Related papers: Graphical Stabilizer Decompositions for Multi-Cont…
Fathoming out quantum state space is a challenging endeavor due to its exponentially growing dimensionality. At the expense of being bound in its expressiveness, the discrete and finite subspace of graph states is easier to investigate via…
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…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
We introduce a construction for protocols for fault-tolerant quantum computing based on code concatenation and transversal gates. These protocols can be interpreted as families of quantum circuits of low-weight stabilizer measurements…
Quantum computing is an emerging technology in which quantum mechanical properties are suitably utilized to perform certain compute-intensive operations faster than classical computers. Quantum algorithms are designed as a combination of…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
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…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
Universal quantum computation requires the implementation of a logical non-Clifford gate. In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical $T$ and $T^{-1}$ gates. For example, this could…
Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles…
We assess numerical stabilization methods employed in fermion many-body quantum Monte Carlo simulations. In particular, we empirically compare various matrix decomposition and inversion schemes to gain control over numerical instabilities…
The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
Cluster states and graph states in general offer a useful model of the stabilizer formalism and a path toward the development of measurement-based quantum computation. Their defining structure - the stabilizer group - encodes all possible…
Quantum random access memories (QRAMs) are pivotal for data-intensive quantum algorithms, but existing general-purpose and domain-specific architectures are hampered by a critical bottleneck: a heavy reliance on non-Clifford gates (e.g.,…
As quantum processors grow in scale and reliability, the need for efficient quantum gate decomposition of circuits to a set of specific available gates, becomes ever more critical. The decomposition of a particular algorithm into a sequence…
Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for…