- QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE HOW TO
- QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE CODE
We find that all the appropriate qubits are active at the right moment by choosing two diagonal planes of live qubits for each code. The controlled-controlled-phase gate is made at the cubic region where the codes intersect.
QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE CODE
The second code has rough boundaries on the left and right sides of its volume and moves upward in the figure. The first code that has rough boundaries on the top and bottom of its volume and the live plane of qubits moves right across the page. We omit the third code as it can travel in parallel to one of the codes already shown. The figure shows a three-dimensional spacetime diagram of two overlapping codes moving orthogonally to one another. We show a system that satisfies all of these constraints in Fig.
Last, if we only maintain a two-dimensional array of the three-dimensional system, it is important that all the qubits that need to interact with one another must be live at the same time. If we only maintain a two-dimensional array of qubits, the plane must contain two distinct primal boundaries that are well separated by two distinct dual boundaries to support the encoded information. If we couple ancilla to the surface code to recover the topological cluster state as specified above, then the rough (smooth) boundaries of the surface code give rise to the primal (dual) boundaries of the cluster state. We require two types of surface code boundaries rough and smooth ( 31). We consider again the cluster state in terms of the three-dimensional surface code. More precisely, they constrain the temporal directions of the model. We first point out that the orientation of boundaries of the topological cluster state is important for the transmission of logical information ( 29). There are several constraints the system must satisfy if we realize a controlled-controlled-phase gate with a two-dimensional system. We can now explain how we can embed the three-dimensional surface code that performs a non-Clifford gate in two dimensions. As we will see, the cluster state offers a natural static language to characterize the dynamical quantum process using a time-independent entangled resource state. The process is well characterized by connecting the surface code with the topological cluster-state model ( 9, 25) a measurement-based model with a finite threshold error rate, below which it will function reliably at a suitably large system size. This is in contrast to the more conventional approach where we make stabilizer measurements on static quantum error–correcting codes to identify errors. Notably, in our scheme, error-detecting measurements are realized dynamically. It is remarked in ( 16) that we should understand fault-tolerant quantum operations, not in terms of quantum error–correcting codes but, instead, by the processes they perform. However, these proposals are unlikely to function reliably as the size of the system diverges. In the past, there has been a significant effort to realize a non-Clifford gate with two-dimensional quantum error–correcting codes ( 22– 24). The non-Clifford gate presented here circumvents fundamental limitations of two-dimensional models ( 17– 21) by dynamically preparing a three-dimensional system using a two-dimensional array of active qubits. As the gate circumvents the need for magic-state distillation, it may reduce the resource overhead of surface-code quantum computation considerably. We therefore expect it to be amenable with near-future technology. Our gate is completed using parity checks of weight no greater than four. These decoding algorithms allow us to draw upon the advantages of three-dimensional models using only a two-dimensional array of live qubits. An important component of the gate is a just-in-time decoder. The operation uses both local transversal gates and code deformations over a time that scales with the size of the qubit array. This alleviates the need for distillation or higher-dimensional components to complete a universal gate set.
QUANTUM ERROR CORRECTION THRESHOLD FOR SURFACE CODE HOW TO
Here we show how to perform a fault-tolerant non-Clifford gate with the surface code a quantum error-correcting code now under intensive development. Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture.