Publications

Application-based benchmarks are increasingly used to quantify and compare quantum computers’ performance. However, because contemporary quantum computers cannot run utility-scale computations, these benchmarks currently test this hardware’s performance on “small” problem instances that are not necessarily representative of utility-scale problems. Furthermore, these benchmarks often employ methods that are unscalable, limiting their ability to track progress towards utility-scale applications. In this work, we present a method for creating scalable and efficient benchmarks from any quantum algorithm or application. Our subcircuit volumetric benchmarking (SVB) method runs subcircuits of varied shape that are “snipped out” from some target circuit, which could implement a utility-scale algorithm. SVB is scalable and it enables estimating a capability coefficient that concisely summarizes progress towards implementing the target circuit. We demonstrate SVB with experiments on IBM Q systems using a Hamiltonian block-encoding subroutine from quantum chemistry algorithms.

Current benchmarking methods for measuring progress towards applications on quantum computers often lack scalability and specificity. This limits their ability to produce generalizable metrics of processor performance. Here, we describe a method for creating scalable application-specific benchmarks using mirrored subcircuits that quantify a device’s ability to execute particular subroutines or entire algorithms. We then apply this method to two quantum chemistry subroutines, performing noisy numerical simulations and interpreting their results within the paradigm of volumetric benchmarking. We show how to extract effective error rates and predict full circuit fidelities from the subcircuit data and demonstrate that we can distinguish differences in performance resulting from structural properties of the circuits.

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM’s publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes $A$, $B$, and $C$, with a fixed angle $\theta$ between $A$ and $B$ and a range of angles $\theta'$ between $B$ and $C$. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM’s publicly accessible quantum computers. The Clauser–Horne–Shimony–Holt (CHSH) inequality governs a linear combination $S$ of expectation values of products of spin projections, taken pairwise. Finding $S > 2$ rules out local, hidden variable theories for entangled quantum systems. We obtained values of $S$ greater than $2$ in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state $\vert 00\rangle$, found the probabilities to observe the states $\vert 00\rangle$, $\vert 01\rangle$, $\vert 10\rangle$, and $\vert 11\rangle$ in multiple runs, and used that information to construct the first column of an error matrix $M$. We repeated this procedure for states prepared as $\vert 01\rangle$, $\vert 01\rangle$, $\vert 10\rangle$, and $\vert 11\rangle$ to construct the full matrix $M$, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of $\theta'$.