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Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…
In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane curves. This problem is solved by applying the upper bound…
We present the bicycle architecture, a modular quantum computing framework based on high-rate, low-overhead quantum LDPC codes identified in prior work. For two specific bivariate bicycle codes with distances 12 and 18, we construct…
The performance of a quantum error-correction process is determined by the likelihood that a random configuration of errors introduced to the system will lead to the corruption of encoded logical information. In this work we compare two…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
Codes defined on graphs and their properties have been subjects of intense recent research. On the practical side, constructions for capacity-approaching codes are graphical. On the theoretical side, codes on graphs provide several…
We refine an old idea for performing fault-tolerant error correction in topological codes by simulating confining interactions between excitations. We implement confinement using an array of local classical processors that measure…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
We consider the surface code under errors featuring both coherent and incoherent components and study the coherence of the corresponding logical noise channel and how this impacts information-theoretic measures of code performance, namely…
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
In this paper we construct multidimensional codes with high dimension. The codes can correct high dimensional errors which have the form of either small clusters, or confined to an area with a small radius. We also consider small number of…
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…