We show that a quantum computer operating with a small number of qubits can simulate the dynamical localization of classical chaos in a system described by the quantum sawtooth map model. The dynamics of the system is computed efficiently up to a time $t\geq \ell$, and then the localization length $\ell$ can be obtained with accuracy $ν$ by means of order $1/ν^2$ computer runs, followed by coarse grained projective measurements on the computational basis. We also show that in the presence of static imperfections a reliable computation of the localization length is possible without error correction up to an imperfection threshold which drops polynomially with the number of qubits.
We show that, in a system with defects, two-particle states may experience destructive quantum interference, or antiresonance. It prevents an excitation localized on a defect from decaying even where the decay is allowed by energy conservation. The system studied is a qubit chain or an equivalent spin chain with an anisotropic ($XXZ$) exchange coupling in a magnetic field. The chain has a defect with an excess on-site energy. It corresponds to a qubit with the level spacing different from other qubits. We show that, because of the interaction between excitations, a single defect may lead to mu…
We study numerically the effects of measurements on dynamical localization in the kicked rotator model simulated on a quantum computer. Contrary to the previous studies, which showed that measurements induce a diffusive probability spreading, our results demonstrate that localization can be preserved for repeated single-qubit measurements. We detect a transition from a localized to a delocalized phase, depending on the system parameters and on the choice of the measured qubit.
Quantum computers are invaluable tools to explore the properties of complex quantum systems. We show that dynamical localization of the quantum sawtooth map, a highly sensitive quantum coherent phenomenon, can be simulated on actual, small-scale quantum processors. Our results demonstrate that quantum computing of dynamical localization may become a convenient tool for evaluating advances in quantum hardware performances.
Anderson localization is a consequence of coherent interference of multiple scattering events in the presence of disorder, which leads to an exponential suppression of the transmission. The decay of the transmission is typically probed at a given energy or frequency. Here we show that this decay affects the dynamics of a qubit coupled to the disordered system and we express the relaxation rate of the qubit in terms of the localization properties. Conversely, adding static disorder to a channel coupled to a qubit will reduce the decoherence rate of the qubit. Hence, when designing electrodes th…
We predict the existence of a novel interaction-induced spatial localization in a periodic array of qubits coupled to a waveguide. This localization can be described as a quantum analogue of a self-induced optical lattice between two indistinguishable photons, where one photon creates a standing wave that traps the other photon. The localization is caused by the interplay between on-site repulsion due to the photon blockade and the waveguide-mediated long-range coupling between the qubits.
A nanomagnet precessing in an external magnetic field can be treated as a source of narrow-bandwidth magnetic noise, that leaves characteristic fingerprints in decoherence of a nearby spin qubit undergoing dynamical decoupling. We show how, by measurements of two-qubit coherence, a noise sensor composed of qubit pair can be used to reconstruct the position of the nanomagnet. Such localization of noise source is possible with only two qubit probes, because the course of coherence decay under appropriately designed dynamical decoupling sequences contain information not only about noises experien…
We demonstrate that, in a many-particle system, particles can be strongly confined to their sites. The localization is obtained by constructing a sequence of on-site energies that efficiently suppresses resonant hopping. The time during which a many-particle state remains strongly localized in an infinite chain can exceed the reciprocal hopping frequency by $\agt 10^6$ already for a narrow energy bandwidth. The results show viability of quantum computers with time-independent qubit coupling.
Quantum walk (QW) in presence of lattice disorders 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 scheme to realize the discrete time QW by placing a pair of superconducting qubits on each site of a 1D lattice and treat…
We used the von Neumann entropy to study the single and many-particle on-site localizations of stationary states for an anisotropic Heisenberg spin-1/2 chain. With a constructed bounded sequence of on-site energies for single and many-particle systems we demonstrate that the von Neumann entropy approaches zero indicating strong on-site localizations for all states. On the contrary, random on-site energy sequence does not lead to strong on-site confinement of all states. Our numerical results indicate that the von Neumann entropy provides a new insight to analyze on-site localizations for these…
We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping between both nearest and remote sites. This sequence leads to quasi-exponential decay of the single-particle transition amplitude. It also leads to strong localization of stationary many-particle states in a finite-length chain. For an {\it infinite} chain, we instead study the time during which {\it all} many-particle states remain strongly localized. We show…
Random scattering of photons in disordered one-dimensional solids gives rise to an exponential suppression of transmission, which is known as Anderson localization. Here, we experimentally study Anderson localization in a superconducting waveguide quantum electrodynamics system comprising eight individually tunable qubits coupled to a photonic continuum of a waveguide. Employing the qubit frequency control, we artificially introduce frequency disorder to the system and observe an exponential suppression of the transmission coefficient in the vicinity of its subradiant dark modes. The localizat…
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localiz…
We show that photons in two tunnel-coupled microwave resonators each containing a single superconduct- ing qubit undergo a sharp non-equilibrium delocalization-localization (self-trapping) transition due to strong photon-qubit coupling. We find that dissipation favors the self-trapped regime and leads to the possibility of observing the transition as a function of time without tuning any parameter of the system. Furthermore, we find that self-trapping of photons in one of the resonators (spatial localization) forces the qubit in the opposite resonator to remain in its initial state (energetic …
One of the main challenges in building a quantum processor is to characterize the environmental noise. Noise characterization can be achieved by exploiting different techniques, such as randomization where several sequences of random quantum gates are applied to the qubit under test to derive statistical characteristics about the affecting noises. A scalable and robust algorithm able to benchmark the full set of Clifford gates using randomization techniques is called randomized benchmarking. In this study, we simulated randomized benchmarking protocols in a semiconducting all-electrical three-…
We have numerically simulated quantum tomography of single-qubit and two-qubit quantum gates with qubits represented by mesoscopic ensembles containing random numbers of atoms. Such ensembles of strongly interacting atoms in the regime of Rydberg blockade are known as Rydberg superatoms. The Stimulated Raman Adiabatic Passage (STIRAP) in the regime of Rydberg blockade is used for deterministic Rydberg excitation in the ensemble, required for storage of quantum information in the collective state of the atomic ensemble and implementation of two-qubit gates. The optimized shapes of the STIRAP pu…
Recurrent neurons, or "simulated" qubits, can store simultaneous true and false with probabilistic behaviors usually reserved for the qubits of quantum physics. Although possible to construct artificially, simulated qubits are intended to explain biological mysteries. It is shown below that they can simulate certain quantum computations and, although less potent than the qubits of quantum physics, they nevertheless are shown to significantly exceed the capabilities of classical deterministic circuits.
Is the most random pattern random? Maximizing localization in a two-dimensional lattice with engineered disorder
Albert-Ludwigs-Universität Freiburg（弗莱堡大学）；National Institute of Information and Communications Technology（信息通信研究机构）；Tokyo University of Science（东京科学大学）
We consider a qubit governed by a sequence of weak measurements, with the measurement strength modified in a time- and state-dependent manner. The resulting trajectory of the qubit in the phase space can be weakly controlled without any direct action on the qubit (control-free control), even only one fixed observable is measured. Here we show a possibility of a weak form of a stochastic ratchet, allowing to create an additional "force" without changing the corresponding effective average potential. Furthermore, if the weak measurement strength is significantly reduced in a way conditioned to s…
We introduce an open-source solver for the Lindblad master equation, based on matrix product states and matrix product operators. Using this solver we study the dynamics of tens of interacting qubits with different connectivities, focusing on a problem where an edge qubit is being continuously driven on resonance, which is a fundamental operation in quantum devices. Because of the driving, induced excitations propagate through the qubits until the system reaches a steady state due to the incoherent terms. We find that with alternating-frequency qubits whose interactions with their off-resonant…
We discuss how the observation of population localization effects in periodically driven systems can be used to quantify the presence of quantum coherence in interacting qubit arrays. Essential for our proposal is the fact that these localization effects persist beyond tight-binding Hamiltonian models. This result is of special practical relevance in those situations where direct system probing using tomographic schemes becomes infeasible beyond a very small number of qubits. As a proof of principle, we study analytically a Hamiltonian system consisting of a chain of superconducting flux qubit…
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A 72, 012331 (2005)]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For gen…
We propose a startling hybrid quantum architecture for simulating a localization-delocalization transition. The concept is based on an array of superconducting flux qubits which are coupled to a diamond crystal containing nitrogen-vacancy (NV) centers. The underlying description is a Jaynes-Cummings-lattice in the strong-coupling regime. However, in contrast to well-studied coupled cavity arrays the interaction between lattice sites is mediated here by the qubit rather than by the oscillator degrees of freedom. Nevertheless, we point out that a transition between a localized and a delocalized …
We use a Heisenberg spin-1/2 chain to investigate how chaos and localization may affect the entanglement of pairs of qubits. To measure how much entangled a pair is, we compute its concurrence, which is then analyzed in the delocalized/localized and in the chaotic/non-chaotic regimes. Our results indicate that chaos reduces entanglement and that entanglement decreases in the region of strong localization. In the transition region from a chaotic to a non-chaotic regime localization increases entanglement. We also show that entanglement is larger for strongly interacting qubits (nearest neighbor…
We investigate how arbitrary number of entangled qubits affects properties of quantum walk. We consider variance, positions with non-zero probability density and entropy as criteria to determine the optimal number of entangled qubits in quantum walk. We show that for a single walker in one-dimensional position space, walk with three entangled qubits show better efficiency in considered criteria comparing to the walks with other number of entangled qubits. We also confirm that increment in number of the entangled qubits results into significant drop in variance of probability density distributi…
We study the effects of localization on quantum state transfer in spin chains. We show how to use quantum error correction and multiple parallel spin chains to send a qubit with high fidelity over arbitrary distances; in particular distances much greater than the localization length of the chain.
The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic $XY$ spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the …
As the number of qubits available on noisy quantum computers grows, it will become necessary to efficiently select a subset of physical qubits to use in a quantum computation. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while r…
In a recent paper, we showed that secondary storage can extend the range of quantum circuits that can be practically simulated with classical algorithms. Here we refine those techniques and apply them to the simulation of Sycamore circuits with 53 and 54 qubits, with the entanglement pattern ABCDCDAB that has proven difficult to classically simulate with other approaches. Our analysis shows that on the Summit supercomputer at Oak Ridge National Laboratories, such circuits can be simulated with high fidelity to arbitrary depth in a matter of days, outputting all the amplitudes.
We show that the entanglement of a $2\times 2$ bipartite state can be improved and maximized probabilistically through single-qubit operations only. An experiment is proposed and it is numerically simulated.
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an explicit class of efficiently simulable circuits (log depth circuits with 2-qubit gates of limited range) to the following: let C be any poly sized quantum circuit (generally of poly depth too) on n qubits comprising 1- and 2- qubit gates and 1-qubit measurements (with 2-qubit gates acting on arbitrary pairs of qubit lines). For each qubit line j let D_j be the num…
We study numerically a disordered transverse-field Ising Hamiltonian with long-range couplings. This model was recently investigated experimentally in a trapped-ion quantum simulator and was found to exhibit features of many-body localization at strong disorder. We use exact diagonalization to study the collective state preservation and the eigenstate entanglement structure as a function of both disorder strength and interaction range. Our numerical results, using the same system sizes as the experiment, verify the observation of many-body localization reported in the recent quantum simulation…
We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities. Such probabilistic gates can be used for scalable quantum computation.
Dephasing decoherence induced by interaction of one qubit with a quantum bath can be simulated classically by random unitary evolution without the need for a bath and this random unitary evolution is equivalent to the quantum case. For a general dephasing model and a single qubit system, we explicitly construct the noise functional and completely specify the random unitary evolution. To demonstrate the technique, we applied our results to three paradigmatic models: spin-boson, central spin, and quantum impurity. For multiple qubits, we identify a class of generalized quantum dephasing models t…
We theoretically consider a cross-resonance (CR) gate implemented by pulse sequences proposed by Calderon-Vargas & Kestner, Phys. Rev. Lett. 118, 150502 (2017). These sequences mitigate systematic error to first order, but their effectiveness is limited by one-qubit gate imperfections. Using additional microwave control pulses, it is possible to tune the effective CR Hamiltonian into a regime where these sequences operate optimally. This improves the overall feasibility of these sequences by reducing the one-qubit operations required for error correction. We illustrate this by simulating rando…
We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for all qubits. We show that at least the simplest such models, which can be realized with localized states in Dirac materials, satisfy integrability conditions that we use to describe pseudospin dynamics in a linearly time-dependent magnetic field. Generalizing to an arbitrary number of qubits, we construct a spin Hamiltonian, which we call the gamma-magnet. This system does not conserve polarization…
We study the computation power of lattices composed of two dimensional systems (qubits) on which translationally invariant global two-qubit gates can be performed. We show that if a specific set of 6 global two qubit gates can be performed, and if the initial state of the lattice can be suitably chosen, then a quantum computer can be efficiently simulated
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom and arbitrarily long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices, however, the number of qubits is highly limited and quantum operation error and qubit coherence are not negligible. Besides, the connectivity of physical qubits in a quantum processing unit (QPU) is also strictly constrained. Thereby, additional operations like SWAP gates have to be inserted to satisfy this constraint while preserving the functionality of the original ci…
Disentanglement and loss of quantum correlations due to one global collective noise effect are described for two-qubit Schrödinger cat and Werner states of a four level trapped ion quantum system. Once the Jaynes-Cummings ionic interactions are mapped onto a Dirac spinor structure, the elementary tools for computing quantum correlations of two-qubit ionic states are provided. With two-qubit quantum numbers related to the total angular momentum and to its projection onto the direction of an external magnetic field (which lifts the degeneracy of the ion's internal levels), a complete analytical …
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional quantum walk scheme with a single-qubit coin that presents, in the considered regimes, a strong localization-like effect on the walker. The result could provide new possible directions for the implementation of quantum algorithms or from the point of view of quantum simulation. We characterize the localization-like effect in terms of the parameters of a step-depe…
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit participates in O(1) two-qubit gates. It is shown that any sparse circuit on n+k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time $2^{O(k)} poly(n)$. Secondly, we study Pauli-based computation (PBC) where allowed operations are non-destructive eigenvalue measurements of n-qubit Pauli operators. The computation …
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et …
In thermal phases, the quantum coherence of individual degrees of freedom is rapidly lost to the environment. Many-body localized (MBL) phases limit the spread of this coherence and appear promising for quantum information applications. However, such applications require not just long coherence times but also a means to transport and manipulate information. We demonstrate that this can be done in a one dimensional model of interacting spins at infinite temperature. Our protocol utilizes protected qubits which emerge at the boundary between topological and trivial phases. State transfer occurs …
Port-based teleportation (PBT) is a teleportation protocol that employs a number of Bell pairs and a joint measurement to enact an approximate input-output identity channel. Replacing the Bell pairs with a different multi-qubit resource state changes the enacted channel and allows the PBT protocol to simulate qubit channels beyond the identity. The channel resulting from PBT using a general resource state is consequently of interest. In this work, we fully characterise the Choi matrix of the qubit channel simulated by the PBT protocol in terms of its resource state. We also characterise the PB…
Classical planar vertex models afford transfer matrices with real and positive entries, which makes this class of models suitable for quantum simulations. In this work, we support this statement by building explicit quantum circuits that implement the actions of the transfer matrices on arbitrary many-qubit states. The number of qubits and the depth of the circuits grow linearly with the size of the system. Furthermore, we present tests using quantum simulators and demonstrate that important physical quantities can be extracted, such as the eigen-vector corresponding to the largest eigenvalue …
