arXiv subjects

Leonardo Banchi

Publications and source records attributed to Leonardo Banchi.

At least 73 records · Page 4Linked to original sources

arXiv2018

Supervised learning of time-independent Hamiltonians for gate design

We present a general framework to tackle the problem of finding time-independent dynamics generating target unitary evolutions. We show that this problem is equivalently stated as a set of conditions over the spectrum of the time-independent gate generator, thus transforming the task to an inverse eigenvalue problem. We illustrate our methodology by identifying suitable time-independent generators implementing Toffoli and Fredkin gates without the need for ancillae or effective evolutions. We show how the same conditions can be used to solve the problem numerically, via supervised learning techniques. In turn, this allows us to solve problems that are not amenable, in general, to direct analytical solution, providing at the same time a high degree of flexibility over the types of gate-design problems that can be approached. As a significant example, we find generators for the Toffoli gate using only diagonal pairwise interactions, which are easier to implement in some experimental architectures. To showcase the flexibility of the supervised learning approach, we give an example of a nontrivial four-qubit gate that is implementable using only diagonal, pairwise interactions.

quant-ph↗

arXiv2018

Pretty Good State Transfer in Qubit Chains - The Heisenberg Hamiltonian

Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a Heisenberg chain with n qubits there is pretty good state transfer between the nodes at the j-th and (n-j+1)-th position if n is a power of 2. Moreover, this condition is also necessary for j=1. We obtain this result by applying a theorem due to Kronecker about Diophantine approximations, together with techniques from algebraic graph theory.

quant-ph↗

arXiv2018

Theory of channel simulation and bounds for private communication

We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse bounds for quantum and private communication, as established in PLOB [Pirandola, Laurenza, Ottaviani, Banchi, arXiv:1510.08863]. We start by introducing a general weak converse bound for private communication based on the relative entropy of entanglement. We discuss how combining this bound with channel simulation and teleportation stretching, PLOB established the two-way quantum and private capacities of several fundamental channels, including the bosonic lossy channel. We then provide a rigorous proof of the strong converse property of these bounds by adopting a correct use of the Braunstein-Kimble teleportation protocol for the simulation of bosonic Gaussian channels. This analysis provides a full justification of claims presented in the follow-up paper WTB [Wilde, Tomamichel, Berta, arXiv:1602.08898] whose upper bounds for Gaussian channels would be otherwise infinitely large. Besides clarifying contributions in the area of channel simulation and protocol reduction, we also present some generalizations of the tools to other entanglement measures and novel results on the maximum excess noise which is tolerable in quantum key distribution.

quant-ph↗

arXiv2017

Quantum Gates Between Distant Qubits via Spin-Independent Scattering

We show how the spin independent scattering of two initially distant qubits, say, in distinct traps or in remote sites of a lattice, can be used to implement an entangling quantum gate between them. The scattering takes place under 1D confinement for which we consider two different scenarios: a 1D wave-guide and a tight-binding lattice. We consider models with contact-like interaction between two fermionic or two bosonic particles. A qubit is encoded in two distinct spins (or other internal) states of each particle. Our scheme enables the implementation of a gate between two qubits which are initially too far to interact directly, and provides an alternative to photonic mediators for the scaling of quantum computers. Fundamentally, an interesting feature is that "identical particles" (e.g., two atoms of the same species) and the 1D confinement, are both necessary for the action of the gate. Finally, we discuss the feasibility of our scheme, the degree of control required to initialize the wave-packets momenta, and show how the quality of the gate is affected by momentum distributions and initial distance. In a lattice, the control of quasi-momenta is naturally provided by few local edge impurities in the lattice potential.

quant-ph↗

arXiv2017

Simulation of non-Pauli Channels

We consider the simulation of a quantum channel by two parties who share a resource state and may apply local operations assisted by classical communication (LOCC). One specific type of such LOCC is standard teleportation, which is however limited to the simulation of Pauli channels. Here we show how we can easily enlarge this class by means of a minimal perturbation of the teleportation protocol, where we introduce noise in the classical communication channel between the remote parties. By adopting this noisy protocol, we provide a necessary condition for simulating a non-Pauli channel. In particular, we characterize the set of channels that are generated assuming the Choi matrix of an amplitude damping channel as a resource state. Within this set, we identify a class of Pauli-damping channels for which we bound the two-way quantum and private capacities.

quant-ph↗

arXiv2017

Driven quantum dynamics: will it blend?

Randomness is an essential tool in many disciplines of modern sciences, such as cryptography, black hole physics, random matrix theory and Monte Carlo sampling. In quantum systems, random operations can be obtained via random circuits thanks to so-called q-designs, and play a central role in the fast scrambling conjecture for black holes. Here we consider a more physically motivated way of generating random evolutions by exploiting the many-body dynamics of a quantum system driven with stochastic external pulses. We combine techniques from quantum control, open quantum systems and exactly solvable models (via the Bethe-Ansatz) to generate Haar-uniform random operations in driven many-body systems. We show that any fully controllable system converges to a unitary q-design in the long-time limit. Moreover, we study the convergence time of a driven spin chain by mapping its random evolution into a semigroup with an integrable Liouvillean and finding its gap. Remarkably, we find via Bethe-Ansatz techniques that the gap is independent of q. We use mean-field techniques to argue that this property may be typical for other controllable systems, although we explicitly construct counter-examples via symmetry breaking arguments to show that this is not always the case. Our findings open up new physical methods to transform classical randomness into quantum randomness, via a combination of quantum many-body dynamics and random driving.

quant-ph↗

arXiv2017

Gating classical information flow through spin chains by quantum phase transitions

To push commercial electronics beyond its current size limits, atomic-scale communication channels and logic units need to be designed, making the use of quantum entities an imperative. In this regime, quantum fluctuations naturally become prominent, and are generally considered to be detrimental. Here we show that for spin-based information processing, these fluctuations can be uniquely exploited to gate the flow of classical binary information across a magnetic chain. Moreover, this information flow can be controlled with a modest external magnetic field that drives the system through different many-body quantum phases in which the orientation of the final spin does or does not reflect the orientation of the initial input. Our results are general for a wide class of anisotropic spin chains that act as magnetic cellular automata, and suggest that quantum fluctuations may play a unique role in driving classical information flow at the atomic scale.

cond-mat.mes-hall↗

arXiv2017

Fundamental Limits of Repeaterless Quantum Communications

Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that are achievable by two remote parties at the ends of a quantum channel, without restrictions on their local operations and classical communication, which can be unlimited and two-way. These two-way assisted capacities represent the ultimate rates that are reachable without quantum repeaters. By constructing an upperbound based on the relative entropy of entanglement and devising a dimension-independent technique dubbed "teleportation stretching", we establish these capacities for many fundamental channels, namely bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels in arbitrary dimension. In particular, we determine the fundamental rate-loss trade-off affecting any protocol of quantum key distribution. Our findings set the ultimate limits of point-to-point quantum communications and provide the most precise and general benchmarks for quantum repeaters.

quant-ph↗

arXiv2017

NOON States via Quantum Walk of Bound Particles

Tight-binding lattice models allow the creation of bound composite objects which, in the strong-interacting regime, are protected against dissociation. We show that a local impurity in the lattice potential can generate a coherent split of an incoming bound particle wave-packet which consequently produces a NOON state between the endpoints. This is non trivial because when finite lattices are involved, edge-localisation effects make their use for non-classical state generation and information transfer challenging. We derive an effective model to describe the propagation of bound particles in a Bose-Hubbard chain. We introduce local impurities in the lattice potential to inhibit localisation effects and to split the propagating bound particle, thus enabling the generation of distant NOON states. We analyse how minimal engineering transfer schemes improve the transfer fidelity and we quantify the robustness to typical decoherence effects in optical lattice implementations. Our scheme potentially have an impact on quantum-enhanced atomic interferometry in a lattice.

quant-ph↗

arXiv2017

Entanglement entropy scaling in solid-state spin arrays via capacitance measurements

Solid-state spin arrays are being engineered in varied systems, including gated coupled quantum dots and interacting dopants in semiconductor structures. Beyond quantum computation, these arrays are useful integrated analog simulators for many-body models. As entanglement between individual spins is extremely short ranged in these models, one has to measure the entanglement entropy of a block in order to truly verify their many-body entangled nature. Remarkably, the characteristic scaling of entanglement entropy, predicted by conformal field theory, has never been measured. Here we show that with as few as two replicas of a spin array, and capacitive double-dot singlet-triplet measurements on neighboring spin pairs, the above scaling of the entanglement entropy can be verified. This opens up the controlled simulation of quantum field theories, as we exemplify with uniform chains and Kondo-type impurity models, in engineered solid-state systems. Our procedure remains effective even in the presence of typical imperfections of realistic quantum devices and can be used for thermometry, and to bound entanglement and discord in mixed many-body states.

cond-mat.str-el↗

arXiv2016

Supervised quantum gate "teaching" for quantum hardware design

We show how to train a quantum network of pairwise interacting qubits such that its evolution implements a target quantum algorithm into a given network subset. Our strategy is inspired by supervised learning and is designed to help the physical construction of a quantum computer which operates with minimal external classical control.

cs.LG↗

arXiv2016

Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions

We put forward a strategy to encode a quantum operation into the unmodulated dynamics of a quantum network without the need of external control pulses, measurements or active feedback. Our optimization scheme, inspired by supervised machine learning, consists in engineering the pairwise couplings between the network qubits so that the target quantum operation is encoded in the natural reduced dynamics of a network section. The efficacy of the proposed scheme is demonstrated by the finding of uncontrolled four-qubit networks that implement either the Toffoli gate, the Fredkin gate, or remote logic operations. The proposed Toffoli gate is stable against imperfections, has a high-fidelity for fault tolerant quantum computation, and is fast, being based on the non-equilibrium dynamics.

quant-ph↗

arXiv2016

Geometric phases and cyclic isotropic cosmologies

In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker universe with a periodic scale factor, in which the universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying the Berry phase of the scalar field, we show that contrarily to what is commonly believed, the scalar field carries information from one bounce to another in the form of a global phase which occurs to be generically non-zero. {The Berry phase is then evaluated numerically in the case of the effective Loop Quantum Cosmology closed Universe. We observe that Berry's phase is nonzero, but that in the quantum regime the particle content is non-negligible.

gr-qc↗

arXiv2016

Photonic Simulation of Entanglement Growth After a Spin Chain Quench

The time evolution of quantum many-body systems is one of the least understood frontiers of physics. The most curious feature of such dynamics is, generically, the growth of quantum entanglement with time to an amount proportional to the system size (volume law) even when the interactions are local. This phenomenon, unobserved to date, has great ramifications for fundamental issues such as thermalisation and black-hole formation, while its optimisation clearly has an impact on technology (e.g., for on-chip quantum networking). Here we use an integrated photonic chip to simulate the dynamics of a spin chain, a canonical many-body system. A digital approach is used to engineer the evolution so as to maximise the generation of entanglement. The resulting volume law growth of entanglement is certified by constructing a second chip, which simultaneously measures the entanglement between multiple distant pairs of simulated spins. This is the first experimental verification of the volume law and opens up the use of photonic circuits as a unique tool for the optimisation of quantum devices.

quant-ph↗

arXiv2015

Integrated information storage and transfer with a coherent magnetic device

Quantum systems are inherently dissipation-less, making them excellent candidates even for classical information processing. We propose to use an array of large-spin quantum magnets for realizing a device which has two modes of operation: memory and data-bus. While the weakly interacting low-energy levels are used as memory to store classical information (bits), the high-energy levels strongly interact with neighboring magnets and mediate the spatial movement of information through quantum dynamics. Despite the fact that memory and data-bus require different features, which are usually prerogative of different physical systems -- well isolation for the memory cells, and strong interactions for the transmission -- our proposal avoids the notorious complexity of hybrid structures. The proposed mechanism can be realized with different setups. We specifically show that molecular magnets, as the most promising technology, can implement hundreds of operations within their coherence time, while adatoms on surfaces probed by a scanning tunneling microscope is a future possibility.

quant-ph↗

arXiv2015

Quantum fidelity for arbitrary Gaussian states

We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.

quant-ph↗

arXiv2015

A Toolbox for Linear Optics in a 1D Lattice via Minimal Control

Tight binding lattices offer a unique platform in which particles may be either static or mobile depending on the potential barrier between the sites. How to harness this mobility in a many-site lattice for useful operations is still an open question. We show how effective linear optics-like operations between arbitrary lattice sites can be implemented by a minimal local control which introduces a local impurity in the middle of the lattice. In particular we show how striking is the difference of the two possible correlations with and without the impurity. Our scheme enables the observation of the Hong-Ou-Mandel effect between distant wells without moving them next to each other with, e.g., tweezers. Moreover, we show that a tunable Mach-Zehnder interferometer is implemented adding a step-like potential, and we prove the robustness of our linear optics scheme to inter-particle interactions.

quant-ph↗

arXiv2015

Perfect wave-packet splitting and reconstruction in a one-dimensional lattice

Particle delocalization is a common feature of quantum random walks in arbitrary lattices. However, in the typical scenario a particle spreads over multiple sites and its evolution is not directly useful for controlled quantum interferometry, as may be required for technological applications. In this paper we devise a strategy to perfectly split the wave-packet of an incoming particle into two components, each propagating in opposite directions, which reconstruct the shape of the initial wavefunction after a particular time $t^*$. Therefore, a particle in a delta-like initial state becomes exactly delocalized between two distant sites after $t^*$. We find the mathematical conditions to achieve the perfect splitting which are satisfied by viable example Hamiltonians with static site-dependent interaction strengths. Our results pave the way for the generation of peculiar many-body interference patterns in a many-site atomic chain (like the Hanbury Brown and Twiss and quantum Talbot effects) as well as for the distribution of entanglement between remote sites. Thus, as for the case of perfect state transfer, the perfect wave-packet splitting can be a new tool for varied applications.

quant-ph↗