Related papers: Signed quantum weight enumerators characterize qub…
A method to compute the optimal success probability of discrimination of N arbitrary quantum states is presented, based on the decomposition of any N-outcome measurement into sequences of nested two-outcome ones. In this way the…
Magic State Distillation is considered to be one of the promising methods for supplying the non-Clifford resources required to achieve universal fault tolerance. Conventional MSD protocols implemented in surface codes often require multiple…
A complex projective $t$-design is a configuration of vectors which is ``evenly distributed'' on a sphere in the sense that sampling uniformly from it reproduces the moments of Haar measure up to order $2t$. We show that the set of all…
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this…
We give a general procedure for weight reducing quantum codes. This corrects a previous work\cite{owr}, and introduces a new technique that we call "coning" to effectively induce high weight stabilizers in an LDPC code. As one application,…
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…
Quantum state tomography (QST) is the procedure for reconstructing unknown quantum states from a series of measurements of different observables. Depending on the physical system, different sets of observables have been used for this…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
This paper develops an algorithmic approach for obtaining estimates of the weight enumerators of Reed-Muller (RM) codes. Our algorithm is based on a technique for estimating the partition functions of spin systems, which in turn employs a…
Identifying the boundary between classical and quantum computation is a central challenge in quantum information. In multi-qubit systems, entanglement and magic are the key resources underlying genuinely quantum behaviour. While…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
The n-qubit real equally weighted states are employed in some quantum algorithms including Deutsch-Jozsa, Grover, Simon, and so on. We qualitatively investigate the entanglement properties of n-qubit real equally weighted states. Firstly,…
Recently, Babenko and Lempitsky introduced Additive Quantization (AQ), a generalization of Product Quantization (PQ) where a non-independent set of codebooks is used to compress vectors into small binary codes. Unfortunately, under this…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels,…
We introduce magic measures to quantify the nonstabilizerness of multiqubit quantum gates and establish lower bounds on the $T$ count for fault-tolerant quantum computation. First, we introduce the stabilizer nullity of multi-qubit unitary,…
Fault-tolerant protocols enable large and precise quantum algorithms. Many such protocols rely on a feed-forward processing of data, enabled by a hybrid of quantum and classical logic. Representing the control structure of such programs can…
Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient…
The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozen of qubits. This success poses a strong demand on efficient and reliable methods for characterization and…
With the advent of practical quantum communication networks drawing closer, there is a growing need for reliable estimation protocols that can efficiently characterize quantum resources with minimum resource overhead requirement. A novel…