Quantum Information

As quantum processors scale, robust and scalable tools to characterize gate-level noise become indispensable. Randomized benchmarking (RB) and its many variants have emerged as the go-to protocols in practice: they yield a single number to characterize a gate set, the average gate fidelity, per irreducible subspace. It has been argued that RB can in principle be extended into a full tomographic framework (RB tomography), but large-scale practical implementations, even of partial tomographic information, have long been hindered by the need for sequence inversion, explicit gate interleaving, and the required measurement statistics. In this talk, we report on a scalable implementation of a flexible and efficient variant of RB tomography called gate-set shadows, on a 36-qubit superconducting processor. From a single, efficiently implemented randomized-circuit experiment, we reconstruct the one- and two-qubit marginals of the average noise channel, learn classically correlated quantum noise including cross-talk, and infer a variety of diagnostic information and performance metrics. We decompose the reconstructed channels into error-generator rates that separate coherent, stochastic, and correlated contributions, and find cross-talk that is structured but not confined to the chip's physical topology, escaping several standard pairwise cross-talk metrics. We further introduce a way to test how much of this reconstructed noise is explained by mechanisms already assumed in the literature, such as detuning, over-rotation, and decoherence: fitting the reconstructed rates against a library of such models and quantifying what is left over. First results suggest that cross-talk can resist explanation by standard noise models more than commonly assumed.

Quantum inference usually begins by measuring quantum data and converting it into classical information. In this talk, I will consider a different setting in which the desired output remains quantum, allowing coherence to be preserved throughout the inference process. Examples include quantum purity amplification, approximate purification and cloning of mixed states, and density matrix exponentiation. I will show that coherent protocols can use exponentially fewer input copies than any measurement mediated strategy. For quantum purity amplification of a principal eigenstate with an input of dimension d, coherent processing achieves error ε using O(1/ε) copies, while incoherent protocols require Ω(d/ε) copies. More broadly, these results motivate a theory of coherent quantum inference and establish entanglement breaking limits as a natural connection between coherent and incoherent information processing.

We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions. This QMA-hard problem is motivated by the Coulomb electron-electron interaction being diagonal in the position basis, a fundamental fact that underpins electronic-structure Hamiltonians in quantum chemistry and condensed matter. We prove that fermionic Gaussian states achieve an approximation ratio of at least 1/3 for such Hamiltonians, independent of sparsity. This shows that classical interactions are sufficient to prevent the vanishing Gaussian approximation ratio observed in SYK-type models. We also give efficient semi-definite programming algorithms for Gaussian approximations to several families of traceless and positive-semidefinite classically interacting Hamiltonians, with the ability to enforce a fixed particle number. The technical core of our results is the concept of a Gaussian blend, a construction for Gaussian states via mixtures of covariance matrices.

We give the first instance-optimal sample complexity bounds for shadow tomography using few-copy measurements in the high-precision regime. More concretely, we study the problem of learning expectation values of a given set of observables of an unknown quantum state to precision $\epsilon$ in $L_p$-norm, using (possibly adaptive) measurements that act on one or a few copies at a time, and we are interested in the regime that $\epsilon$ is below some concrete and potentially dimension-dependent threshold. In this setup, we prove the necessary and sufficient number of copies, for any given set of observables, is characterized by a simple optimization formula involving a quadratic form of the inverse Fisher information matrix up to a logarithmic factor. Our results establish a rigorous correspondence between quantum learning and quantum metrology. 

I will discuss some surprising examples of quantum circuits that can be realized in constant T-depth. Some of these constructions, such as single-qubit rotation and its programmable variants, as well as  quantum part of Shor's factoring algorithm, require a catalyst state. But there are also other constructions that do not, such as reversible encoded addition.