# Quantum Computing: First Simulations, Diagnostics and Another Material

Quantum Computers continue to make significant gains today including the successful simulation of a topological phase transition and reduction in the amount of power required to diagnose failures. As well as a new quantum material.

Researchers from Rice University have come up with an algorithm that could reduce the energy required to troubleshoot quantum computers, the next generation of computing expected to increase computation speeds by several orders of magnitude.

Quantum computers are powerful, but unruly and difficult to monitor. Their hardware still requires immensely cold temperatures and the entangled particles storing data (Qubits) are extremely sensitive to fluctuations in environmental conditions. On top of all this – the more useful a quantum computer becomes the harder it is to troubleshoot.

In a system with five qubits, the state can be represented by a 2-to-the-5 times 2-to-the-5 matrix, so it’s a 32-by-32 matrix.That’s not big. But in a 20-qubit system like the one at IBM, the state can be characterized by a million-by-million matrix. If we were taking full measurements with regular tomography techniques, we would need to poll the system roughly a million-squared times in order to get enough information to recover its state.Anastasios Kyrillidis, Assistant Professor of Computer Science

In order to solve this problem Professor Kyridillis and his team use quantum state tomography to reduce the complexity of incoming information. Just like medical tomography captures images of our body in slices quantum tomography captures snapshots of the quantum computer in different “states”.

When a quantum computer executes an algorithm, it starts at a specific state; think of it as the input to the algorithm.As the computer progresses through steps of the algorithm, it’s going through many states. The state at the very end is the answer to your algorithm’s question.Anastasios Kyrillidis, Assistant Professor of Computer Science

In order to reduce the amount of information required to process before validating this “final state” computer scientists deployed an algorithm known as Projected Factored Gradient Decent (ProjFGD).

The key to ProjFGD is “compressed sensing” which manages to reduce incoming information while sill guaranteeing accurate results. It is accomplished through understanding the constraints of signal transmission i.e. what features of the environment limit expression of the signal in certain ways? In so doing scientists were able to make accurate “assumptions” about the incoming data so they don’t need to process every single bit.

According to Kyrillidis this should reduce the number of measurements for a 20-qubit system to about a million from a million squared (a million times a million) which would mean a very significant decrease in the amount of processing required to troubleshoot a quantum computer.

Speaking of quantum operations, Canadian quantum computer firm D-Wave simulated a “topological phase transition” otherwise known as a transition from one “quantum state of matter” to the next. Essentially what they’ve done is simulate discoveries that lead to better quantum computers on the quantum computer itself.

Some proposals for quantum computation suggest that we use “alternate states of matter” to create advanced molecular circuit boards. Alternate states of matter, otherwise known as quantum states of matter demonstrate emergent geometric and/or periodic properties that cannot be explained by observing any of the individual particles alone.

By adjusting the temperature or amount/direction of magnetism surrounding a group of distinct compounds they appear to transform in lock-step, taking on particular formations or pulsing in periodic sequence. Such anomalous correlations can only be explained through invoking quantum mechanics for conventional relativity does not allow simultaneous communication across space and time.

What D-wave has managed to do with their quantum computer is perform calculations that simulate, mathematically, the transition from one quantum state of matter (i.e. formation, sequence) to the next. Which is called a “topological phase transition”

In a sense they are simulating the first “breathe” of a more advanced quantum computer (based on quantum states of matter) with a less advanced one (based on entangled photons). The practical implications of which are obvious.

Speaking of topology – recent research published in nature magazine demonstrates a new how material created from sputtering nanometre sized grains over top of an older quantum material made of selenium-bizmuth can improve memory storage.

By varying the size of each grain researchers were able to predictably alter electron flow throughout the material. This is another example of how certain conditions create emergent topological behavior that cannot be explained by conventional relativity alone.

“As the size of the grains decreased, we experienced what we call ‘quantum confinement’ in which the electrons in the material act differently, giving us more control over the electron behavior,” said the study’s co-author, Tony Low.

The new material is 18 times more efficient than our current processing/memory hardware.

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