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arXiv:1207.6063 · Physical Review A

Mediated gates between spin qubits

Jianjia Fei, Dong Zhou, Yun-Pil Shim, Sangchul Oh, Xuedong Hu, Mark G. Friesen

Published Dec 26, 2012• 14 citations
arXivHTMLPDF

Abstract

In a typical quantum circuit, nonlocal quantum gates are applied to nonproximal qubits. If the underlying physical interactions are short-range (e.g., exchange interactions between spins), intermediate swap operations must be introduced, thus increasing the circuit depth. Here we develop a class of ``mediated'' gates for spin qubits, which act on nonproximal spins via intermediate ancilla qubits. At the end of the operation, the ancillae return to their initial states. We show how these mediated gates can be used (1) to generate arbitrary quantum states and (2) to construct arbitrary quantum gates. We provide some explicit examples of circuits that generate common states [e.g., Bell, Greenberger-Horne-Zeilinger (GHZ), $W$, and cluster states] and gates (e.g., $\sqrt{swap}$, swap, $cnot$, and Toffoli gates). We show that the depths of these circuits are often shorter than those of conventional $swap$-based circuits. We also provide an explicit experimental proposal for implementing a mediated gate in a triple-quantum-dot system.

DOI
10.1103/physreva.86.062328

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In a typical quantum circuit, nonlocal quantum gates are applied to nonproximal qubits. If the underlying physical interactions are short-range (e.g., exchange interactions between spins), intermediate swap operations must be introduced, thus increasing the circuit depth. Here we develop a class of ``mediated'' gates for spin qubits, which act on nonproximal spins via intermediate ancilla qubits. At the end of the operation, the ancillae return to their initial states. We show how these mediated gates can be used (1) to generate arbitrary quantum states and (2) to construct arbitrary quantum gates. We provide some explicit examples of circuits that generate common states [e.g., Bell, Greenberger-Horne-Zeilinger (GHZ), WWW, and cluster states] and gates (e.g., swap\sqrt{swap}swap​, swap, cnotcnotcnot, and Toffoli gates). We show that the depths of these circuits are often shorter than those of conventional swapswapswap-based circuits. We also provide an explicit experimental proposal for implementing a mediated gate in a triple-quantum-dot system.
Pairwise exchange couplings have long been the standard mechanism for entangling spin qubits in semiconductor systems. However, implementing quantum circuits based on pairwise exchange gates often requires a lengthy sequence of elementary gate operations. In this work, we present an alternative approach: multi-qubit entangling gate operations that simultaneously drive the exchange couplings between multiple pairs of spin qubits. We explore three spin qubit systems in linear or triangular configurations. We derive analytical expressions for these multi-exchange entangling operations and demonstrate how to use the resulting three-qubit gates to construct quantum circuits capable of generating standard entangled states such as GHZ and W states, and the Toffoli gate, by optimizing control parameters. Our results show that this multi-qubit strategy significantly reduces the number of required operations, offering a pathway to more efficient, shallower, and more coherent circuits for spin-qubit processors.
Near-term quantum computers often have connectivity constraints, i.e. restrictions, on which pairs of qubits in the device can interact. Optimally mapping a quantum circuit to a hardware topology under these constraints is a difficult task. While numerous approaches have been proposed to optimize qubit routing, the resulting gate count and depth overheads of the compiled circuits remain high due to the short-range coupling of qubits in many near-term devices. Resource states, such as Bell or Einstein-Podolsky-Rosen (EPR) pairs, can be used to mediate operations that facilitate long-range interactions between qubits. In this work, we studied some of the practical trade-offs involved in using resource states for qubit routing. We developed a method that leverages an existing state-of-the-art compiler to optimize the routing of circuits with both standard gates and EPR mediated remote controlled-NOT gates. This was then used to compile different benchmark circuits for a square grid topology, where a fraction of the qubits are used to store EPR pairs. We demonstrate that EPR-mediated operations can substantially reduce the total number of gates and depths of compiled circuits when used with an appropriate optimizing compiler that accounts for practical overheads. Our results highlight the relevance of developing efficient compilation tools that can integrate EPR-mediated operations.
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The Heisenberg exchange interaction between neighboring quantum dots allows precise voltage control over spin dynamics, due to the ability to precisely control the overlap of orbital wavefunctions by gate electrodes. This allows the study of fundamental electronic phenomena and finds applications in quantum information processing. Although spin-based quantum circuits based on short-range exchange interactions are possible, the development of scalable, longer-range coupling schemes constitutes a critical challenge within the spin-qubit community. Approaches based on capacitative coupling and cavity-mediated interactions effectively couple spin qubits to the charge degree of freedom, making them susceptible to electrically-induced decoherence. The alternative is to extend the range of the Heisenberg exchange interaction by means of a quantum mediator. Here, we show that a multielectron quantum dot with 50-100 electrons serves as an excellent mediator, preserving speed and coherence of the resulting spin-spin coupling while providing several functionalities that are of practical importance. These include speed (mediated two-qubit rates up to several gigahertz), distance (of order of a micrometer), voltage control, possibility of sweet spot operation (reducing susceptibility to charge noise), and reversal of the interaction sign (useful for dynamical decoupling from noise).
Large-scale Greenberger-Horne-Zeilinger~(GHZ) state is useful for quantum technologies but difficult to be prepared. Here, we propose fast measurement-based preparation of large-scale GHZ states by a four-qubit quantum phase gate with nuclear-spin qubits of alkaline-earth-like atoms, which is named as quantum ferromagnetic gate~(QFG) due to its analogy to the alignment of molecular magnetic moments in a classical magnet. A high-fidelity Rydberg-mediated QFG can be realized in a time of 6π/Ωm6π/Ω_{\text{m}}6π/Ωm​ with ΩmΩ_{\text{m}}Ωm​ the maximal Rydberg Rabi frequency. From a product state of three data atom and one ancilla atom, a gluing circuit with one QFG, two single-qubit gates, and a projective measurement of the ancilla can generate a 3-qubit GHZ state, and repetition of this gluing circuit can lead to 9, 27, 81, 243, ⋯\cdots⋯-qubit GHZ states. Analyses based on currently available techniques show that a 243-qubit GHZ state is realizable, and more qubits can be entangled with higher detection fidelity.