Correcting non-independent and non-identically distributed errors with surface codes

A common approach to studying the performance of quantum error correcting
codes is to assume independent and identically distributed single-qubit errors.
However, realistic errors in experimental mult ...

The XYZ$^2$ hexagonal stabilizer code

We consider a topological stabilizer code on a honeycomb grid, the "XYZ$^2$"
code. The code is inspired by the Kitaev honeycomb model and is a simple
realization of a "matching code" discussed by Woot ...

Handling Leakage with Subsystem Codes

Leakage is a particularly damaging error that occurs when a qubit state falls
out of its two-level computational subspace. Compared to independent
depolarizing noise, leaked qubits may produce many mo ...

Quantum circuit for toric code state preparation via graph states

Given the wide applicability of topological states for fault-tolerant quantum
computation, an important outstanding question is how to generate these states
within the quantum circuit model, and if it ...

Sparse Quantum Codes from Quantum Circuits

We describe a general method for turning quantum circuits into sparse quantum
subsystem codes. The idea is to turn each circuit element into a set of
low-weight gauge generators that enforce the input ...

Stabilizer Slicing: Coherent Error Cancellations in LDPC Codes

Coherent errors are a dominant noise process in many quantum computing
architectures. Unlike stochastic errors, these errors can combine
constructively and grow into highly detrimental overrotations. ...

Fault-tolerant Compass Codes

We study a class of gauge fixings of the Bacon-Shor code at the circuit
level, which includes a subfamily of generalized surface codes. We show that
for these codes, fault tolerance can be achieved by ...

Direct measurement of Bacon-Shor code stabilizers

A Bacon-Shor code is a subsystem quantum error-correcting code on an $L
\times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually
inferred from the measurements of $(L-1)^2$ weight-2 ga ...

Universal fault-tolerant quantum computation with Bacon-Shor codes

We present a fault-tolerant universal gate set consisting of Hadamard and
controlled-controlled-Z (CCZ) on Bacon-Shor subsystem codes. Transversal
non-Clifford gates on these codes are intriguing in t ...

Optimal Bacon-Shor codes

We study the performance of Bacon-Shor codes, quantum subsystem codes which
are well suited for applications to fault-tolerant quantum memory because the
error syndrome can be extracted by performing ...