CLIFFORD GROUP QUANTUM ERROR CORRECTION CODE
“The next step is to simulate the code and see how well it works in practice.” “I’ve shown this to work theoretically, mathematically,” says Brown. Over a period of time, the three surface codes replicate the three-dimensional code that can perform the non-Clifford gate function(s). The process is repeated over and over on the fly with the help of just-in-time gauge fixing, a procedure for stacking together the two-dimensional slices onto a chip, as well as dealing with any occurring errors. This is carried out by taking thin slices of the 3D surface code and collapsing them down into a 2D space. The non-Clifford gate uses three overlapping copies of the surface code that locally interact over a period of time. The three codes interact together during each step as the bottom code is passed under the other two to produce the two-dimensional gate. This diagram illustrates the staged progression of one surface code being slid underneath the other two surface codes over time. “This has opened up possibilities we didn’t have before.”
“Given it is understood to be impossible to use two-dimensional code like the surface code to do the work of a non-Clifford gate, I have used a three-dimensional code and applied it to the physical two-dimensional surface code scheme using time as the third dimension,” explains Brown. A paper he published on this development appeared in Science Advances on 22 May. To overcome this problem, Brown has developed a new type of non-Clifford-gate error-correcting method that removes the need for overhead-heavy distillation. “However, the combination of Clifford and non-Clifford gates can be prohibitive because it eats up so much of a quantum computer’s resources that there’s little left to deal with the problem at hand.” “Without magic-state distillation or its equivalent, quantum computers are like electronic calculators without the division button they have limited functionality,” says Benjamin Brown, an EQUS researcher at the University of Sydney’s School of Physics. One of these, the Clifford gate set, must work in combination with magic-state distillation-a purification protocol that uses multiple noisy quantum states to perform non-Clifford gate operations. Physicists describe two types of quantum gate operations (distinguished by their different mathematical approaches) that are necessary to achieve universal computing. Classical computing analogues would be AND gates, XOR gates, and the like. The benefit: When qubits are measured, they reveal errors in neighboring qubits.įor a quantum computer to tackle complicated tasks, error-correction codes need to be able to perform quantum gate operations these are small logic operations carried out on qubit information that, when combined, can run algorithms. The surface code uses the phenomenon known as entanglement (quantum connectivity) to enable single qubits to share information with other qubits on a lattice layout. That’s because of its robustness and the fact that it’s well suited to being set out on a two-dimensional plane (which makes it amenable to being laid down on a chip). When it comes to correcting errors arising during quantum operations, an error-correction method known as the surface code has drawn a lot of research attention.
CLIFFORD GROUP QUANTUM ERROR CORRECTION FREE
“My approach to suppressing errors could free up a lot of the hardware from error correction and will allow the computer to get on with doing useful stuff.”
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