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Expectation values of observables are routinely estimated using so-called classical shadows$\unicode{x2014}$the outcomes of randomized bases measurements on a repeatedly prepared quantum state. In order to trust the accuracy of shadow…
Expectation value estimation is ubiquitous in quantum algorithms. The expectation value of a Hamiltonian, which is essential in various practical applications, is often estimated by measuring a large number of Pauli strings on quantum…
Many routines that one might want to run on a quantum computer can benefit from adaptive circuits, relying on mid-circuit measurements and feed-forward operations. Any such measurement has to be compiled into a sequence of elementary gates…
Quantum state tomography (QST) remains the prevailing method for benchmarking and verifying quantum devices; however, its application to large quantum systems is rendered impractical due to the exponential growth in both the required number…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
We propose a tomographic protocol for estimating any $ k $-body reduced density matrix ($ k $-RDM) of an $ n $-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and…
Randomized compiling reduces the effects of errors on quantum computers by tailoring arbitrary Markovian errors into stochastic Pauli noise. Here we prove that randomized compiling also tailors non-Markovian errors into local stochastic…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to…
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…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…
Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…
The method of classical shadows heralds unprecedented opportunities for quantum estimation with limited measurements [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020)]. Yet its relationship to established quantum…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
Cross-classified data frequently arise in scientific fields such as education, healthcare, and social sciences. A common modeling strategy is to introduce crossed random effects within a regression framework. However, this approach often…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
The one-way model of Measurement-Based Quantum Computing and the gate-based circuit model give two different presentations of how quantum computation can be performed. There are known methods for converting any gate-based quantum circuit…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
We give the first tight sample complexity bounds for shadow tomography and classical shadows in the regime where the target error is below some sufficiently small inverse polynomial in the dimension of the Hilbert space. Formally we give a…