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arXiv:1208.3656 · Physical Review Letters

Quantum Simulation via Filtered Hamiltonian Engineering: Application to Perfect Quantum Transport in Spin Networks

Ashok Ajoy, Paola Cappellaro

Published May 29, 2013• 51 citations
arXivHTMLPDF

Abstract

We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.

DOI
10.1103/physrevlett.110.220503

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We propose a method for Hamiltonian engineering that requires no local control but only relies on collective qubit rotations and field gradients. The technique achieves a spatial modulation of the coupling strengths via a dynamical construction of a weighting function combined with a Bragg grating. As an example, we demonstrate how to generate the ideal Hamiltonian for perfect quantum information transport between two separated nodes of a large spin network. We engineer a spin chain with optimal couplings starting from a large spin network, such as one naturally occurring in crystals, while decoupling all unwanted interactions. For realistic experimental parameters, our method can be used to drive almost perfect quantum information transport at room temperature. The Hamiltonian engineering method can be made more robust under decoherence and coupling disorder by a novel apodization scheme. Thus, the method is quite general and can be used to engineer the Hamiltonian of many complex spin lattices with different topologies and interactions.
Quantum simulation presents itself as one of the biggest advantages of developing quantum computers. Simulating a quantum system classically is almost impossible beyond a certain system size whereas a controllable quantum system inherently has the resources and computing space to simulate another system. Analog quantum simulation is one of the ways of quantum simulation through which a known system mimics an unknown system. A key aspect of this is the ability to generate the target Hamiltonian using control operations which is referred to as Hamiltonian engineering. One way of doing this is to apply pulse sequences over a length of time such that the average Hamiltonian over this period is the desired one. In this thesis, we discuss the method of filtered Hamiltonian engineering which works in a similar fashion. Using this technique, we create a star topology from a general network of spins. Quantum communication between two parties is an important task for its applications in information theory as well as for its use in a quantum computer. A typical solution to this is using teleportation through the means of shared entangled qubits. Teleportation is not ideal for short-range communication such as between two units in a quantum computer. It has been shown that information can be transported from one node of a quantum spin network to another by natural evolution of the system over time. Such networks are better suited for solid-state based computing architectures as well as for short-range communication. The Hamiltonian that permits such transport however places stringent requirements on the parameters of the network. While individual control of spins cannot be avoided in most cases, excess control can introduce noise. In this thesis, we work on a few models of spin networks that permit information transport with minimal requirements on the parameters of the network.
Quantum spin networks can be used to transport information between separated registers in a quantum-information processor. To find a practical implementation, the strict requirements of ideal models for perfect state transfer need to be relaxed, allowing for complex coupling topologies and general initial states. Here we analyze transport in complex quantum spin networks in the maximally mixed state and derive explicit conditions that should be satisfied by propagators for perfect state transport. Using a description of the transport process as a quantum walk over the network, we show that it is necessary to phase-correlate the transport processes occurring along all the possible paths in the network. We provide a Hamiltonian that achieves this correlation and use it in a constructive method to derive engineered couplings for perfect transport in complicated network topologies.
Spin chains have been proposed as wires to transport information between distributed registers in a quantum information processor. Unfortunately, the challenges in manufacturing linear chains with engineered couplings has hindered experimental implementations. Here we present strategies to achieve perfect quantum information transport in arbitrary spin networks. Our proposal is based on the weak coupling limit for pure state transport, where information is transferred between two end spins that are only weakly coupled to the rest of the network. This regime allows ignoring the complex, internal dynamics of the bulk network and relying on virtual transitions or on the coupling to a single bulk eigenmode. We further introduce control methods capable of tuning the transport process and achieve perfect fidelity with limited resources, involving only manipulation of the end qubits. These strategies could be thus applied not only to engineered systems with relaxed fabrication precision, but also to naturally occurring networks; specifically, we discuss the practical implementation of quantum state transfer between two separated nitrogen vacancy (NV) centers through a network of nitrogen substitutional impurities.
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians . Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an 'Eulerian decoupling cycle,' that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation . We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls . In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaevʼs honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.
Dynamical decoupling and Hamiltonian engineering are well-established techniques that have been used to control qubit systems. However, designing the corresponding methods for qudit systems has been challenging due to the lack of a Bloch sphere representation, more complex interactions, and additional control constraints. By identifying several general structures associated with such problems, we develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Our formalism significantly simplifies qudit pulse-sequence design while naturally incorporating robustness conditions necessary for experimental practicality. We experimentally demonstrate these techniques in a strongly interacting, disordered ensemble of spin-1 nitrogen-vacancy centers, achieving more than an order-of-magnitude improvement in coherence time over existing pulse sequences. We further describe how our techniques enable the engineering of exotic many-body phenomena such as quantum many-body scars, and open up new opportunities for quantum metrology with enhanced sensitivities. These results enable wide-reaching new applications for dynamical decoupling and Hamiltonian engineering in many-body physics and quantum metrology. Published by the American Physical Society 2024
Abstract To transport high-quality quantum state between two distant qubits through one-dimensional spin chains, the perfect state transfer (PST) method serves as the first choice, due to its natively perfect transfer fidelity that is independent of the system dimension. However, the PST requires a precise modulation of the local pulse parameters as well as an accurate timing of dynamic evolution, and is thus very sensitive to variations in practice. Here, we propose a protocol for achieving quantum-preserved transport of excitations using an array of Rydberg-dressed atoms, enabled by optimal control of minimally global parameters. By treating the weak coupling of two marginal array atoms as a perturbation, an effective spin-exchange model with highly tunable interactions between the external weak and the inner strong driving atoms can be established, which allows for coherent excitation transfer even with large atomic position fluctuation. We furthermore show that the existence of long-time excitation propagation unattainable for systems under antiblockade facilitation conditions. Our results highlight an easily-implemented scheme for studying the dynamics of spin systems using Rydberg atoms and may guide the avenue to the engineering of complex many-body dynamics.