Related papers: Pauli Partitioning with Respect to Gate Sets
Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
We study measurements of the unitary generalization of Pauli operators. First, an analytical (constructive) solution to the eigenproblem of these operators is presented. Next, in the case of two subsystems, the Schmidt form of the…
Transformations which convert between Fermionic modes and qubit operations have become a ubiquitous tool in quantum algorithms for simulating systems. Similarly, collections of Pauli operators might be obtained from solutions of non-local…
The Pauli measurements (the measurements that can be performed with Clifford operators followed by measurement in the computational basis) are a fundamental object in quantum information. It is well-known that there is no assignment of…
As quantum computers approach the fault tolerance threshold, diagnosing and characterizing the noise on large scale quantum devices is increasingly important. One of the most important classes of noise channels is the class of Pauli…
A variety of quantum algorithms employ Pauli operators as a convenient basis for studying the spectrum or evolution of Hamiltonians or measuring multi-body observables. One strategy to reduce circuit depth in such algorithms involves…
Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and…
Quantum magic, quantified by nonstabilizerness, measures departures from stabilizer structure and underlies potential quantum speedups. We introduce an efficient classical framework for computing stabilizer R\'enyi entropies and stabilizer…
Measuring properties of quantum systems is a fundamental problem in quantum mechanics. We provide a simple method for estimating the expectation value of observables with an unknown quantum state. The idea is to use a data structure to…
Evaluating an expectation value of an arbitrary observable $A\in{\mathbb C}^{2^n\times 2^n}$ through na\"ive Pauli measurements requires a large number of terms to be evaluated. We approach this issue using a method based on Bell…
We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize…
We introduce a hierarchical algorithm for identifying the largest Pauli coefficients of an unknown $n$-qubit quantum state. The algorithm traverses a prefix-based tree whose nodes represent partial sums of squared Pauli coefficients, always…
The Pauli-based Circuit Optimization, Analysis and Synthesis Toolchain (PCOAST) was recently introduced as a framework for optimizing quantum circuits. It converts a quantum circuit to a Pauli-based graph representation and provides a set…
Standard randomized benchmarking protocols entail sampling from a unitary 2 design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2…
Current quantum computers suffer from a limited number of qubits and high error rates, limiting practical applicability. Different techniques exist to mitigate these effects and run larger algorithms. In this work, we analyze one of these…
Randomized benchmarking is a powerful technique to efficiently estimate the performance and reliability of quantum gates, circuits and devices. Here we propose to perform randomized benchmarking in a coherent way, where superpositions of…
An arbitrary operator corresponding to a physical observable cannot be measured in a single measurement on currently available quantum hardware. To obtain the expectation value of the observable, one needs to partition its operator to…
As quantum technology advances, quantum simulation becomes increasingly promising, with significant implications for quantum many-body physics and quantum chemistry. Despite being one of the most accessible simulation methods, the product…
Randomized benchmarking is an experimental procedure intended to demonstrate control of quantum systems. The procedure extracts the average error introduced by a set of control operations. When the target set of operations is intended to be…