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The control of cryogenic qubits in today’s super-conducting quantum computer prototypes presents significant scalability challenges due to the massive costs of generating/routing the analog control signals that need to be sent from a classical controller at room temperature to the quantum chip inside the dilution refrigerator. Thus, researchers in industry and academia have focused on designing in-fridge classical controllers in order to mitigate these challenges. Due to the maturity of CMOS logic, many industrial efforts (Microsoft, Intel) have focused on Cryo-CMOS as a near-term solution to design in-fridge classical controllers. Meanwhile, Supercon-ducting Single Flux Quantum (SFQ) is an alternative, less mature classical logic family proposed for large-scale in-fridge controllers. SFQ logic has the potential to maximize scalability thanks to its ultra-high speed and very low power consumption. However, architecture design for SFQ logic poses challenges due to its unconventional pulse-driven nature and lack of dense memory and logic. Thus, research at the architecture level is essential to guide architects to design SFQ-based classical controllers for large-scale quantum machines.In this paper, we present DigiQ, the first system-level design of a Noisy Intermediate Scale Quantum (NISQ)-friendly SFQ-based classical controller. We perform a design space exploration of SFQ-based controllers and co-design the quantum gate decompositions and SFQ-based implementation of those decompositions to find an optimal SFQ-friendly design point that trades area and power for latency and control while ensuring good quantum algorithmic performance. Our co-design results in a single instruction, multiple data (SIMD) controller architecture, which has high scalability, but imposes new challenges on the calibration of control pulses. We present software-level solutions to address these challenges, which if unaddressed would degrade quantum circuit fidelity given the imperfections of qubit hardware.To validate and characterize DigiQ, we first implement it using hardware description languages and synthesize it using state-of-the-art/validated SFQ synthesis tools. Our synthesis results show that DigiQ can operate within the tight power and area budget of dilution refrigerators at >42,000-qubit scales. Second, we confirm the effectiveness of DigiQ in running quantum algorithms by modeling the execution time and fidelity of a variety of NISQ applications. We hope that the promising results of this paper motivate experimentalists to further explore SFQ-based quantum controllers to realize large-scale quantum machines with maximized scalability. 

Simulating the time evolution of a physical system at quantum mechanical levels of detail - known as Hamiltonian Simulation (HS) - is an important and interesting problem across physics and chemistry. For this task, algorithms that run on quantum computers are known to be exponentially faster than classical algorithms; in fact, this application motivated Feynman to propose the construction of quantum computers. Nonetheless, there are challenges in reaching this performance potential. Prior work has focused on compiling circuits (quantum programs) for HS with the goal of maximizing either accuracy or gate cancellation. Our work proposes a compilation strategy that simultaneously advances both goals. At a high level, we use classical optimizations such as graph coloring and travelling salesperson to order the execution of quantum programs. Specifically, we group together mutually commuting terms in the Hamiltonian (a matrix characterizing the quantum mechanical system) to improve the accuracy of the simulation. We then rearrange the terms within each group to maximize gate cancellation in the final quantum circuit. These optimizations work together to improve HS performance and result in an average 40% reduction in circuit depth. This work advances the frontier of HS which in turn can advance physical and chemical modeling in both basic and applied sciences. 

Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the (ρ,δ)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance δ to the ideal state ρ. This predicate (ρ,δ) can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the (ρ,δ)-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations. 

Quantum computers are traditionally operated by programmers at the granularity of a gate-based instruction set. However, the actual device-level control of a quantum computer is performed via analog pulses. We introduce a compiler that exploits direct control at this microarchitectural level to achieve significant improvements for quantum programs. Unlike quantum optimal control, our approach is bootstrapped from existing gate calibrations and the resulting pulses are simple. Our techniques are applicable to any quantum computer and realizable on current devices. We validate our techniques with millions of experimental shots on IBM quantum computers, controlled via the OpenPulse control interface. For representative benchmarks, our pulse control techniques achieve both 1.6x lower error rates and 2x faster execution time, relative to standard gate-based compilation. These improvements are critical in the near-term era of quantum computing, which is bottlenecked by error rates and qubit lifetimes.