We present a general formalism to the problem of perfect state-transfer (PST), where the state involves multiple excitations of the quantum network. A key feature of our formalism is that it allows for inclusion of nontrivial interactions between the excitations. Hence, it is perfectly suited to addressing the problem of PST in the context of various types of physical realizations. The general formalism is also flexible enough to account for situations where multiple excitations are "focused" onto the same site.
We propose a scheme for perfect excitation of a single two-level atom by a single photon in free space. The photon state has to match the time reversed photon state originating from spontaneous decay of a two-level system. We discuss its experimental preparation. The state is characterized by a particular asymmetric exponentially-shaped temporal profile. Any deviations from this ideal state limit the maximum absorption. Although perfect excitation requires an infinite amount of time we demonstrate that there is a class of initial one-photon quantum states which can achieve almost perfect absor…
Recently, the photon absorption attracts lots of interest and plays an important role in a variety of applications. Here, we propose a valuable scheme to investigate the perfect photon absorption in a hybrid atom-optomechanical system both under and beyond the low-excitation limit. The perfect photon absorption persists both in the linear atomic excitation regime and nonlinear atomic excitation regime, below the threshold of the optical bistability/multistability, respectively. We also show that the optical nonlinearity raised by the nonlinear optomechanical interaction and nonlinear atomic ex…
We study transfer of single photon in an one-dimensional finite Glauber-Fock cavity array whose coupling strengths satisfy a square root law. The evolved state in the array can be mapped to an upper truncated coherent state if the cavities are resonant. Appropriate choices of resonance frequencies provide perfect transfer of a photon between any two cavities in the array. Perfect transfer of the photon allows perfect quantum state transfer between the cavities. Our findings may help in realizing quantum communication and information processing in photonic lattices.
We develop a family of perfect quantum error correcting codes that correct for phase errors that arise on any qubit, at any time, during a perfect state transfer experiment. These ensure that we find the optimal operating regime for corrected state transfer. For a specific class of system, we further show that while dephasing noise can be corrected, depolarising noise cannot.
Perfect (quantum) state transfer has been proved to be an effective model for quantum information processing. In this paper, we give a characterization of cubelike graphs having perfect edge state transfer. By using a lifting technique, we show that every bent function, and some semi-bent functions as well, can produce some graphs having PEST. Some concrete constructions of such graphs are provided. Notably, using our method, one can obtain some classes of infinite graphs possessing PEST.
Certain non-uniformly coupled spin chains can exhibit perfect transfer of quantum states from end to end. Motivated by recent experimental implementations, we extend the simplest such chain to next-to-nearest neighbour (NNN) couplings. It is shown analytically that perfect state transfer can be maintained under the extension and that end-to-end entanglement generation (fractional revival) can occur.
We find analytic models that can perfectly transfer, without state initializati$ or remote collaboration, arbitrary functions in two- and three-dimensional interacting bosonic and fermionic networks. We elaborate on a possible implementation of state transfer through bosonic or fermionic atoms trapped in optical lattices. A significant finding is that the state of a spin qubit can be perfectly transferred through a fermionic system. Families of Hamiltonians, both linear and nonlinear, are described which are related to the linear Boson model and that enable the perfect transfer of arbitrary fu…
We study perfect state transfer on quantum networks represented by weighted graphs. Our focus is on graphs constructed from the join and related graph operators. Some specific results we prove include: (1) The join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al. [clms09] where the regular graph is a complete graph or a complete graph with a missing link. In contrast, the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. This implies that adding weights in a comp…
The transfer of data is a fundamental task in information systems. Microprocessors contain dedicated data buses that transmit bits across different locations and implement sophisticated routing protocols. Transferring quantum information with high fidelity is a challenging task, due to the intrinsic fragility of quantum states. We report on the implementation of the perfect state transfer protocol applied to a photonic qubit entangled with another qubit at a different location. On a single device we perform three routing procedures on entangled states with an average fidelity of 97.1%. Our pro…
We present a perfect state transfer protocol via a qubit chain with the evolution governed by the $xx$ Hamiltonian. In contrast to the recent protocol announced in [Phys. Rev. Lett. {\bf 101}, 230502 (2008)], our method does not demand any remote-cooperated initialization and sending classical information about measurement outcomes. We achieve the perfect state transfer only with the assumption of access to two spins at each end of the chain, while the initial state of the whole chain is irrelevant.
The natural notion of almost perfect state transfer (APST) is examined. It is applied to the modelling of efficient quantum wires with the help of $XX$ spin chains. It is shown that APST occurs in mirror-symmetric systems, when the 1-excitation energies of the chains are linearly independent over rational numbers. This result is obtained as a corollary of the Kronecker theorem in Diophantine approximation. APST happens under much less restrictive conditions than perfect state transfer (PST) and moreover accommodates the unavoidable imperfections. Some examples are discussed.
We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph $G$ has perfect state transfer if and only if its quotient $G/π$, under any equitable partition $π$, has perfect state transfer, we exhibit graphs with perfect state transfer between two vertices but which lack automorphism swapping them. This answers a question of Godsil (Discrete Mathematics 312(1):129-147, 2011). We also show that the Cartesian product of quotient graphs $\Box_{k} G_{k}/π_{k}$ is isomorphic to the quotient graph $\Box_{k} G_{k}/π$, for some equitable partition $π$. This provide…
We review the subject of perfect state transfer; how one designs the (fixed) interactions of a chain of spins so that a quantum state, initially inserted on one end of the chain, is perfectly transferred to the opposite end in a fixed time. The perfect state transfer systems are then used as a constructive tool to design Hamiltonian implementations of other primitive protocols such as entanglement generation and signal amplification in measurements, before showing that, in fact, universal quantum computation can be implemented in this way.
A general formalism of the problem of perfect state transfer is presented. We show that there are infinitely many Hamiltonians which may provide solution to this problem. In a first attempt to give a classification of them we investigate their possible forms and the related dynamics during the transfer. Finally, we show how the present formalism can be used for the engineering of perfect quantum wires of various topologies and coupling configurations.
The Wigner-Weisskopf-type model describing the energy transfer between two centers mediated by a continuum of energy levels is studied. This work is motivated by the recent interest in transport phenomena at nanoscale in biology and quantum engineering. The analytical estimation for the energy transfer efficiency is derived in the weak coupling regime and the conditions for the almost perfect transfer are discussed. The embedding of the standard tight-binding model into Wigner-Weisskopf one which includes the environmental noise is presented.
In this paper, we consider a continuous-time quantum walk based search algorithm. We introduce equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the finding time of the search algorithm. In addition, we gave some examples of graphs that we can calculate the success probability and the finding time.
By using some techniques such as spectral distribution and stratification associated with the graphs, employed in [1,2] for the purpose of Perfect state transfer (PST) of a single qubit over antipodes of distance-regular spin networks and PST of a $d$-level quantum state over antipodes of pseudo-distance regular networks, PST of an m-qubit GHZ state is investigated. To do so, we employ the particular distance-regular networks (called Johnson networks) J(2m,m) to transfer an m-qubit GHZ state initially prepared in an arbitrary node of the network (called the reference node) to the corresponding…
Perfect state transfer between two marked vertices of a graph by means of discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit calculation that for the coined quantum walks on star graph and complete graph with self-loops perfect state transfer between the sender and receiver vertex is achieved for arbitrary number of vertices $N$ in $O(\sqrt{N})$ steps of the walk. Finally, we show that Szegedy's walk with queries on complete graph allows for state transfer with unit fidelity in the limit o…
We consider quantum excitation energy transport (EET) in a network of two-state nodes in the Markovian approximation by employing the Lindblad formulation. We find that EET from an initial site, where the excitation is inserted to the sink, is generally inefficient due to the inhibition of transport by localization of the excitation wave packet in a symmetric, fully-connected network. We demonstrate that the EET efficiency can be significantly increased up to %100 by perturbing hopping transport between the initial node and the one connected directly to the sink, while the rate of energy trans…
We investigate quantum state transfer in XY spin chains and propose a recursive procedure to construct the nonuniform couplings of these chains with arbitrary length to achieve perfect state transfer(PST). We show that this method is capable of finding all possible coupling schemes for PST. These schemes, without external control fields, only involve preengineered couplings but not dynamical control of them, so they can be simply realized experimentally. The analytical solutions provide all information for coupling design.
We show how to perfectly transfer, without state initialization and remote collaboration, arbitrary functions in interacting boson lattices. We describe a possible implementation of state transfer through bosonic atoms trapped in optical lattices or polaritons in on-chip coupled cavities. Significantly, a family of Hamiltonians, both linear and nonlinear, is found which are related to the Bose-Hubbard model and that enable the perfect transfer of arbitrary functions. It is shown that the state transfer between two sites in two-dimensional lattices can result in quantum interference due to the …
It is shown how to perfectly transfer an arbitrary qudit state in interacting boson networks. By defining a family of Hamiltonians related to Bose-Hubbard model, we describe a possible method for state transfer through bosonic atoms trapped in these networks with different kinds of coupling strengths between them. Particularly, by taking the underlying networks of so called group schemes as interacting boson networks, we show how choose suitable coupling strengths between the nodes, in order that an arbitrary qudit state be transferred from one node to its antipode, perfectly. In fact, by empl…
Superconducting quantum circuits, fabricated with multiple layers, are proposed to implement perfect quantum state transfer between nodes of a hypercube network. For tunable devices such as the phase qubit, each node can transmit quantum information to any other node at a constant rate independent of the distance between qubits. The physical limits of quantum state transfer in this network are theoretically analyzed, including the effects of disorder, decoherence, and higher-order couplings.
We suggest a scheme that allows arbitrarily perfect state transfer even in the presence of random fluctuations in the couplings of a quantum chain. The scheme performs well for both spatially correlated and uncorrelated fluctuations if they are relatively weak (say 5%). Furthermore, we show that given a quite arbitrary pair of quantum chains, one can check whether it is capable of perfect transfer by only local operations at the ends of the chains, and the system in the middle being a "black box". We argue that unless some specific symmetries are present in the system, it will be capable of pe…
We systematically investigated perfect state transfer between antipodal nodes of discrete time quantum walks on variants of the cycles C_4, C_6 and C_8 for three choices of coin operator. Perfect state transfer was found, in general, to be very rare, only being preserved for a very small number of ways of modifying the cycles. We observed that some of our useful modifications of C_4 could be generalised to an arbitrary number of nodes, and present three families of graphs which admit quantum walks with interesting dynamics either in the continuous time walk, or in the discrete time walk for ap…
A recent numerical study of short chains found near-perfect quantum state transfer between the boundary sites of a spin-1/2 XX chain if a sufficiently strong magnetic field acts on these sites. We show that the phenomenon is based on a pair of states strongly localized at the boundaries of the system and provide a simple quantitative analytical explanation.
We demonstrate that perfect state transfer can be achieved using an engineered spin chain and clean local end-chain operations, without requiring the initialization of the state of the medium nor fine tuning of control-pulses. This considerably relaxes the prerequisites for obtaining reliable transfer of quantum information across interacting-spin systems. Moreover, it allows us to shed light on the interplay among purity, entanglement and operations on a class of many-body systems potentially useful for quantum information processing tasks.
We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part of the graph is considered. We show that in this case the dynamics of the quantum walk is independent of the size of the second part and reduces to the one for the star graph where perfect state transfer is achieved. Second, we consider the situation where the sender and the receiver vertex are in the opposite parts of the graph. In such a case the state tr…
We exploit a ferromagnetic chain of interacting $d$-level ($d>2$) particles for arbitrary perfect transfer of quantum states with $(d-1)$ levels. The presence of one extra degree of freedom in the Hilbert space of particles, which is not used in encoding, allows to achieve perfect transfer even in a uniform chain through a repeated measurement procedure with consecutive single site measurements. Apart from the first iteration, for which the time of evolution grows linearly with the size of the chain, in all other iterations, the evolution times are short and does not scale with the length. The…
In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an Inverse Eigenvalue Problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.
We suggest a protocol for perfect quantum communication through spin chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-1/2 particles can be achieved in a timescale of the order of N^1.7|ln(P)|. We demonstrate …
The three- spin chain with Heisenberg XY- interaction is simulated in a three- qubit nuclear magnetic resonance (NMR) quantum computer. The evolution caused by the XY- interaction is decomposed into a series of single- spin rotations and the $J$- coupling evolutions between the neighboring spins. The perfect state transfer (PST) algorithm proposed by M. Christandl et al [Phys. Rev. Lett, 92, 187902(2004)] is realized in the XY- chain.
Motivated by the need for communication of coherent state-based qubits in quantum computers, we introduce a method for perfect transferring of an arbitrary superposition of coherent states between two distant nodes of a linear array of three semiconductor QDs. The QDs trapped in a system of coupled cavities. In this method, the field mode of the cavities, as the resource of transferring of quantum states, are only virtually excited which minimizes the effect of decoherence due to photon loss.
We propose a protocol for perfect quantum state transfer that is resilient to a broad class of realistic experimental imperfections, including noise sources that could be modelled either as independent Markovian baths or as certain forms of spatially correlated environments. We highlight interesting connections between the fidelity of state transfer and quantum stochastic resonance effects. The scheme is flexible enough to act as an effective entangling gate for the generation of genuine multipartite entanglement in a control-limited setting. Possible experimental implementations using superco…
We show a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flippings, and extend this method to distribution of an arbitrary unknown multi-qubit entangled state between every pair of sites in the multi-dimensional network. Furthermore, we study the routing of quantum information on this network in a quantum walk architecture, which can be used as quantum information processors to communicate between separated qubits.
This work presents an exactly soluble scheme to address the problem of optimal transfer of quantum states through a set of $s$ harmonic oscillators composing a network with connected ends as a closed quantum circuit. For this purpose we start from a general quadratic Hamiltonian form. The relationship between the parameters of the Hamiltonian, the network size, and the time interval required for such transfer are explicitly shown. Particular physical realizations of this Hamiltonian, transfer of entangled states, including transfer of states at the expense of a quantum entanglement, are also c…
We study perfect state transfer of quantum walks on signed graphs. Our aim is to show that negative edges are useful for perfect state transfer. Specific results we prove include: (1) The signed join of a negative 2-clique with any positive (n,3)-regular graph has perfect state transfer even if the unsigned join does not. Curiously, the perfect state transfer time improves as n increases. (2) A signed complete graph has perfect state transfer if its positive subgraph is a regular graph with perfect state transfer and its negative subgraph is periodic. This shows that signing is useful for crea…
The time-reversal mirror (TRM) prescribes the reverse playback of a signal to focalize an acoustic excitation as a Loschmidt echo. In the quantum domain, the perfect inverse filter (PIF) processes this signal to ensure an exact reversion provided that the excitation originated outside the cavity delimited by the transducers. We show that PIF takes a simple form when the initial excitation is created inside this cavity. This also applies to the acoustical case, where it corrects the TRM and improves the design of an acoustic bazooka. We solve an open chaotic cavity modeling a quantum bazooka an…
We propose to use ferromagnetic systems for entanglement generation and distribution together with perfect state transfer between distant parties in a qubit chain. The scheme relies on an effective 2-qubit dynamics, realized by leaving two empty sites in a uniformly filled chain. This allows long-range interacting qubit chains to serve as quantum channels for both tasks with optimal performances. Remarkably, the entanglement between sender and receiver sites is independent of both the transmission distance and of system size. This property opens new perspectives for short and mid-range quantum…
We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number chains employed in the scheme. The system consists of $M$ uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits a theorem is proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits.
Perfect state transfer between qubits on a uniformly coupled network, with interactions specified by a graph, has advantages over an engineered chain, such as much faster transfer times (independent of the distance between the input and output vertices). This is achieved by many couplings working in parallel. The trade-offs seem to be the need for increasing connectivity between qubits, and a large number of vertices in the graph. The size of existing graph constructions scale exponentially in the transfer distance, making these schemes impractical over anything but the shortest distances. Thi…
We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator does not depend on the state to be transferred. We show that perfect state transfer over an arbitrary distance can be achieved only if the walk is driven by an identity or a flip coin operator. Other biased coin operators and Hadamard coin allow perfect state transfer over finite distances only. Furthermore, we show that quantum walks ending with a perfect st…
We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to $N$-qubit spin networks of identical qubit couplings, we show that $2\log_3 N$ is the m…
In this paper we propose a scheme for quasi-perfect state transfer in a network of dissipative harmonic oscillators. We consider ideal sender and receiver oscillators connected by a chain of nonideal transmitter oscillators coupled by nearest-neighbor resonances. From the algebraic properties of the dynamical quantities describing the evolution of the network state, we derive a criterion, fixing the coupling strengths between all the oscillators, apart from their natural frequencies, enabling perfect state transfer in the particular case of ideal transmitter oscillators. Our criterion provides…
The coherent transfer of excitations between different locations of a quantum many-body system is of primary importance in many research areas, from transport properties in spintronics and atomtronics to quantum state transfer in quantum information processing. We address the transfer of $n>1$ bosonic and fermionic excitations between the edges of a one-dimensional chain modeled by a quadratic hopping Hamiltonian, where the block edges, embodying the sender and the receiver sites, are weakly coupled to the quantum wire. We find that perturbatively perfect coherent transfer is attainable in the…
We study the protocol known as quantum state transfer for a strongly coupled antiferromagnetic spin chain or ring (acting as a spin bus), with weakly coupled external qubits. By treating the weak coupling as a perturbation, we find that perfect state transfer (PST) is possible when second order terms are included in the expansion. We also show that PST is robust against variations in the couplings along the spin bus and between the bus and the qubits. As evidence of the quantum interference which mediates PST, we show that the optimal time for PST can be smaller with larger qubit separations, …
We introduce an analytical $XX$ spin chain with asymmetrical transport properties. It has an even number $N+1$ of sites labeled by $n=0,\cdots N$. It does not exhibit perfect state transfer (PST) from end-to-end but rather from the first site to the next to last one. In fact, PST of one-excitation states takes place between the even sites: $n\leftrightarrow N-n-1$, $n=0,2,\cdots, N-1$; while states localized at a single odd site undergo fractional revival (FR) over odd sites only. Perfect return is witnessed at double the PST/FR time. The couplings and local magnetic fields are related to the …
Although a complete picture of the full evolution of complex quantum systems would certainly be the most desirable goal, for particular Quantum Information Processing schemes such an analysis is not necessary. When quantum correlations between only specific elements of a many-body system are required for the performance of a protocol, a more distinguished and specialised investigation is helpful. Here, we provide a striking example with the achievement of perfect state transfer in a spin chain without state initialisation, whose realisation has been shown to be possible in virtue of the correl…
The basic idea of spin chain engineering for perfect quantum state transfer (QST) is to find a set of coupling constants in the Hamiltonian, such that a particular state initially encoded on one site will evolve freely to the opposite site without any dynamical controls. The minimal possible evolution time represents a speed limit for QST. We prove that the optimal solution is the one simulating the precession of a spin in a static magnetic field. We also argue that, at least for solid-state systems where interactions are local, it is more realistic to characterize the computation power by the…
A continuous-time quantum random walk describes the motion of a quantum mechanical particle on an underlying graph. The graph itself is associated with a Hilbert space of dimension equal to the number of vertices. The dynamics of the walk is governed by the unitary operator $\mathcal{U}(t) = e^{iAt}$, where $A$ is the adjacency matrix of the graph. An important notion in the quantum random walk is the transfer of a quantum state from one vertex to another. If the fidelity of the transfer is unity, we call it a perfect state transfer. Many graph families have been shown to admit PST or periodic…
Following the prescription of Ref. \cite{PST} in which perfect state transference (PST) of a qubit over distance regular spin networks was discussed, in this paper PST of an arbitrary $d$-level quantum state (qudit) over antipodes of more general networks called pseudo distance-regular networks, is investigated. In fact, the spectral analysis techniques used in the previous work \cite{PST}, and algebraic structures of pseudo distance-regular graphs are employed to give an explicit formula for suitable coupling constants in the Hamiltonians so that the state of a particular qudit initially enco…
We study perfect state transfer in Kendon's model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectra, and construct an infinite family of $4$-regular circulant graphs that admit perfect state transfer. Prior to our work, the only known infinite families of examples were variants of cycles and diamond chains.
In a one-dimensional Heisenberg chain, we show that there are no sets of coupling strengths such that the evolution perfectly transfers a quantum state between the two ends of the chain without the addition of magnetic fields. In lieu of perfect transfer, we consider a range of options for achieving high quality transfer, whether in finite time, or via "pretty good" transfer where one waits long times in the hope of getting arbitrarily close to perfect transfer. In attempting to engineer arbitrarily accurate transfer, we explore a new paradigm that facilitates time estimates for achieving any …
Realizing a controllable network with multiple degrees of interaction is a challenge to physics and engineering. Here, we experimentally report an on-chip reconfigurable network based on nanoelectromechanical resonators with nearest-neighbor (NN) and next-nearest-neighbor (NNN) strong couplings. By applying different parametric voltages on the same on-chip device, we carry out perfect coherent transfer in NN and NNN coupled array networks. Moreover, the low-loss resonators ensure the desired evolution to achieve perfect transfer and the demonstration of the parity-dependent phase relation at t…
A quantum memory is a system that enables transfer, storage, and retrieval of optical quantum states by ON/OFF switching of the control signal in each stages of the memory. In particular, it is known that, for perfect transfer of a single-photon state, appropriate shaping of the input pulse is required. However, in general, such a desirable pulse shape has a complicated form, which would be hard to generate in practice. In this paper, for a wide class of linear quantum memory systems, we develop a method that reduces the complexity of the input pulse shape of a single-photon while maintaining …
