Quantum Information Channels and Distributed Quantum Computing

Information Theory (Winter 2020)
Authors: Matthew Radzihovsky, Mason Swofford, Alex Fuster

The state of quantum computing has rapidly advanced in recent years due to widespread public attention and its allure for solving problems such as integer factorization, faster than linear search, and estimating the ground state energy in complex molecules. If achieved, quantum computers will revolutionalize the computational world which has applications in medicine, cryptography, and machine learning and artificial intelligence among other industries. There has been a race to create quantum computers with numerous quantum bit (qubit) candidates ranging from electron spins, photons, ions, or even topological qubits. This race has been taking place at university labs led by CalTech, Maryland, Stanford, as well as frontier companies such as Google, Microsoft, and Honeywell.

In spite of the large advances in quantum computing, the computing hardware is still at a small scale due to challenges unique to quantum hardwares originating from gate errors and decoherence. As a result, individual quantum computers are limited to solving problems involving few qubits and limited number of gate operations. Some of the effects of decoherence and gate errors can be mitigated by Quantum Error Correction (QEC), however, know QEC algorithms requires large numbers of ancilla qubit overhead to be feasible in current systems. To solve these issues, computing over a network of quantum computers connected by quantum channels has been proposed.

Distributed quantum computing (DQC) is a means of leveraging the computational power of a quantum network in order to solve a problem too large for any single quantum computer. Each node on a quantum network is connected via a classical and quantum channel and manages its own classical register for storing bits of information such as quantum system measurements. Nodes may not modify or interact with qubits that they do not manage without physically receiving the qubits from a different node, performing teleportation, or via non-local operations.

Current experimental distributed quantum computing is quite primitive. There have been demonstrations of simple protocols such as quantum teleportation proving the possibility of more advanced quantum computing. However, this next step of performing more advanced algorithms of larger entangled systems has yet to be demonstrated.

Here we give a distributed quantum computing demonstration showing how distributed quantum computing protects against a middle-man attack.

Middle-Man Attack Demo:

Middle-Man Attack is a demonstration of quantum networks resistance against intruders. This demo extends superdense coding by allowing two agents, Alice and Bob, to send numerous classical bits using bell state pairs. However, in this protocol, there is an intruder agent, Eve, who attempts to intercept and measure the information. Despite successfully intercepting Alice and Bob’s message, due to Eve not sharing a bell state pair with Alice, Eve only measures random noise. Moreover, Bob is able to detect if an intruder has intercepted the message.

The middle-man attack involves four agents, Alice, Bob, Charlie, and Eve. Following the superdense coding protocol, Charlie prepares the bell state pair and distributes the entangled qubits to Alice and Bob, where Alice operates on her bell state pair from Charlie based on the classical bits she wishes to send to Bob, and then sends her bell state pair to Bob. This process can be repeated for any number of classical bits that Alice wishes to send.

The attack occurs when Eve intercepts Alice’s qubits on the way to Bob, measures the qubits, and re-transmits them to Bob. Due to Eve not having a bell state pair and her measurement collapsing the state of the qubit, Eve only intercepts random noise, while Bob can immediately detect the presence of an intruder.

The quantum circuit is as follows:

The remarkable protection with quantum communication is that if a middle-man (Eve) tries to intercept the qubit and learn the information, since she does not have a entangled bit, she only gets random noise. Furthermore, Bob receives a corrupted qubit and is thus alerted to an intruder. Therefore, contrary to classical information channels, this quantum information channel is protected against middle-man attacks and alerts the parties of an intruder.

To visualize this, consider this simulation of a middle man attack using an image (using pyQuil). We have a fun random picture that we wish to send each pixel from Alice to Bob. However, there is a intruder Eve who intercepts and measures the qubits. Notice that Eve can only recreate random information, while Bob only receives half the qubits, so that he is alerted to the intruder Eve.

Activity: Information Channels

For our activity at Ravenswood Middle School, we planned to have students learn about error correcting codes for information channels which translates to quantum channels and eventually distributed quantum computing. Unfortunately, due to COVID-19 we were unable to follow through on this activity, but we are hoping with the linked video and blog post students will get a taste of information theory and the possibilities of quantum computers and distributed quantum computing.

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