January 28, 2016

__Quantum physics affects everyone in their daily lives. It is the foundation for most technologies around us, especially computers. Computers have drastically changed our society in the past century. They are present everywhere, solving problems efficiently and speeding up our technological developments. Utilizing the connections between these computers demonstrates the power of the Internet. Today, I have access to the largest library of knowledge on my desk and in my pocket. I can communicate with almost anyone in a matter of minutes.__

Moore’s law describes the doubling of computing power every year through scaling down the size of transistors. It is remarkable to think that the computer in your cell phone is more powerful than all of NASA’s computers when they landed astronauts on the moon. However, Moore’s law is predicted to end within a decade. Computer power is already slowing down due to fundamental limitations in silicon-based computing from the laws of thermodynamics and quantum mechanics. We are at another paradigm shift in computation.

Quantum mechanics is weird. Objects exist in a state of uncertainty until we make an observation. Distant particles appear to “communicate” with each other instantaneously. Why not take advantage of these new rules in a different kind of computer? This was the proposal of the great physicist Richard Feynman when he noticed that quantum systems are difficult to model with classical computers. A quantum computer would compute by the laws of quantum mechanics instead of the laws of classical physics and offer significant advantages.

Quantum computers can solve problems that are infeasible for classical computers. Being able to factor integers efficiently has profound consequences. Our bank accounts, emails, and other communications are kept secure through the use of protocols like RSA and Diffie-Hellman. They are based on the observation that factoring large integers is an intractable problem for classical computers. Quantum computers offer an exponential speed increase as demonstrated by Shor’s algorithm, but will also bring about better means to keep communication secure.

Combinatorial optimization has important applications in operations research, artificial intelligence, machine learning, and software engineering. Using quantum computers, we can also efficiently simulate quantum environments with significant applications in our understanding of physics, chemistry, and molecular biology.

Quantum computers have powerful capabilities which make them fascinating, but the interesting problem is how to build one. One of the biggest obstacles in building quantum computers is decoherence and noise. Quantum error-correcting codes are essential to fault-tolerant systems and this is a project I’m working on: making entanglement and quantum error correction more efficient.

Current means of entangling qubits are limited to extremely short distances. I am exploring the theoretical conditions of performing a joint measurement on qubits in a semiconductor structure using transport electrons in a nearby channel.

The basic idea of a joint measurement is to perform a measurement on the system without knowing individual states. These joint measurements can be used to entangle qubits and form the basis of fault-tolerant error correction procedures that are currently not accessible in experiment. Coupling between the qubits and conductance channel creates a scattering potential for transport electrons that depends on the spin states of the trapped electrons. Transmission amplitudes therefore depend on the joint state of all trapped spins.

For two qubits, we couple them to a conductance channel such that when they are pointing “up”, a potential barrier is on and when they are pointing “down”, there is no potential barrier. Using a resonant tunneling scheme, we can find conditions in which when both barriers are on or both barriers are off, there is a transmission of almost 1. This corresponds to the case when both qubits are pointing in the same direction. When only one barrier is on, transmission is reduced to almost 0 corresponding to the case when the qubits are pointing in opposite directions. We can therefore measure this property of the system without knowing the individual state of a qubit.

Furthermore, the sensitivity of performing a joint measurement to realistic imperfections will have to be calculated. This involves considering imprecise gate voltages, high-frequency components, and dephasing noise. 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.

The important question in this project is to find the conditions on inter-qubit distances, barrier heights, and incident energies that allow good distinguishability between even and odd parity states while also taking effects of disorder into account.

The obstacle of decoherence is not easily overcome. There is significant research going into physically realizing quantum computers. New algorithms will have to be devised to take advantage of the new capabilities offered by quantum computers. Although much work has yet to be done, the potential benefits are enormous. The second quantum revolution will transform our society as much as how modern technology forms the basis of our work today.

**Bibliography**

Ambainis, Andris. “What Can We Do with a Quantum Computer?” *Institute for Advanced Study*. Institute for Advanced Study, n.d. Web. 28 Jan. 2016. (https://www.ias.edu/ias-letter/ambainis-quantum-computing).

Hagar, Amit, and Michael Cuffaro. “Quantum Computing.” *Stanford Encyclopedia of Philosophy*. Summer 2015 ed. N.p.: Stanford University, 2006. N. pag. Print.

Vazirani, Umesh. “Quantum Computation.” *Computer Science Division*. UC Regents, n.d. Web. 28 Jan. 2016. (https://www.cs.berkeley.edu/~vazirani/f04quantum/quantum.html).

Wang, Yazhen. “Quantum Computation and Quantum Information.” *Statistical Science* 27.3 (2012): n. pag. Print.