Quantum walk (QW) on a disordered lattice leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting qubits still remains pending. The major challenge in simulating QW with superconducting qubits emerges from the fact that on-chip superconducting qubits cannot hop between two adjacent lattice sites. Here we overcome this barrier and develop a gate-based scheme to realize the discrete time QW by placing a pair of qubits on each site of a one-dimensional (1D) lattice and treating an excitation as a walker. It is also shown that various lattice disorders can be introduced and fully controlled by tuning the qubit parameters in our quantum walk circuit. We observe a distinct signature of transition from the ballistic regime to a localized QW with an increasing strength of disorder. Finally, an eight-qubit experiment is proposed where the signatures of such localized and delocalized regimes can be detected with existing superconducting technology. Our proposal opens up the possibility of exploring various quantum transport processes with promising superconducting qubits.
Quantum walk (QW) on a disordered lattice leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting qubits still remains pending. The major challenge in simulating QW with superconducting qubits emerges from the fact that on-chip superconducting qubits cannot hop between two adjacent lattice sites. Here we overcome this barrier and develop a gate-based scheme to realize the discrete time QW by placing a pair of qubits on each site of a one-dimensional (1D) lattice and treating an excitation as a walker. It is also shown that various lattice disorders can be introduced and fully controlled by tuning the qubit parameters in our quantum walk circuit. We observe a distinct signature of transition from the ballistic regime to a localized QW with an increasing strength of disorder. Finally, an eight-qubit experiment is proposed where the signatures of such localized and delocalized regimes can be detected with existing superconducting technology. Our proposal opens up the possibility of exploring various quantum transport processes with promising superconducting qubits.
Abstract Particle transport and localization phenomena in condensed-matter systems can be modeled using a tight-binding lattice Hamiltonian. The ideal experimental emulation of such a model utilizes simultaneous, high-fidelity control and readout of each lattice site in a highly coherent quantum system. Here, we experimentally study quantum transport in one-dimensional and two-dimensional tight-binding lattices, emulated by a fully controllable 3 × 3 array of superconducting qubits. We probe the propagation of entanglement throughout the lattice and extract the degree of localization in the Anderson and Wannier-Stark regimes in the presence of site-tunable disorder strengths and gradients. Our results are in quantitative agreement with numerical simulations and match theoretical predictions based on the tight-binding model. The demonstrated level of experimental control and accuracy in extracting the system observables of interest will enable the exploration of larger, interacting lattices where numerical simulations become intractable.
The interplay between disorder and topology triggers interesting effects for the propagation of quantum particles in low-dimensional network structures. For instance, the occurrence of Anderson localization, a commonly observed effect in a quantum network with static disorder, can be suppressed by introducing topology-a phenomenon dubbed as topological Anderson localization transition [1] . In one-dimensional systems, for example, disorder induces localization on a short length scale while topology counters that through long-range correlations, yielding divergent correlation length and extremely slow spreading at quantum criticality. However, its experimental demonstration still remains an outstanding challenge as that would require, in contrast to Anderson localization transition, addi¬tional control over internal degrees of freedom, which is hard to implement, for instance, in cold-atom systems [2] . Quantum walks (QWs), a quantum analog of random walks, comprising quantum coin toss and conditioned step operations are already established for studying quantum transport phenomena, such as, disorder and topology [5] . Based on our theoretical proposal [3] , here, we provide an experimental route using time-multiplexed quantum walk [4] for evidencing the targeted phenomenon.
The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time quantum walker which exhibits disorder-free localization. The quantum walker moves on a one-dimensional lattice and interacts with on-site spins by coherently rotating them around a given axis at each step. Since the spins do not have dynamics of their own, the system poses the local spin components along the rotation axis as an extensive number of conserved moments. When the interaction is weak, the spread of the walker shows subdiffusive behavior having downscaled ballistic tails in the evolving probability distribution at intermediate timescales. However, as the interaction gets stronger the walker gets completely localized in total absence of disorder in both lattice and initial state. Using a matrix-product-state ansatz, we investigate the relaxation and entanglement dynamics of the on-site spins due to their coupling with the quantum walker. Surprisingly, we find that, even in the delocalized regime, entanglement growth and relaxation occur slowly, unlike majority of the other models displaying a localization transition.
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.
Summary form only given. In 1958 P.W. Anderson predicted that the wave-function of a quantum particle can be localized in the presence of a static disordered potential [1]. This phenomenon arises from the destructive interference of waves propagating in static disordered media. As a consequence, in these conditions, particle and energy transport through a disordered medium are expected to be strongly suppressed and an initially localized wave packet does not spread out with time. In this work we experimentally study the localization properties of a pair of non-interacting particles obeying bosonic/fermionic statistics by simulating a one-dimensional QW of a two-photon polarization-entangled state in a disordered medium. Quantum walk is the quantum counterpart of classical random walk: a walker jumping between different sites of a lattice with a given probability. In the quantum case the walker is a quantum system, whose quantum properties affect the transport. When multi-particle walkers travel within the QW their bosonic or fermionic nature strongly affects the transport. Here we implement different quantum statistics by exploiting of the polarization-entangled bi-photon input state. The QW circuit has been experimentally realized by femtosecond laser writing which provides a perfect phase stability [2]. In particular, we realized an 8-step quantum walk circuit composed by an array of polarization independent beam splitters arranged in a cascade configuration of Mach-Zehnder (MZ) interferometers (see Fig.1a).
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.