Related papers: Magic state distillation with punctured polar code…
Virtual distillation has been proposed as an error mitigation protocol for estimating the expectation values of observables in quantum algorithms. It proceeds by creating a cyclic permutation of $M$ noisy copies of a quantum state using a…
Triorthogonal matrices were introduced in Quantum Information Theory in connection with distillation of magic states (Bravyi and Haah (2012)). We give an algorithm to construct binary triorthogonal matrices from binary self-dual codes.…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
Given stabilizer operations and the ability to repeatedly prepare a single-qubit mixed state rho, can we do universal quantum computation? As motivation for this question, "magic state" distillation procedures can reduce the general…
We provide a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation…
This paper proposes a method to optimize communication code rates via the application of neural polar decoders (NPDs). Employing this approach enables simultaneous optimization of code rates over input distributions while providing a…
We prove that families of polar codes with multiple kernels over certain symmetric channels can be viewed as polar decreasing monomial-Cartesian codes, offering a unified treatment for such codes, over any finite field. We define decreasing…
We construct new families of multi-error-correcting quantum codes for the amplitude damping channel. Our key observation is that, with proper encoding, two uses of the amplitude damping channel simulate a quantum erasure channel. This…
The polar codes are proven to be capacity-achieving and are shown to have equivalent or even better finite-length performance than the turbo/LDPC codes under some improved decoding algorithms over the additive white Gaussian noise (AWGN)…
The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{N}$ is considered. The sequence of channels is assumed to be completely known to both the…
Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can…
In this paper, we study the connection between polar codes and product codes. Our analysis shows that the product of two polar codes is again a polar code, and we provide guidelines to compute its frozen set on the basis of the frozen sets…
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…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Magic states are a scarce resource for two-dimensional qubit stabilizer codes. Magic state cultivation was recently proposed to reduce the cost of magic state preparation by measuring the transversal Clifford operator of the color code.…
We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density…
This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation…
The polar transformation of a binary erasure channel (BEC) can be exactly approximated by other BECs. Ar{\i}kan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class…
Unrolling a decoding algorithm allows to achieve extremely high throughput at the cost of increased area. Look-up tables (LUTs) can be used to replace functions otherwise implemented as circuits. In this work, we show the impact of…
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…