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arXiv:2101.09544 · Physical Review A

Transmission-based tomography for spin qubits

Amritesh Sharma, Ashwin A. Tulapurkar

Published May 26, 2021• 4 citations
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Abstract

We consider a system of static spin qubits embedded in a one-dimensional spin-coherent channel and develop a scheme to readout the state of one and two qubits separately. We use unpolarized flying qubits for this purpose that scatter off from the static qubits due to localized Heisenberg exchange interaction. Analyzing the transmission coefficient as a function of density matrix elements along with additional unitary gates we reconstruct the state of static qubits.

DOI
10.1103/physreva.103.052430

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We consider a system of static spin qubits embedded in a one-dimensional spin-coherent channel and develop a scheme to readout the state of one and two qubits separately. We use unpolarized flying qubits for this purpose that scatter off from the static qubits due to localized Heisenberg exchange interaction. Analyzing the transmission coefficient as a function of density matrix elements along with additional unitary gates we reconstruct the state of static qubits.
We propose a theoretical protocol for reconstructing the density matrix of a single-electron spin qubit using spin-polarized transport. The system consists of a quantum dot coupled to ferromagnetic reservoirs and subject to a magnetic field lying in the xyxyxy plane of the Bloch sphere. Spin-dependent tunneling events measured along the x±x\pmx±, y±y\pmy±, and z±z\pmz± quantization axes give rise to probability distributions that encode the quantum state of the qubit. The open-system dynamics are described using a Lindblad master equation, which captures the time evolution of the spin under continuous coupling to the reservoirs. By counting tunneling events for four different magnetic alignments, we formulate a scheme for reconstructing the full density matrix of the qubit. The resulting simulation data are analyzed using machine-learning techniques to process the measured probability distributions and infer the corresponding density matrix elements. The proposed model enables complete access to the open-system density matrix, including both population probabilities and relative phase information. Successful state reconstruction demonstrates the validity and robustness of the approach, highlighting its applicability to experimentally accessible spin-transport platforms.
We present a scheme for full quantum state tomography tailored for two spin qubits in a double quantum dot. A set of 15 quantum states allows to determine the density matrix in this two-qubit space by projective measurement. In this paper, we choose a set gained from mutually unbiased bases. We determine how those 15 projections can be represented by charge measurements after a spin-to-charge conversion and the application of quantum gates. The quantum gates include exchange-based gates as well as rotations by electron spin resonance (ESR). We assume the experimental realization of ESR operations to be more difficult than the exchange gate operation with respect to fidelity and speed. Therefore it is an important result that the ESR gates can be limited to a $\ensuremath{\pi}/2$ rotation for one of the electron spins per measurement.
We show how the spin independent scattering between two identical flying qubits can be used to implement an entangling quantum gate between them. We consider one dimensional models with a delta interaction in which the qubits undergoing the collision are distinctly labeled by their opposite momenta. The logical states of the qubit may either be two distinct spin (or other internal) states of a fermion or a boson or two distinct momenta magnitudes of a spinless boson. Our scheme could be added to linear optics-like quantum information processing to enhance its efficiency, and can also aid the scaling of quantum computers based on static qubits without resorting to photons. Three distinct ingredients -- the quantum indistinguishability of the qubits, their interaction, and their dimensional confinement, come together in a natural way to enable the quantum gate.
We present a method for encoding and transporting qubits within a dimerized Heisenberg spin-12\frac{1}{2}21​ chain. Logical qubits are localized at the domain walls that separate the two possible dimerized states. The domain walls can be moved to produce ``flying spin qubits.'' The topological nature of these states makes them stable against local perturbations of the exchange profile. Pairs of domain walls can be used to generate Einstein-Podolsky-Rosen pairs of entangled qubits. We discuss speed limitations within an exactly solvable three-spin model and describe a possible physical realization using quantum dot arrays.
We show that the state of a flying qubit may be transferred to a chain of identical, (near) ferromagnetically polarised, but non-interacting, static spin-1/2 particles in a passive way. During this process the flying qubit is coherently polarised, emerging in the direction of the majority static spins. We also show that this process is reversible for at least two flying qubits injected sequentially and thus has the potential to be exploited as a passive quantum memory to encode the flying qubits without the necessity of resetting between successive encoding operations. We show that the quantum information may be spread over many static spins in the memory chain, making the mechanism resistent to spin decoherence and other imperfections. Among some potential architectures, we discuss implementing the memory in a photonic waveguide embedded with quantum dots, which is resilient to various possible errors.