# Research Plan

January 15, 2016

Advances in the manufacturing of semiconductor structures have allowed observations of different types of electronic spin qubits. These systems are potentially useful for the construction of a quantum computer and provide insight into many-body entanglement, an important feature for quantum computation. However, current means of entangling the qubits are limited to extremely short distances.

This research project opens a new direction in the field by exploring the idea of performing a joint measurement on spatially separated electronic spins with transport electrons in a nearby conductance channel. A joint measurement on multiple qubits gives information about the system without revealing the individual state of each qubit. These joint measurements can be used to entangle non-interacting qubits and form the basis of fault-tolerant error correction procedures that are not currently accessible in solid-state spin qubit systems.

Electrostatic coupling between the qubits and conductance channel create a scattering potential for transport electrons that depends on the spin states of the trapped electrons. Transmission resonances therefore depend on the joint state of all trapped spins. In the case of two qubits and transport electrons injected at a certain energy, there is a resonant height of the symmetric double-barrier potential such that transmission is 100%. By tuning the couplings with voltage gates such that a barrier is zero if its spin is down, and at resonant height if its spin is up, a measurement of transmission results either in 0 or 1. This joint measurement indicates whether both spins are in the same direction, but does not distinguish between whether they are both up or both down.

This resonant tunneling scheme along with ancilla spin can be used to entangle spatially separated spins, an idea in linear optics from the Knill-Laflamme-Milburn proposal. It is also important to note the essential role of parity measurement in quantum error correction such as in the four-qubit joint measurement. Typically, joint measurements are envisioned as being performed by multiple two-qubit operations between data qubits and ancillas. The direct approach proposed here would eliminate simplify the process with performing the joint measurement only once, and remove the requirement that ancillas and data qubits be in close range.

This project will analyze the conditions that must be satisfied before joint measurements before they can actually be implemented in experiment. The research objective is to calculate the requirements for measurements to distinguish between states of multi-spin system without resolving the individual states. This involves modelling the potential, the width of resonance, the energy spread of transport electrons, etc. Furthermore, the sensitivity of joint measurement to realistic imperfections will have to be calculated. This involves considering imprecise gate voltages, noise, decoherence, etc. The capabilities of multi-qubit joint measurements will also be considered – how to create highly entangled multi-qubit states when one has direct access to multi-qubit joint measurements.

To model the potential barrier, begin with transfer matrix calculations for a one-dimensional scattering potential. A square-barrier potential model will be considered for preliminary results. Then, a realistic model of the potential with detailed device modelling will be considered.

The important research question to answer is what conditions on inter-qubit distances, barrier heights, and incident energies allow good distinguishability between even and odd parity states while also taking effects of disorder (high-frequency components, dephasing noise) into account. An analysis will be conducted on the effect of varying different parameters on transmission. When there is one barrier present, transmission should be nearly zero. On the other hand, when both barriers are present, transmission should be nearly 100%. Then extend to considering the capabilities of N-qubit parity measurements.

The goal is to calculate the theoretical conditions for performing such a measurement and it is expected to model potential accurately. This project is theoretical in nature and thus there are no experimental risks or safety precautions applicable.

This work is important scientifically because the combination of resonant tunneling and measurement-based quantum information processing in the context of each other will have direct applications in quantum information as well as studies of many-body entanglement.

The end of Moore’s law is predicted to occur within 10 years due to fundamental limitations in silicon-based computing. Quantum computation offers significant advantages because they are able to solve problems that are infeasible for classical computers. Efficiently simulating quantum environments will have profound impacts in our understanding of physics, chemistry, and molecular biology. Factoring large integers is one of the fundamental building blocks to encryption today. Quantum computers will bring about new, better means to keep communication secure. Combinatorial optimization has important applications in operations research, artificial intelligence, machine learning, and software engineering.

Bibliography

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Knill, E., Laflamme, R., & Milburn, G. J. (2001). A scheme for efficient quantum computation with linear optics. *Nature*, *409*.

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