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We introduce a class of 3D color codes, which we call stacked codes, together with a fault-tolerant transformation that will map logical qubits encoded in two-dimensional (2D) color codes into stacked codes and back. The stacked code allows…
We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX…
Various algorithms have been developed to simulate quantum circuits on classical hardware. Among the most prominent are approaches based on \emph{stabilizer decompositions} and \emph{tensor network contraction}. In this work, we present a…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
New families of classical and quantum optimal negacyclic convolutional codes are constructed in this paper. This optimality is in the sense that they attain the classical (quantum) generalized Singleton bound. The constructions presented in…
We present a set of efficiently implementable logical multi-qubit gates in concatenated quantum error correction codes using parity qubits. In particular, we show how fault-tolerant high-weight rotation gates of arbitrary angle can be…
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two…
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much…
We develop an analytical framework to study the synchronization of a quantum self-sustained oscillator to an external signal. Our unified description allows us to identify the resource on which quantum synchronization relies, and to compare…
The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control, and generates results in…
In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…
A common approach to the provably stable design of reactive behavior, exemplified by operational space control, is to reduce the problem to the design of virtual classical mechanical systems (energy shaping). This framework is widely used,…
This work presents a precise connection between Clifford circuits, Shor's factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all…
This manuscript introduces various notions of k-locality of stabilizer codes inherited from the associated stabilizer groups. A choice of generators for the group leads to a Hamiltonian with the code in its groundspace, while a Hamiltonian…
We present a novel formalism to both understand and construct mixers that preserve a given subspace. The method connects and utilizes the stabilizer formalism that is used in error correcting codes. This can be useful in the setting when…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…