Related papers: Pauli Partitioning with Respect to Gate Sets
In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction…
Quantum measurements can be described by operators that assign conditional probabilities to different outcomes while also describing unavoidable physical changes to the system. Here, we point out that operators describing information gain…
Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…
Recently, a purely quantum version of polar codes has been proposed in [1] based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as channel combining operation. Here, we…
How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation. We analyse a Floquet model with disorder, characterised by a…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms and will become more relevant as an essential building block for quantum error correction. However, mid-circuit…
Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
We propose a new fractional statistics for arbitrary dimensions, based on an extension of Pauli's exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space,…
We propose a new quantum computing formalism named Pauli quantum computing. In this formalism, we use the Pauli basis $I$ and $X$ on the non-diagonal blocks of density matrices to encode information and treat them as the computational basis…
In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in…
Assessment of practical quantum information processing (QIP) remains partial without understanding limits imposed by noise. Unfortunately, mere description of noise grows exponentially with system size, becoming cumbersome even for modest…
We generalize the polynomial-time outcome-complete simulation algorithm for stabilizer circuits in arXiv:2309.08676 to track global phases exactly, yielding what we call phased outcome-complete simulation. The original algorithm enabled…
The extraction of information from a quantum system unavoidably implies a modification of the measured system itself. It has been demonstrated recently that partial measurements can be carried out in order to extract only a portion of the…