Related papers: Computation of a new error bound for tensor comple…
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…
Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
We consider the tensor equation whose coefficient tensor is a nonsingular M-tensor and whose right side vector is nonnegative. Such a tensor equation may have a large number of nonnegative solutions. It is already known that the tensor…
Characterization of noise in current near-term quantum devices is of paramount importance to fully use their computational power. However, direct quantum process tomography becomes unfeasible for systems composed of tens of qubits. A…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
Parameterised quantum circuits (PQCs) hold great promise for demonstrating quantum advantages in practical applications of quantum computation. Examples of successful applications include the variational quantum eigensolver, the quantum…
Recently, many structured tensors are defined and their properties are discussed in the literature. In this paper, we introduce a new class of structured tensors, called exceptionally regular tensor, which is relevant to the tensor…
Uncertainty quantification (UQ) for open-ended language generation remains a critical yet underexplored challenge, especially under black-box constraints where internal model signals are inaccessible. In this paper, we introduce…
We show that for all $\varepsilon>0$, for sufficiently large $q\in\mathbb{N}$ power of $2$, for all $\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least…
The use of analog classical systems for computation is generally thought to be a difficult proposition due to the susceptibility of these devices to noise and the lack of a clear framework for achieving fault-tolerance. We present…
This paper is concerned with the hard thresholding operator which sets all but the $k$ largest absolute elements of a vector to zero. We establish a {\em tight} bound to quantitatively characterize the deviation of the thresholded solution…
In the Tensor PCA problem introduced by Richard and Montanari (2014), one is given a dataset consisting of $n$ samples $\mathbf{T}_{1:n}$ of i.i.d. Gaussian tensors of order $k$ with the promise that $\mathbb{E}\mathbf{T}_1$ is a rank-1…
We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we…
In this work, we revisit algorithms for Tensor PCA: given an order-$r$ tensor of the form $T = G+\lambda \cdot v^{\otimes r}$ where $G$ is a random symmetric Gaussian tensor with unit variance entries and $v$ is an unknown boolean vector in…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…
A bound on the error introduced by truncating a quantum addition is given. This bound shows that only a few controlled rotation gates will be necessary to get a reliable computation.
We consider the problem of implementing distributed protocols, despite adversarial channel errors, on synchronous-messaging networks with arbitrary topology. In our first result we show that any $n$-party $T$-round protocol on an undirected…
Consider a 2-D square array of qubits of extent $L\times L$. We provide a proof that the minimum weight perfect matching problem associated with running a particular class of topological quantum error correction codes on this array can be…