Related papers: Low-depth random Clifford circuits for quantum cod…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by…
Here we revisit one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating every eigenvalue of an $n$-qubit Pauli noise channel to error $\epsilon$. Prior work [14] proved no-go theorems for this…
We introduce the domain wall color code, a new variant of the quantum error-correcting color code that exhibits exceptionally high code-capacity error thresholds for qubits subject to biased noise. In the infinite bias regime, a…
Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics. Unscrambling this information is possible given perfect knowledge of the…
We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a…
We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find…
We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
We study quantum networks with tree structures, in which information propagates from a root to leaves. At each node in the network, the received qubit unitarily interacts with fresh ancilla qubits, after which each qubit is sent through a…
Quantum computers have enabled solving problems beyond the current computers' capabilities. However, this requires handling noise arising from unwanted interactions in these systems. Several protocols have been proposed to address efficient…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
We investigate super dense coding in the presence of noise, i.e. the subsystems of the entangled resource state have to pass a noisy unital quantum channel between the sender and the receiver. We discuss explicitly the case of Pauli…
We present relaxed criteria for quantum error correction which are useful when the specific dominant noise process is known. These criteria have no classical analogue. As an example, we provide a four-bit code which corrects for a single…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved.…
Transversal encoded gatesets are highly desirable for fault tolerant quantum computing. However, a quantum error correcting code which exactly corrects for local erasure noise and supports a universal set of transversal gates is ruled out…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…