Related papers: Lower Bounds on Stabilizer Rank
Measurement based quantum computing is preformed by adding non-Clifford measurements to a prepared stabilizer states. Entangling gates like CZ are likely to have lower fidelities due to the nature of interacting qubits, so when preparing a…
For a quantum state represented as an $n\times n$ density matrix $\sigma \in M_n$, let ${\cal S}(\sigma)$ be the compact convex set of quantum states $\rho = (\rho_{ij}) \in M_{m\cdot n}$ with the first partial trace equal to $\sigma$,…
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum…
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
We provide a first-order oracle complexity lower bound for finding stationary points of min-max optimization problems where the objective function is smooth, nonconvex in the minimization variable, and strongly concave in the maximization…
Quantum error correction (QEC) is a way to protect quantum information against noise. It consists of encoding input information into entangled quantum states known as the code space. Furthermore, to classify if the encoded information is…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
Stabilizer states admit compact classical descriptions, but many downstream tasks still require their full amplitude vectors. Since the output itself has size $2^n$, the main algorithmic question is whether one can materialize an $n$-qubit…
A fooling-set matrix has nonzero diagonal, but at least one in every pair of diagonally opposite entries is 0. Dietzfelbinger et al. '96 proved that the rank of such a matrix is at least $\sqrt n$. It is known that the bound is tight (up to…
A lower bound on the amount of noise that must be added to a GHZ-like entangled state to make it separable (also called the random robustness) is found using the transposition condition. The bound is applicable to arbitrary numbers of…
Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser…
In quantum computing, non-stabilizerness -- the magic -- refers to the computational advantage of certain quantum states over classical computers and is an essential ingredient for universal quantum computation. Employing the second order…
The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state $\psi_I$ may need so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S. Lloyd,…
The No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings, 2014 -- which posits the existence of a local Hamiltonian with a super-constant quantum circuit lower bound on the complexity of all low-energy states --…
Quantum Information scrambling (QI-scrambling) is a pivotal area of inquiry within the study of quantum many-body systems. This research derives mathematical upper and lower bounds for the scrambling rate by applying the Maligranda…
Quantum linear system (QLS) solvers are a fundamental class of quantum algorithms used in many potential quantum computing applications, including machine learning and solving differential equations. The performance of quantum algorithms is…
Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
State-of-the-art noisy intermediate-scale quantum computers require low-complexity techniques for the mitigation of computational errors inflicted by quantum decoherence. Symmetry verification constitutes a class of quantum error mitigation…