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An Experimental Microarchitecture for a Superconducting Quantum Processor
X. Fu, M. A. Rol, C. C. Bultink, J. van Someren, N. Khammassi, I. Ashraf, R. F. L. Vermeulen, J. C. de Sterke, W. J. Vlothuizen, R. N. Schouten, C. G. Almudever, L. DiCarlo, K. Bertels
TL;DR
Experimental quantum processors need control that bridges compiler output and hardware, but quantum instructions are typically not directly executable on a processor. The paper builds QMA, a flexible microarchitecture for quantum-classical mixed code, and validates its FPGA prototype with an AllXY experiment on a superconducting qubit. The experiment reports that measured fidelities match ideal readout fidelity for each operation combination.
Problem
Quantum compilers typically produce instructions that are not directly executable on processors, while existing control methods have resource consumption, configuration times, and complexity that scale poorly with qubit count.
Source: §1 · p. 1Method
The paper builds QMA, a control microarchitecture that accepts quantum-classical mixed code and uses codeword events, queued event timing, and multilevel instruction decoding.
Source: §1 · p. 1, §9 · p. 11Results
Measured fidelity for each AllXY operation combination matches well with ideal readout fidelity, demonstrating generation of the right pulses and preservation of precise operation timing.
Source: §8 · p. 11Takeaways & Limitations
The FPGA prototype successfully ran an OpenQL-generated AllXY experiment on a superconducting qubit using auxiliary classical instructions and QMIS instructions.
Source: §1 · p. 2, §9 · p. 11The prototype lacks a fully functioning physical microcode unit, so high-level QIS instructions are not implemented.
Source: §7.2 · p. 10
Abstract
from arXiv · showhide
Quantum computers promise to solve certain problems that are intractable for classical computers, such as factoring large numbers and simulating quantum systems. To date, research in quantum computer engineering has focused primarily at opposite ends of the required system stack: devising high-level programming languages and compilers to describe and optimize quantum algorithms, and building reliable low-level quantum hardware. Relatively little attention has been given to using the compiler output to fully control the operations on experimental quantum processors. Bridging this gap, we propose and build a prototype of a flexible control microarchitecture supporting quantum-classical mixed code for a superconducting quantum processor. The microarchitecture is based on three core elements: (i) a codeword-based event control scheme, (ii) queue-based precise event timing control, and (iii) a flexible multilevel instruction decoding mechanism for control. We design a set of quantum microinstructions that allows flexible control of quantum operations with precise timing. We demonstrate the microarchitecture and microinstruction set by performing a standard gate-characterization experiment on a transmon qubit.
1 INTRODUCTION
The paper addresses the gap between quantum compilers and experimental processors by proposing QMA, a control microarchitecture that accepts quantum-classical mixed code. Its codeword events, queued timing control, multilevel decoding, and microinstruction set are demonstrated in an FPGA prototype through an AllXY qubit experiment.
1 INTRODUCTION
- QMA accepts quantum-classical mixed code and is designed to translate compiler output into flexible, precisely timed control for a superconducting quantum processor.Existing control methods have high resource consumption, long configuration times, and complexity that scale poorly with qubit count; compiler instructions are typically not directly executable on processors.Source: §1 · p. 1
- Codeword-based event control assigns an index to each event, including pulse generation and measurement, so runtime codewords trigger the corresponding events.This abstracts control using complex analog pulses into an interface of binary signals.Source: §1 · pp. 1–2
- Queue-based timing control buffers events decoded during instruction execution and triggers them at deterministic, precise times despite nondeterministic instruction timing.Multilevel decoding successively translates quantum instructions into microinstructions, micro-operations, and codewords; QMIS is designed for flexible, precisely timed quantum operations.Source: §1 · p. 2
- An FPGA implementation of QMA was experimentally validated by running AllXY on a superconducting qubit with control converted from a high-level language by a quantum compiler.The paper identifies AllXY as a standard gate-characterization experiment.Source: §1 · p. 2
2 BACKGROUND
The background introduces qubit states and gates, then describes the transmon platform used for validation. It explains how the device is tuned, measured, and driven with control pulses.
2.1 Qantum Computing Basics
- A qubit is described as a superposition of logical states whose measurement in the logical basis yields either state with probabilities set by the squared amplitudes.Single-qubit gates are rotations on the Bloch sphere, including X, Y, and Z rotations; CNOT and CZ are examples of two-qubit gates.Source: §2.1 · p. 2
2.2 Superconducting Qbits
- The experiment uses a transmon in planar circuit quantum electrodynamics, where the ground and first-excited circuit states serve as the qubit states.The transition frequency can be tuned over several gigahertz on nanosecond timescales by controlling magnetic flux through the Josephson-junction loop.Source: §2.2 · p. 2
- A readout resonator’s qubit-state-dependent frequency is interrogated through a feedline, and the transmitted signal is demodulated, integrated, and discriminated to infer the measurement result.The described pulsed measurement typically lasts 300 ns to 2 µs.Source: §2.2 · p. 2
- Single-qubit gates use calibrated microwave pulses at the qubit transition frequency, with pulse envelopes and carrier phase setting the rotation axis and amplitude setting the rotation angle.The pulses are typically 20 ns; arbitrary single-qubit gates can be decomposed into X and Y rotations at the cost of longer sequences.Source: §2.2 · p. 2
- The common two-qubit CZ gate is implemented with calibrated flux-bias pulses between qubits coupled to a common resonator or capacitor.The paper notes typical pulse duration of about 40 ns and excludes CZ gates from its validation.Source: §2.2 · p. 3
3 RELATED WORK
Prior quantum instruction sets provide intermediate representations but generally do not specify the control microarchitecture needed to execute instructions on a physical processor. This paper adopts a microcode approach to support flexible, technology-independent instruction definition.
3 RELATED WORK
- Existing quantum languages and instruction sets compile applications into intermediate instructions but lack an explicit control microarchitecture for executing them on a real processor.Examples include virtual-instruction sets, QPOL, QASM-HL, Qil, and OPENQASM.Source: §3 · p. 3
- Earlier architecture work addresses technology-specific processor fabrication, qubit organization, or broad research domains, and uses “microarchitecture” differently from this paper.The paper distinguishes its focus on control microarchitecture.Source: §3 · p. 3
- The adopted microcode approach translates complex machine instructions into sequences of micro-operations, supporting flexible instruction definitions on the same hardware.Prior work also extended translation to three levels, from machine instructions to microinstructions and then micro-operations.Source: §3 · p. 3
- Microcode is presented as a fit for quantum computing because frequent routines such as error correction can be optimized, while complex algorithm operations may not be directly implementable by processors.The cited proposal applies microcode tuning to frequent routines.Source: §3 · p. 3
4 MICROARCHITECTURAL CHALLENGES
The section uses AllXY to expose challenges in controlling quantum processors: analog pulses require scalable storage and flexible feedback, operations require precise nanosecond timing, and instruction sets must reflect execution constraints.
4.1 Motivational Example
- AllXY probes single-qubit calibration with 21 gate pairs, repeated 25,600 rounds to estimate |1⟩ fidelity against an ideal staircase.The experiment applies two back-to-back gates to an initialized qubit before measurement.Source: §4.1 · p. 3
4.2 Complex Analog Waveform Control
- Single-qubit operations use analog pulses with variable envelopes, frequencies, durations, and timing, and waveform-generator storage scales with pulse duration and sampling rate.A pulse of duration T_d requires 2 · T_d · R_s samples for its I and Q components.Source: §4.2 · pp. 3–4
4.2.1 Measurement Result Discrimination.
- Software-based measurement discrimination takes hundreds of microseconds, exceeding the below-100-µs coherence-time boundary required for real-time feedback.It also implies hardware resource consumption that the authors say cannot scale to many qubits.Source: §4.2.1 · p. 4
4.2.2 Flexible Combination of Operations.
- Pre-uploading combined waveforms requires 21 waveforms for AllXY, while dynamically determined operations require feedback that autonomous waveform generators cannot provide.The authors identify this approach as difficult to scale to larger qubit counts.Source: §4.2.2 · p. 4
4.2.3 Accurate Timing Control.
- Nanosecond timing errors can change a gate’s rotation axis; with 50 MHz modulation, a 5 ns delay can turn an x rotation into a y rotation.Some experiments also require back-to-back gates and measurement.Source: §4.2.3 · p. 4
4.3 Instruction Definition
- Existing quantum instruction sets mostly describe and optimize applications without accounting for processor-interface constraints such as timing.Runtime hardware limitations and changing gate implementations also constrain compile-time technology-dependent instructions.Source: §4.3 · pp. 4–5
5 QUANTUM MICROARCHITECTURE
QMA combines a classical host and quantum coprocessor to execute mixed classical-quantum code, translating instructions into precisely timed control events. Its codeword, queue, and multilevel-decoding schemes separate analog pulse control from instruction execution and support flexible gate control.
5 QUANTUM MICROARCHITECTURE
- QMA uses codeword-based event control, queue-based precise timing, and multilevel decoding to address analog waveform control and instruction-definition challenges.The schemes use codeword triggers for pulse generation and measurement, queues for precisely timed events, and successive instruction decoding.Source: §5 · p. 5
5.1 Codeword-Based Event Control
- Codeword triggers become pulses with fixed latency, while measurement discrimination converts analog measurement signals into binary results.The interface abstracts analog waveform control from the upper digital layers; fast, flexible feedback is possible in principle without uploading waveforms at runtime.Source: §5.1 · p. 6, §5.1.2 · p. 6
5.1.1 Codeword-Triggered Pulse Generation.
- For AllXY, storing seven primitive-operation pulses requires 420 Bytes, versus 2520 Bytes for 21 two-gate waveforms.The paper states that memory use remains the same for more complex operation combinations, making the savings more significant.Source: §5.1.1 · p. 6
5.1.2 Measurement Discrimination.
- The measurement discrimination unit starts on a codeword trigger and converts a single qubit’s analog measurement signal into a binary result for readback or feedback.Prior customized-FPGA discrimination is reported to have latency below 1 µs.Source: §5.1.2 · p. 6
5.2 Qeue-Based Event Timing Control
- Queue-based timing separates as-fast-as-possible instruction execution from deterministic event output; the AllXY timeline uses a 5 ns cycle.A timing queue buffers labeled time points, event queues hold operations, and the timing controller fires matching events when the deterministic-domain clock reaches their labels.Source: §5.2 · p. 6
5.3.1 Instruction Definition.
- QMA’s quantum instruction set combines quantum operations with auxiliary classical arithmetic, logic, and flow-control instructions.The classical instructions support measurement-based feedback and hierarchical algorithm descriptions.Source: §5.3.1 · p. 7
5.3.2 Instruction Decoding.
- Multilevel decoding successively maps quantum instructions to microinstructions, micro-operations, and codeword triggers, allowing technology-independent instructions to use technology-dependent primitives.Horizontal microcode supports one instruction expanding into multiple microinstructions and one microinstruction into multiple micro-operations.Source: §5.3.2 · pp. 7–9
- The micro-operation unit sequences codeword triggers with predefined timing to emulate operations unavailable as primitive pulses and reduce communication with the analog-digital interface.For superconducting qubits, the paper gives a Z-gate sequence that uses Y followed by X, up to an irrelevant global phase.Source: §5.3.2 · p. 9
6 EVALUATION
The evaluation contrasts QMA’s centralized control with the distributed Raytheon BBN APS2 architecture. QMA uses one executable and explicit quantum semantics and timing, while its instruction stream may constrain output rates as qubit counts grow.
6 EVALUATION
- QMA uses one executable with explicit quantum semantics and timing, while APS2 uses parallel module executables and low-level output instructions.QMA synchronizes outputs at specified timing points rather than relying on a trigger-distribution module or interconnect network.Source: superconducting qubits · p. 9
- QMA’s analog-digital interface and timing-control unit scale linearly with qubit count and can be distributed, but a single instruction stream may limit output rate as demand grows.The paper notes that a VLIW architecture could provide a larger instruction issue rate.Source: superconducting qubits · p. 9
7 IMPLEMENTATION
The control box implements QMA across a master controller and three AWGs, while the prototype supports only part of the planned instruction stack.
7.1 Qantum Control Box
- Four FPGA boards comprise the control box: one master controller and three two-channel AWGs.The master controller digitizes measurement signals and triggers measurement and AWG pulse generation; each AWG uses 14-bit DACs and codeword-triggered pulse generation with an 80 ns fixed delay.Source: §7.1 · pp. 9–10
7.2 QMA Implementation
- The prototype partially implements the instruction cache, execution controller, physical microcode unit, timing control unit, and quantum-classical interface.The remaining system is planned for future release, and high-level quantum instructions are not implemented because the physical microcode unit is incomplete.Source: §7.2 · p. 10
- OpenQL compiles descriptions into auxiliary classical and QMIS instructions, which the execution controller and physical microcode unit dispatch and schedule.The microcode unit decomposes QMIS instructions into micro-operations; the timing control unit implements queue-based event timing.Source: §7.2 · p. 10
8 EXPERIMENTAL RESULTS
The AllXY experiment used OpenQL-generated instructions to control qubit operations; measured fidelities matched the ideal readout fidelity, demonstrating pulse generation and timing control.
Experimental scope
- The authors also performed T1, T2 Ramsey, T2 Echo, and randomized benchmarking experiments, but report only AllXY in the paper.AllXY instructions were generated from an OpenQL description.Source: §8 · pp. 10–11
Experimental setup
- The setup used a 10-transmon chip at 20 mK and AWG 2 to generate calibrated single-qubit control pulses for qubit 2.The measured qubit transition frequency was 6.466 GHz; the experiment used a 6.516 GHz carrier with −50 MHz single-sideband modulation.Source: §8 · pp. 10–11, Figure 8 · p. 11
AllXY procedure
- The experiment measured 42 pulse combinations over 25,600 rounds, averaging results for each combination; each of the 21 unique combinations was measured twice.The 0th, 18th, and 19th combinations supplied calibration points for readout-error-corrected fidelity.Source: §8 · p. 11
AllXY results
- 7 lookup-table pulses covered all operation combinations, and measured AllXY fidelity matched ideal readout fidelity with precise operation timing preserved.The implementation used 140 ns × Rs samples, with moderate memory use and better scalability than the conventional method.Source: §8 · p. 11
9 CONCLUSION
The paper presents QMA and QMIS for flexible, precisely timed control of a superconducting processor, validates a prototype with AllXY, and identifies further implementation work.
9 CONCLUSION
- QMA combines codeword-based event control, queue-based precise timing, and multilevel instruction decoding with QMIS for describing quantum operations.The microarchitecture takes compiler-generated instructions as input to control a superconducting quantum processor.Source: §9 · p. 11
- The FPGA prototype successfully performed AllXY on a superconducting qubit using OpenQL-generated auxiliary classical and QMIS instructions.Changing the input program provides a straightforward way to define quantum experiments.Source: §9 · pp. 11–12
- Future work includes a VLIW instruction set, expanded microcode for quantum instructions, and real-time feedback control.Source: §9 · p. 12