## Program

#### SESSION 9a: Simulations in the NISQ era (Alvarado D)

Chair: (Christopher Jackson)
3:45pm - 4:15pmNathan Lysne, University of Arizona
What a small-scale, highly-accurate quantum processor can teach us about analog quantum simulation
Abstract. Quantum systems that offer reasonably accurate control over tens of qubits have now been realized in several contexts. It is thought such noisy intermediate-scale quantum (NISQ) devices may be capable of classically hard tasks such as analog quantum simulation (AQS). Yet, it remains unclear if a quantum processor without error correction and fault tolerance can compute meaningful results when subject to realistic imperfections. To probe this question we have developed a universal, highly accurate analog quantum processor operating in the 16D Hilbert space comprised of the total atomic spin of individual Cs atoms in the electronic ground state. Advances in optimal control enables us to drive arbitrary unitary transformations with very high fidelity (>99%) which we can use to perform simulations of any quantum system that fits in this Hilbert space. In particular, we have studied the feasibility of simulating several model Hamiltonians that exhibit features of interest to AQS, such as chaos and hypersensitivity (the quantum kicked top), and quantum phase transitions (the Lipkin-Meshkov-Glick and transverse Ising models). Experimentally, we demonstrate AQS of each of these models, with high fidelity at the quantum state level and accurate tracking of dynamical features. With this small-scale highly accurate quantum simulator, we can now reintroduce errors in a controlled fashion and study how they impact AQS of complex dynamics, in the laboratory as well as numerical modeling.
4:15pm - 4:45pmGopikrishnan Muraleedharan, University of New Mexico CQuIC
Quantum computational supremacy in the sampling of Bosonic random walkers on a one-dimensional lattice
Abstract. A quantum device that performa a computational task more efficiently than a current state-of-the-art classical computer is said to demonstrate quantum computational supremacy QCS. One path to achieving QCS in the short term is via sampling complexity; random samples are drawn from a probability distribution by measuring a complex quantum state in a defined basis. Surprisingly, a gas of identical noninteracting bosons can yield sampling complexity due solely to quantum statistics, as shown by Aaronson and Arkhipov, and dubbed boson sampling the context of identical photons scattering from a linear optical network. We generalize this to noninteracting bosonic quantum random walkers on a 1D lattice, and study the complexity of the resulting probability distribution obtained in static and time dependent lattices. We consider physical realizations based on controlled transport of ultra-cold atoms in a spinor optical lattice as well as a quantum gas microscope using optical tweezers. We quantify analytically and numerically how a sequence of random Hamiltonian evolution approaches Haar random SU ($$d$$) unitary. This, together with identical particle interference can yield QCS. We also study how much pseudorandomness is necessary to demonstrate QCS in terms of closeness to a t-design.
4:45pm - 5:15pmNoah Davis, University of Texas, Austin
Simulating and evaluating the coherent Ising machine
Abstract. Physical annealing techniques present methods for taking advantage of qubits without the need for universal quantum computers. Particularly, annealing systems may offer calculation speed-ups for certain NP-hard optimization problems such as the Max-Cut problem and the Sherrington-Kirkpatrick model. Among promising annealing systems, the coherent Ising machine (CIM) has demonstrated particular potential for solving dense examples of these problems. A CIM uses classical measurement and feedback to couple the degenerate optical parametric oscillators which make up its logical qubits. We use the master equations governing this measurement-feedback system to simulate an idealized (but still classically controlled) CIM on a high performance computing cluster. We present an analysis of this simulation and compare it to experimental instances of CIMs along with other popular annealing methods.
5:15pm - 5:45pmLucas Kocia, National Institute of Standards and Technology, Maryland
Stationary phase method in discrete Wigner functions and classical simulation of quantum circuits
Abstract. We apply the periodized stationary phase method to discrete Wigner functions of systems with odd prime dimension using results from $$p$$-adic number theory. We derive the Wigner-Weyl-Moyal (WWM) formalism with higher order $$hbar$$ corrections representing contextual corrections to non-contextual Clifford operations. We apply this formalism to a subset of unitaries that include diagonal gates such as the $${\pi}/{8}$$ gates. We characterize the stationary phase critical points as a quantum resource injecting contextuality and show that this resource allows for the replacement of the $$p^{2t}$$ points that represent $$t$$ magic state Wigner functions on $$p$$-dimensional qudits by $$\le p^{t}$$ points. We find that the $${\pi}/{8}$$ gate introduces the smallest higher order $$hbar$$ correction possible, requiring the lowest number of additional critical points compared to the Clifford gates. We then establish a relationship between the stabilizer rank of states and the number of critical points and exploit the stabilizer rank decomposition of two qutrit $${\pi}/{8}$$ gates to develop a classical strong simulation of a single qutrit marginal on $$t$$ qutrit $${\pi}/{8}$$ gates that are followed by Clifford evolution, and show that this only requires calculating $$3^{\frac{t}{2}+1}$$ critical points corresponding to Gauss sums. This outperforms the best alternative qutrit algorithm for any number of $${\pi}/{8}$$ gates to full precision.
5:45pm - 6:15pmLukasz Cincio, Los Alamos National Laboratory
Learning short- and constant-depth algorithms: application to state overlap and entanglement spectroscopy
Abstract. Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap ${\rm Tr}(\rho\sigma)$ between two quantum states $\rho$ and $\sigma$. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines. Here, our machine-learning approach finds algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Taking this as inspiration, we also present a novel constant-depth algorithm for computing the integer R\'enyi entropies, ${\rm Tr}(\rho^n})$, where our circuit depth is independent of both the number of qubits in $\rho$ as well as the exponent $n$. These integer R\'enyi entropies are useful, e.g., for computing the entanglement spectrum for condensed matter applications. Finally, we demonstrate that both our state overlap algorithm and our R\'enyi entropy algorithm have increased robustness to noise relative to their state-of-the-art counterparts in the literature.

SQuInT Chief Organizer
Akimasa Miyake, Associate Professor
amiyake@unm.edu

SQuInT Local Organizers
Rafael Alexander, Postdoctoral Fellow
Chris Jackson, Postdoctoral Fellow