Related papers: Classification of Small Triorthogonal Codes
We consider geometric methods of ``rotating" the toric code in higher dimensions to reduce the qubit count. These geometric methods can be used to prepare higher dimensional toric code states using single shot techniques, and in turn these…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
Quantum error correction and fault-tolerance have provided the possibility for large scale quantum computations without a detrimental loss of quantum information. A very natural class of gates for fault-tolerant quantum computation is the…
Magic state distillation (MSD) is a quantum algorithm that enables performing logical non-Clifford gates with in principle arbitrarily low noise level. It is herein typically assumed that logical Clifford gates can be executed without…
Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error-correcting code. The recent discovery…
We show that the physical consistency of magic state distillation imposes new constraints on the weight enumerators of classical error-correcting codes. We establish that for $|T\rangle$-state distillation protocols based on linear…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct…
Reed-Muller codes are some of the oldest and most widely studied error-correcting codes, of interest for both their algebraic structure as well as their many algorithmic properties. A recent beautiful result of Saptharishi, Shpilka and Volk…
The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the…
Magic state distillation (MSD) is a purification protocol that plays a central role in fault tolerant quantum computation. Repeated iteration of the steps of a MSD protocol, generates pure single non-stabilizer states, or magic states, from…
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group S_n. The code corresponds to bases for the trivial representation, and all other irreducible…
Secure multi-party quantum computation (MPQC) protocol is a versatile tool that enables error-free distributed quantum computation to a group of $n$ mutually distrustful quantum nodes even when some of the quantum nodes do not follow the…
Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal…
In a model of fault-tolerant quantum computation with quick and noiseless polyloglog-time auxiliary classical computation, we construct a fault tolerance protocol with constant-space and $\widetilde{O}(\log N)$-time overhead, where…
A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential…
We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…
The physical symmetries of a system play a central role in quantum error correction. In this work we encode a qubit in a collection of systems with angular-momentum symmetry (spins), extending the tools developed in Phys. Rev. Lett. 127,…
Ternary quantum systems are being studied because these provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the…