large curvature limit, while also realizing perfect and block-perfect holographic quantum error correcting codes. Furthermore, the renormalization group description of the resulting model is shown to be analogous to the strong disorder renormalization group, thus giving the first example of an exact quantum error correcting code that gives rise to a well-understood critical system. These systems exhibit a large range of fractional central charges, tunable by the choice of bulk tiling. Our approach thus provides a precise physical interpretation of tensor network models on regular hyperbolic geometries and establishes quantitative connections to a wide range of existing models.

hep-th↗

arXiv2020

Quantum Distance to Uncontrollability and Quantum Speed Limits

Distance to Uncontrollability is a crucial concept in classical control theory. Here, we introduce Quantum Distance to Uncontrollability as a measure how close a universal quantum system is to a non-universal one. This allows us to provide a quantitative version of the Quantum Speed Limit, decomposing the bound into a geometric and dynamical component. We consider several physical examples including globally controlled solid state qubits and a cross-Kerr system, showing that the Quantum Distance to Uncontrollability provides a precise meaning to spectral crowding, weak interactions and other bottlenecks to universality. We suggest that this measure should be taken into consideration in the design of quantum technology.

quant-ph↗

arXiv2020

Space-efficient binary optimization for variational computing

In the era of Noisy Intermediate-Scale Quantum (NISQ) computers it is crucial to design quantum algorithms which do not require many qubits or deep circuits. Unfortunately, the most well-known quantum algorithms are too demanding to be run on currently available quantum devices. Moreover, even the state-of-the-art algorithms developed for the NISQ era often suffer from high space complexity requirements for particular problem classes. In this paper, we show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem (TSP), a paradigmatic optimization task, at the cost of having deeper variational circuits. While the focus is on this particular problem, we claim that the approach can be generalized for other problems where the standard bit-encoding is highly inefficient. Finally, we also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models. All the proposed encodings remain efficient to implement within the Quantum Approximate Optimization Algorithm framework.

quant-ph↗

arXiv2020

Quantum Optimization for the Graph Coloring Problem with Space-Efficient Embedding

Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient quantum optimization algorithm for the graph coloring problem. Our circuits are deeper than the ones of the standard approach. However, the number of required qubits is exponentially reduced in the number of colors. We present extensive numerical simulations demonstrating the performance of our approach. Furthermore, to explore currently available alternatives, we perform a study of random graph coloring on a quantum annealer to test the limiting factors of that approach, too.

quant-ph↗

arXiv2020

Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations

We study the scaling of logarithmic negativity between adjacent subsystems in critical fermion chains with various inhomogeneous modulations through numerically calculating its recently established lower and upper bounds. For random couplings, as well as for a relevant aperiodic modulation of the couplings, which induces an aperiodic singlet state, the bounds are found to increase logarithmically with the subsystem size, and both prefactors agree with the predicted values characterizing the corresponding asymptotic singlet state. For the marginal Fibonacci modulation, the prefactors in front of the logarithm are different for the lower and the upper bound, and vary smoothly with the strength of the modulation. In the delocalized phase of the quasi-periodic Harper model, the scaling of the bounds of the logarithmic negativity as well as that of the entanglement entropy are compatible with the logarithmic scaling of the homogeneous chain. At the localization transition, the scaling of the above entanglement characteristics holds to be logarithmic, but the prefactors are significantly reduced compared to those of the translationally invariant case, roughly by the same factor.

cond-mat.dis-nn↗

arXiv2020

Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.

quant-ph↗

arXiv2020

Quantum phases of collective SU(3) spin systems with bipartite symmetry

We study a bipartite collective spin-$1$ model with exchange interaction between the spins. The bipartite nature of the model manifests itself by the spins being divided into two equal-sized subsystems; within each subsystem the spin-spin interactions are of the same strength, across the subsystems they are also equal, but the two coupling values within and across the subsystem are different. Such a set-up is inspired by recent experiments with ultracold atoms. Using the $\mathrm{SU}(3)$-symmetry of the exchange interaction and the permutation symmetry within the subsystems, we can employ representation theoretic methods to diagonalize the Hamiltonian of the system in the entire parameter space of the two coupling-strengths. These techniques then allow us to explicitly construct and explore the ground-state phase diagram. The phase diagram turns out to be rich containing both gapped and gapless phases. An interesting observation is that one of the five phases features a strong bipartite symmetry breaking, meaning that the two subsystems in the ground states are in different $\mathrm{SU}(3)$ representations.

cond-mat.stat-mech↗

arXiv2019

On the Universality of the Quantum Approximate Optimization Algorithm

The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in alternation with the goal being to approach the ground state of the cost Hamiltonian. Recently, it has been suggested that one might use such a set-up as a parametric quantum circuit with possibly some other goal than reaching ground states. From this perspective, a recent work [S. Lloyd, arXiv:1812.11075] argued that for one-dimensional local cost Hamiltonians, composed of nearest neighbor ZZ terms, this set-up is quantum computationally universal, i.e., all unitaries can be reached up to arbitrary precision. In the present paper, we give the complete proof of this statement and the precise conditions under which such a one-dimensional QAOA might be considered universal. We further generalize this type of universality for certain cost Hamiltonians with ZZ and ZZZ terms arranged according to the adjacency structure of certain graphs and hypergraphs.

quant-ph↗

arXiv2019

A communication solution for portable detectors of the Cosmic Ray Extremely Distributed Observatory

The search for Cosmic-Ray Ensembles (CRE), groups of correlated cosmic rays that might be distributed over very large areas, even of the size of the planet, requires a globally spread and dense network of detectors, as proposed by the Cosmic-Ray Extremely Distributed Observatory (CREDO) Collaboration. This proposal motivates an effort towards exploring the potential of using even very much diversified detection technologies within one system, with detection units located even in hard-to-reach places, where, nevertheless, the sensors could work independently - without human intervention. For these reasons we have developed a dedicated communication solution enabling the connection of many different types of detectors, in a range of environments. The proposed data transmission system uses radio waves as an information carrier on the 169MHz frequency band in a contrast to the typical commercially used frequencies in a IoT systems (868MHz). The connectivity within the system is based on the star topology, which ensures the least energy consumption. The solution is now being prepared to being implemented using the prototype detection system based on the CosmicWatch open hardware design: a portable, pocket size, and economy particle detector using the scintillation technique. Our prototype detector is equipped with a dedicated software that integrates it with the already operational CREDO server system.

astro-ph.IM↗

arXiv2019

Sublogarithmic behaviour of the entanglement entropy in fermionic chains

In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the Rényi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szegő Theorem or the Fisher-Hartwig conjecture.

cond-mat.stat-mech↗

arXiv2019

Cosmic ray ensembles from ultra-high energy photons propagating in the galactic and intergalactic space

Propagation of ultra-high energy photons in the galactic and intergalactic space gives rise to cascades comprising thousands of photons. Using Monte Carlo simulations, we investigate the development of such cascades in the solar magnetosphere, and find that the photons in the cascades are distributed over hundreds of kilometers as they arrive at the top of the Earth's atmosphere. We also perform similar study for cascades starting as far as 10 Mpc away from us using relevant magnetic field models. A few photons correlated in time are expected to arrive at the Earth from the latter type of cascade. We present our simulation results and discuss the prospects for detection of these cascades with the Cosmic-Ray Extremely Distributed Observatory.

astro-ph.HE↗

arXiv2019

Short time behavior of continuous time quantum walks on graphs

Dynamical evolution of systems with sparse Hamiltonians can always be recognized as continuous time quantum walks (CTQWs) on graphs. In this paper, we analyze the short time asymptotics of CTQWs. In recent studies, it was shown that for the classical diffusion process the short time asymptotics of the transition probabilities follows power laws whose exponents are given by the usual combinatorial distances of the nodes. Inspired by this result, we perform a similar analysis for CTQWs both in closed and open systems, including time-dependent couplings. For time-reversal symmetric coherent quantum evolutions, the short time asymptotics of the transition probabilities is completely determined by the topology of the underlying graph analogously to the classical case, but with a doubled power-law exponent. Moreover, this result is robust against the introduction of on-site potential terms. However, we show that time-reversal symmetry breaking terms and non-coherent effects can significantly alter the short time asymptotics. The analytical formulas are checked against numerics, and excellent agreement is found. Furthermore, we discuss in detail the relevance of our results for quantum evolutions on particular network topologies.

quant-ph↗

arXiv2019

Approximate recovery with locality and symmetry constraints

Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable operations. Moreover, these constraints combine non-trivially with the potential requirement that operations be performed locally. The combination of symmetry and locality constraints influence our ability to perform quantum error correction in two counterposing ways. On the one hand, they constrain the effect of noise, limiting its possible action over the quantum system. On the other hand, these constraints also limit our ability to perform quantum error correction, or generally to reverse the effect of a noisy quantum channel. We analyze the conditions that local channels should satisfy in the constrained setting, and characterize the resulting optimal decoding fidelity. In order to achieve this result, we introduce a concept of local complementary channel, and prove a new local information-disturbance tradeoff.

quant-ph↗

arXiv2018

Generalized quantum Zeno dynamics and ergodic means

We prove the existence of uniform limits for certain sequences of products of contractions and elements of a family of uniformly continuous propagators acting on a Hilbert or a Banach space. From the point of view of Quantum Physics, the considered sequences can represent the evolution of a system whose dynamics, described by a continuous propagator, is disturbed by a sequence of generic quantum operations (e.g., projective measurements or unitary pulses). This includes and also generalizes the so-called quantum Zeno dynamics. The time-evolution obtained from the limits of the considered sequences are described by propagators generated by ergodic means. The notion of such ergodic means is generalized in this paper to also include propagators of time-dependent generators, and thus our results can be used to develop new forms of active decoherence suppression. In a similar way, we also consider the effective time-evolution obtained from adding to the possibly time-dependent generator of the original propagator a generator of a uniformly continuous contraction semi-group with asymptotically increasing weight in the sum. By proving a generalized adiabatic theorem, it is shown that also for this set-up the resulting time-evolution is governed by a suitable ergodic mean.

math-ph↗

arXiv2018

Entanglement Entropy of Disordered Quantum Wire Junctions

We consider different disordered lattice models composed of $M$ linear chains glued together in a star-like manner, and study the scaling of the entanglement between one arm and the rest of the system using a numerical strong-disorder renormalization group method. For all studied models, the random transverse-field Ising model (RTIM), the random XX spin model, and the free-fermion model with random nearest-neighbor hopping terms, the average entanglement entropy is found to increase with the length $L$ of the arms according to the form $S(L)=\frac{c_{\rm eff}}{6}\ln L+const$. For the RTIM and the XX model, the effective central charge $c_{\rm eff}$ is universal with respect to the details of junction, and only depends on the number $M$ of arms. Interestingly, for the RTIM $c_{\rm eff}$ decreases with $M$, whereas for the XX model it increases. For the free-fermion model, $c_{\rm eff}$ depends also on the details of the junction, which is related to the sublattice symmetry of the model. In this case, both increasing and decreasing tendency with $M$ can be realized with appropriate junction geometries.

cond-mat.stat-mech↗