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1. Hybrid Quantum-Classical Computing Architectures

   Suchara, Martin ; Alexeev, Yuri ; Chong, Frederic ; Finkel, Hal ; Hoffmann, Henry ; Larson, Jeffrey ; Osborn, James ; and Smith, Graeme ( November 2018 , Proceedings of the 3rd International Workshop on Post-Moore Era Supercomputing, 2018.)

   We describe how classical supercomputing can aid unreliable quantum processors of intermediate size to solve large problem instances reliably. We advocate using a hybrid quantum-classical architecture where larger quantum circuits are broken into smaller sub-circuits that are evaluated separately, either using a quantum processor or a quantum simulator running on a classical supercomputer. Circuit compilation techniques that determine which qubits are simulated classically will greatly impact the system performance as well as provide a tradeoff between circuit reliability and runtime. We describe how classical supercomputing can aid unreliable quantum processors of intermediate size to solve large problem instances reliably. Wemore »advocate using a hybrid quantum-classical architecture where larger quantum circuits are broken into smaller sub-circuits that are evaluated separately, either using a quantum processor or a quantum simulator running on a classical supercomputer. Circuit compilation techniques that determine which qubits are simulated classically will greatly impact the system performance as well as provide a tradeoff between circuit reliability and runtime.« less
2. CutQC: using small Quantum computers for large Quantum circuit evaluations

   https://doi.org/10.1145/3445814.3446758  

   Tang, Wei ; Tomesh, Teague ; Suchara, Martin ; Larson, Jeffrey ; Martonosi, Margaret ( April 2021 , Proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems)

   Quantum computing (QC) is a new paradigm offering the potential of exponential speedups over classical computing for certain computational problems. Each additional qubit doubles the size of the computational state space available to a QC algorithm. This exponential scaling underlies QC’s power, but today’s Noisy Intermediate-Scale Quantum (NISQ) devices face significant engineering challenges in scalability. The set of quantum circuits that can be reliably run on NISQ devices is limited by their noisy operations and low qubit counts. This paper introduces CutQC, a scalable hybrid computing approach that combines classical computers and quantum computers to enable evaluation of quantum circuitsmore »that cannot be run on classical or quantum computers alone. CutQC cuts large quantum circuits into smaller subcircuits, allowing them to be executed on smaller quantum devices. Classical postprocessing can then reconstruct the output of the original circuit. This approach offers significant runtime speedup compared with the only viable current alternative -- purely classical simulations -- and demonstrates evaluation of quantum circuits that are larger than the limit of QC or classical simulation. Furthermore, in real-system runs, CutQC achieves much higher quantum circuit evaluation fidelity using small prototype quantum computers than the state-of-the-art large NISQ devices achieve. Overall, this hybrid approach allows users to leverage classical and quantum computing resources to evaluate quantum programs far beyond the reach of either one alone.« less
3. Training of quantum circuits on a hybrid quantum computer

   https://doi.org/10.1126/sciadv.aaw9918  

   Zhu, D. ; Linke, N. M. ; Benedetti, M. ; Landsman, K. A. ; Nguyen, N. H. ; Alderete, C. H. ; Perdomo-Ortiz, A. ; Korda, N. ; Garfoot, A. ; Brecque, C. ; et al ( October 2019 , Science Advances)

   Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of themore »quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.« less
4. Quantum computational advantage attested by nonlocal games with the cyclic cluster state

   https://doi.org/https://doi.org/10.1103/PhysRevResearch.4.033068  

   Daniel, Austin K. ; Zhu, Yinyue ; Huerta Alderete, C. ; Buchemmavari, Vikas ; Green, Alaina M. ; Nguyen, Nhung H. ; Thurtell, Tyler G. ; Zhao, Andrew ; Linke, Norbert M. ; Miyake, Akimasa ( July 2022 , Physical review research)

   We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a subset of its Pauli stabilizers on a quantum computer is compared to that of classical Boolean circuits with the same, nearest-neighboring gate connectivity. Using a circuit-based trapped-ion quantum computer, we prepare and measure a six-qubit cyclic cluster state with an overall fidelity of 60.6% and 66.4%, before and after correcting for measurement-readout errors, respectively. Our experimental results indicate that whilemore »this fidelity readily passes conventional (or depth-0) Bell bounds for local hidden-variable models, it is on the cusp of demonstrating a higher probability of success than what is possible by depth-1 classical circuits. Our games offer a practical and scalable set of quantitative benchmarks for quantum computers in the pre-fault-tolerant regime as the number of qubits available increases.« less
5. Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits

   https://doi.org/10.1145/3313276.3316404  

   Watts, Adam Bene ; Kothari, Robin ; Schaeffer, Luke ; Tal, Avishay ( June 2019 , Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing)

   Recently, Bravyi, Gosset, and Konig (Science, 2018) exhibited a search problem called the 2D Hidden Linear Function (2D HLF) problem that can be solved exactly by a constant-depth quantum circuit using bounded fan-in gates (or QNC^0 circuits), but cannot be solved by any constant-depth classical circuit using bounded fan-in AND, OR, and NOT gates (or NC^0 circuits). In other words, they exhibited a search problem in QNC^0 that is not in NC^0. We strengthen their result by proving that the 2D HLF problem is not contained in AC^0, the class of classical, polynomial-size, constant-depth circuits over the gate set ofmore »unbounded fan-in AND and OR gates, and NOT gates. We also supplement this worst-case lower bound with an average-case result: There exists a simple distribution under which any AC^0 circuit (even of nearly exponential size) has exponentially small correlation with the 2D HLF problem. Our results are shown by constructing a new problem in QNC^0, which we call the Parity Halving Problem, which is easier to work with. We prove our AC^0 lower bounds for this problem, and then show that it reduces to the 2D HLF problem.« less