Evidence for the utility of quantum computing before fault tolerance.

Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors.

Error Mitigation for Universal Gates on Encoded Qubits.

The Eastin-Knill theorem states that no quantum error-correcting code can have a universal set of transversal gates. For Calderbank-Shor-Steane codes that can implement Clifford gates transversally, it suffices to provide one additional non-Clifford gate, such as the T gate, to achieve universality. Common methods to implement fault-tolerant T gates, e.

Error mitigation extends the computational reach of a noisy quantum processor.

Quantum computation, a paradigm of computing that is completely different from classical methods, benefits from theoretically proved speed-ups for certain problems and can be used to study the properties of quantum systems. Yet, because of the inherently fragile nature of the physical computing elements (qubits), achieving quantum advantages over classical computation requires extremely low error rates for qubit operations, as well as substantial physical qubits, to realize fault tolerance via quantum error correction. However, recent theoretical work has shown that the accuracy of computation (based on expectation values of quantum observables) can be enhanced through an extrapolation of results from a collection of experiments of varying noise.

Supervised learning with quantum-enhanced feature spaces.

Machine learning and quantum computing are two technologies that each have the potential to alter how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous in pattern recognition, with support vector machines (SVMs) being the best known method for classification problems. However, there are limitations to the successful solution to such classification problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate.

Error Mitigation for Short-Depth Quantum Circuits.

Two schemes are presented that mitigate the effect of errors and decoherence in short-depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation are introduced. Near-term applications of early quantum devices, such as quantum simulations, rely on accurate estimates of expectation values to become relevant.

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.

Quantum computers can be used to address electronic-structure problems and problems in materials science and condensed matter physics that can be formulated as interacting fermionic problems, problems which stretch the limits of existing high-performance computers. Finding exact solutions to such problems numerically has a computational cost that scales exponentially with the size of the system, and Monte Carlo methods are unsuitable owing to the fermionic sign problem. These limitations of classical computational methods have made solving even few-atom electronic-structure problems interesting for implementation using medium-sized quantum computers.

Preparing projected entangled pair states on a quantum computer.

We present a quantum algorithm to prepare injective projected entangled pair states (PEPS) on a quantum computer, a class of open tensor networks representing quantum states. The run time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS's parent Hamiltonian.

Stochastic matrix product states.

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows us to define the analogue of Schmidt coefficients for steady states of nonequilibrium stochastic processes. We discuss a new measure for correlations which is analogous to entanglement entropy, the entropy cost S(C), and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state.

Graphene with geometrically induced vorticity.

At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes.