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We study the classical simulation complexity in both the weak and strong senses, of matchgate (MG) computations supplemented with all combinations of settings involving inclusion of intermediate adaptive or nonadaptive computational basis…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
Let $G$ be a finite group acting on $\mathbb{C}^N$. We study the problem of identifyng the class in $\mathbb{C}^N / G$ of a given signal: this encompasses several types of problems in signal processing. Some instances include certain…
We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to…
We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality in general. We are interested in the…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
The digital quantum simulation of lattice gauge theories is expected to become a major application of quantum computers. Measurement-based quantum computation is a widely studied competitor of the standard circuit-based approach. We…
We show that recent experiments in hybrid qubit-oscillator devices that measure the phase-space characteristic function of the oscillator via the qubit can be seen through the lens of functional calculus and path integrals, drawing a clear…
In this paper we continue to explore "hybrid" quantum circuit models in one-dimension with both unitary and measurement gates, focussing on the entanglement properties of wavefunction trajectories at long times, in the steady state. We…
We describe a method to use measurements and correction operations in order to implement the Clifford group in a stabilizer code, generalising a result from [Bombin,2011] for topological subsystem colour codes. In subsystem stabilizer codes…
Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…