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We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
A recent mathematical framework for optimizing resistor networks to achieve values in the M{\Omega} through G{\Omega} levels was employed for two specific cases. Objectives here include proof of concept and identification of possible…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
A method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a…
We design forward and backward fault-tolerant conversion circuits, which convert between the Steane code and the 15-qubit Reed-Muller quantum code so as to provide a universal transversal gate set. In our method, only 7 out of total 14 code…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Simulation of stabilizer circuits is a well-studied problem in quantum information processing, with a number of highly optimized algorithms available. Yet, we argue that further improvements can arise from the theoretical structure of…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
Perturbation theories provide valuable insights on quantum many-body systems. Systems of interacting particles, like electrons, are often treated perturbatively around exactly solvable Gaussian points. Systems of interacting qubits have…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization.…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
A general optimization framework is proposed for simultaneously transmitting and reflecting reconfigurable surfaces (STAR-RISs) with coupled phase shifts, which converges to the Karush-Kuhn-Tucker (KKT) optimal solution under some mild…
The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the…
$\textit{Normalizer circuits}$ [1,2] are generalized Clifford circuits that act on arbitrary finite-dimensional systems $\mathcal{H}_{d_1}\otimes ... \otimes \mathcal{H}_{d_n}$ with a standard basis labeled by the elements of a finite…
Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
The development of practical methods for synthesis and verification of complex photonic circuits presents a grand challenge for the nascent field of quantum engineering. Of course, classical electrical engineering provides essential…
We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the…
We propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code;…