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Systematic Crosstalk Mitigation for Superconducting Qubits via Frequency-Aware Compilation

Yongshan Ding, Pranav Gokhale, Sophia Fuhui Lin, Richard Rines, Thomas Propson, Frederic T. Chong

arXiv:2008.09503v1quant-ph

TL;DR

Crosstalk and frequency crowding complicate high-fidelity control of superconducting transmon programs. The paper uses software-based frequency-aware compilation to tune frequencies and schedule instructions, and reports performance comparable to tunable-coupler hardware with simpler fixed-coupler hardware.

Abstract

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One of the key challenges in current Noisy Intermediate-Scale Quantum (NISQ) computers is to control a quantum system with high-fidelity quantum gates. There are many reasons a quantum gate can go wrong -- for superconducting transmon qubits in particular, one major source of gate error is the unwanted crosstalk between neighboring qubits due to a phenomenon called frequency crowding. We motivate a systematic approach for understanding and mitigating the crosstalk noise when executing near-term quantum programs on superconducting NISQ computers. We present a general software solution to alleviate frequency crowding by systematically tuning qubit frequencies according to input programs, trading parallelism for higher gate fidelity when necessary. The net result is that our work dramatically improves the crosstalk resilience of tunable-qubit, fixed-coupler hardware, matching or surpassing other more complex architectural designs such as tunable-coupler systems. On NISQ benchmarks, we improve worst-case program success rate by 13.3x on average, compared to existing traditional serialization strategies.

I. INTRODUCTION

Crosstalk can damage quantum states and accumulate during program execution, while frequency crowding makes it harder to assign qubit frequencies as systems scale and programs use more parallelism. The paper proposes software that tunes frequencies and schedules instructions to mitigate crosstalk and decoherence.

I. INTRODUCTION

  • Crosstalk errors, including excitation exchange and leakage, can damage quantum states and accumulate as a program executes.For superconducting transmons, gate speeds are three to four orders of magnitude faster than qubit lifetime.Source: §I · p. 1
  • As systems scale and programs use more parallelism, frequency crowding makes it harder to satisfy constraints on qubit and gate frequencies.The paper describes crosstalk as unwanted interactions between coupled qubits and notes that frequency separation reduces residual coupling.Source: §I · p. 1
  • The paper proposes program-specific frequency tuning and instruction scheduling to mitigate crosstalk and decoherence on tunable-qubit, fixed-coupler systems.The approach maps frequency-aware compilation to coloring a crosstalk graph.Source: §I · p. 2
  • The paper analyzes architectural tunability trade-offs and evaluates its mitigation algorithm on BV, QAOA, QGAN, ISING, and XEB benchmarks.It targets tunable qubits with fixed couplers as a balance between control and hardware complexity.Source: Figure 1 · p. 1, §I · p. 2

II. BACKGROUND

Transmon qubits use their lowest two energy levels for computation, with operating frequencies adjustable by magnetic flux. Quantum programs use single- and two-qubit gates, while decoherence and unintended interactions can introduce errors.

A. Basics of Superconducting Qubits

  • Transmons use their two lowest energy levels as computational states, and magnetic flux can change their operating frequency.Tunable transmons have frequency sweet spots that are relatively stable against flux noise.Source: A. Basics of Superconducting Qubits · pp. 2–3

B. Operations and Noises

  • Quantum gates are unitary operations, and a compiler transforms a high-level program into low-level control pulses.The qubits are driven with microwave voltage signals and local magnetic-flux pulses.Source: B. Operations and Noises · p. 3

1) Single-qubit Gates and Decoherence Noise:

  • Single-qubit rotations use microwave drives, while environmental relaxation and dephasing contribute to decoherence error.Rx and Ry use in-phase and out-of-phase microwave signals, respectively; a Hadamard can combine them.Source: 1) Single-qubit Gates and Decoherence… · p. 3

2) Two-qubit Gates and Crosstalk Noise:

  • Two-qubit gates such as iSWAP and CZ are implemented by tuning interacting qubits to desired frequencies and holding them there.Unwanted interactions can occur when connected qubits are accidentally tuned on or near resonance, including during simultaneous gates.Source: 2) Two-qubit Gates and Crosstalk Noise · pp. 3–4

III. RELATED WORK

Prior crosstalk strategies use reduced connectivity, frequency tuning, or tunable couplers, while many compilation studies prioritize execution time over gate errors. The paper proposes frequency-aware software optimization and argues that tunable-qubit, fixed-coupler hardware can be competitive.

III. RELATED WORK

  • Prior approaches reduce connectivity, tune qubit frequencies, or use tunable couplers, while many compilation studies largely neglect gate errors such as crosstalk.Reduced connectivity increases mapping and re-mapping overhead; tunable couplers require scheduling their activation.Source: §III · p. 4
  • Frequency-tunable qubits with fixed couplers and software mitigation are presented as competitive without connectivity reduction.The paper calls this an optimization sweet spot between constrained fixed-frequency designs and tunable-coupler systems with added fabrication and control-noise overhead.Source: §III · p. 4

IV. SYSTEMATIC CROSSTALK MITIGATION

  • The proposed frequency-aware software reduces crosstalk and decoherence through strategic frequency tuning and instruction scheduling.The algorithm is designed for program-specific tuning on tunable-qubit, fixed-coupler systems.Source: §IV · p. 4, §III · p. 4

A. Understanding Crosstalk Constraints

Frequency crowding makes it harder to satisfy idle- and interaction-frequency constraints as systems grow and programs use more parallelism. The paper proposes dynamically tuning frequencies and scheduling instructions for each program, separating potentially crosstalking gates in frequency or time.

A. Understanding Crosstalk Constraints

  • Frequency crowding makes idle-frequency constraints and neighboring gates’ interaction-frequency constraints harder to satisfy as systems and program parallelism grow.Each qubit has a limited frequency range, while connected qubits need sufficient separation during idle and gate operations.Source: A. Understanding Crosstalk Constraints · p. 4

B. Frequency Tuning and Instruction Scheduling

  • The proposed scheme dynamically tunes the device and schedules instructions for each input program, separating parallel gates in frequency or time.The paper describes this as a systematic, program-aware approach to frequency tuning.Source: B. Frequency Tuning and Instruction… · pp. 4–5
  • Frequency assignment must balance separating neighboring idle frequencies against limited tunability and the small set of preferred operating frequencies.The paper studies a flux-tunable transmon architecture with 2-D mesh-like connectivity, while stating that its algorithm accepts arbitrary device topologies.Source: B. Frequency Tuning and Instruction… · pp. 4–5

C. Resolving Frequency Crowding via Graph Coloring

The paper uses graph coloring to assign separated idle and interaction frequencies. A connectivity graph handles idle assignments, while a crosstalk graph captures which simultaneous interactions must avoid sharing a frequency.

1) Idle Frequencies and Connectivity Graph:

  • Coloring the connectivity graph assigns idle frequencies so connected qubits do not share a frequency; a 2-D mesh needs only two colors.When those frequencies are sufficiently separated, higher-energy excitation frequencies are also separated, reducing interactions through the leakage channel.Source: 1) Idle Frequencies and Connectivity… · p. 5

2) Interaction Frequencies and Crosstalk Graph:

  • The crosstalk graph represents potential interference between two-qubit gates, identifying interactions that must use distinct frequencies.It is constructed from the connectivity graph by relating edges whose corresponding qubits fall within the crosstalk range.Source: 2) Interaction Frequencies and… · pp. 5–6
  • In a 5 × 5 mesh, the center interaction frequency must be avoided by nearby edges within crosstalk range.The figure shows idle-frequency coloring separately from the interaction-frequency exclusions.Source: Figure 7 · p. 6, 2) Interaction Frequencies and… · p. 6
  • For any N × N 2-D mesh, the crosstalk graph can be colored with 8 colors, the minimum needed; frequency-crowding crosstalk remains mostly localized as mesh size increases.Source: 2) Interaction Frequencies and… · p. 6

3) Generalization to Higher Distance:

The method generalizes the crosstalk graph to capture interactions at distance d, then uses graph construction and coloring within a frequency-aware compilation pipeline. The pipeline slices programs into time layers, maps colors to frequencies with an SMT solver, and schedules feasible instructions.

3) Generalization to Higher Distance:

  • The distance-d crosstalk graph connects vertices for connectivity-graph edges that share a vertex or are linked by a path of length d.This generalizes the treatment beyond nearest-neighbor crosstalk to possible residual coupling with next-neighbor qubits.Source: 3) Generalization to Higher Distance · p. 6

A. Frequency-Aware Compilation: Overview

  • For each program layer, the compiler colors an active crosstalk-graph subgraph, maps colors to frequencies with an SMT solver, and schedules feasible gates and qubit frequencies.It throttles parallelism when necessary; its inputs include device and program characteristics and an optimization level.Source: A. Frequency-Aware Compilation: Overview · p. 6

B. Optimization Details

  • The optimization details are presented as reducing crosstalk likelihood while scaling favorably with system size.The paper describes the approach as a long-term solution for frequency tuning superconducting qubits.Source: B. Optimization Details · p. 6

1) Crosstalk Graph Construction:

  • Crosstalk-graph construction starts from the connectivity graph’s line graph and connects gate-edge pairs when their qubit endpoints are within distance d.The resulting graph abstracts possible crosstalk channels between qubit pairs.Source: 1) Crosstalk Graph Construction · pp. 6–7

2) Circuit Slicing and Subgraph Coloring:

Circuit slicing lets the compiler assign frequencies dynamically to the couplings active in each time step. It colors each active subgraph, then uses an SMT solver to map colors to frequencies under crosstalk constraints.

2) Circuit Slicing and Subgraph Coloring:

  • Program-specific slicing reduces frequency crowding by coloring only couplings active in each time step, rather than assigning frequencies for all possible couplings statically.Active couplings are qubit pairs currently involved in two-qubit gates; the active subgraph is colored to minimize the number of colors.Source: 2) Circuit Slicing and Subgraph Coloring · p. 7
  • Coloring the active subgraph yields non-colliding interaction frequencies, while idle or single-qubit qubits use frequencies assigned by coloring the connectivity graph.The described coloring method is a polynomial-time Welsh-Powell greedy approximation.Source: 2) Circuit Slicing and Subgraph Coloring · p. 7

3) SMT Solver Optimization:

  • The SMT solver assigns colors to frequencies within the allowed range while satisfying crosstalk constraints, using binary search to maximize the feasible separation threshold.The ordering also assigns higher frequencies to colors used more often, based on the stated relation between interaction frequency and gate time.Source: 3) SMT Solver Optimization · p. 7

4) Frequency Partitioning:

The method partitions tunable frequencies, combines native-gate decompositions to improve fidelity, and schedules gates to balance crosstalk against decoherence.

4) Frequency Partitioning:

  • Frequency assignments separate interaction and parking frequencies, leaving an exclusion region unused to avoid flux-noise-sensitive frequencies and interactions between idle and active qubits.Coupling colors select interaction frequencies; qubits outside the selected interaction graph remain at parking frequencies.Source: 4) Frequency Partitioning · p. 7

5) Hybrid Circuit Decomposition:

  • Hybrid decomposition assigns CNOT gates to CZ and SWAP gates to √iSWAP, which can improve fidelity because each gate is cheaper with its selected native operation.The figure compares CNOT and SWAP decompositions using iSWAP or CZ.Source: 5) Hybrid Circuit Decomposition · p. 8, Figure 8 · p. 8

6) Noise-Aware Queueing Scheduler:

  • The noise-aware scheduler delays gates when too many crosstalk-graph neighbors are already active, trading limited serialization against circuit depth and decoherence.It prioritizes gates by criticality and predicted noise conflicts, aiming to balance crosstalk reduction with minimal impact on the program critical path.Source: 6) Noise-Aware Queueing Scheduler · p. 8

VI. EVALUATION

The evaluation compares program-specific frequency-aware compilation with four tuning and scheduling baselines across NISQ benchmarks. It estimates worst-case success using crosstalk and decoherence errors, validating the heuristic against noisy simulation on small circuits.

A. Tuning and Scheduling Baselines

  • ColorDynamic computes optimized frequencies for each program time step and combines circuit slicing, strategic decomposition and serialization, graph coloring, and SMT solving.The four comparison baselines are naive compilation, gmon with tunable couplers, uniform frequency with serialization, and static frequency-aware compilation.Source: A. Tuning and Scheduling Baselines · p. 8

B. Benchmarks

  • The benchmark suite includes near-term quantum applications and simultaneous-gate circuits, with circuit sizes of 4, 9, 16, and 25 qubits.The simultaneous-gate circuits are included to demonstrate crosstalk effects on gate fidelity.Source: B. Benchmarks · pp. 8–9, Table II · p. 9

C. Experimental Setup

  • The heuristic estimates worst-case program success by combining crosstalk gate error and qubit decoherence error.Decoherence is modeled using T1 and T2 during idle or gate time.Source: C. Experimental Setup · p. 9
  • Full noisy-circuit simulation becomes intractable beyond tens of qubits, so the authors validate the heuristic estimator on small circuits where simulation is possible.Compilation experiments use a 2D grid of frequency-tunable transmons and Python/Qiskit tooling.Source: C. Experimental Setup · p. 9

VII. RESULTS

ColorDynamic improves worst-case program success over serialization and static strategies while approaching the estimated performance of tunable-coupler hardware. Its scheduling limits decoherence costs, and compilation remains practical at larger scales.

B. Impact on Serialization

  • 1.02x average decoherence error versus Baseline G and 0.90x versus Baseline U; serialization can deepen circuits and increase decoherence.Fig. 10 compares circuit depth and decoherence error across mitigation algorithms.Source: B. Impact on Serialization · p. 9, Figure 10 · p. 10

A. Program Success Rate

  • 13.3x better success rate on average than Baseline U; ColorDynamic also performs comparably to Baseline G and outperforms static Baseline S across benchmarks.The Fig. 9 worst-case success-rate comparison omits qaoa(16) and ising(16) because their estimated rates were below 10^-4; Baseline G assumes perfect coupler deactivation.Source: A. Program Success Rate · p. 9, Figure 9 · p. 10

C. Scalability and Complexity

  • Compilation time stays below 30 seconds on systems up to 81 qubits for highly parallel XEB, with graph coloring and SMT optimization kept tractable through small subproblems.The number of SMT variables and constraints scales with the number of colors obtained from coloring.Source: C. Scalability and Complexity · pp. 9–10

D. Sensitivity on Tunability

ColorDynamic’s benchmark results indicate that a small number of frequency colors can suffice, while residual coupling degrades gmon performance. The method also shows success-rate improvements across varied device connectivity and is presented as extensible to tunable-qubit architectures.

D. Sensitivity on Tunability

  • 1 or 2 colors is the observed optimal operating point, depending on benchmark parallelism; two frequency sweet spots are presented as good candidates for near-term algorithms, with diminishing returns from more.The figure examines the balance between frequency choices and serialization.Source: D. Sensitivity on Tunability · p. 10

E. Gmon’s Sensitivity to Residual Coupling

F. General Device Connectivity

  • 3.97x geometric-mean success-rate improvement over Baseline U across benchmarks; best performance is usually on connectivity that is neither too sparse nor denser than a grid.Compilation time is kept low at about 10 seconds in practice, though it increases in extreme, unrealistically dense connectivity cases.Source: F. General Device Connectivity · p. 11, Figure 13 · p. 11

VIII. CONCLUSION

  • The conclusion presents ColorDynamic as software crosstalk mitigation that can make fixed-coupler architectures competitive with tunable-coupler systems and may simplify fabrication.The approach is described as extensible to tunable-qubit architectures and as a generic calibration problem for isolating or interacting qubits.Source: §VIII · p. 11

APPENDIX A EXAMPLE IDLE AND INTERACTION FREQUENCIES BY

The appendix illustrates ColorDynamic’s idle and interaction frequency assignments for a 4 × 4 qubit system and describes a heuristic model for crosstalk-related gate errors. It also gives tuning and gate-performance context for tunable transmons.

APPENDIX B GATE ERRORS DUE TO CROSSTALK

  • The heuristic gate-error model plots |01⟩↔|10⟩ and |11⟩↔|20⟩ transition probabilities against external magnetic flux and time.For frequency-tunable transmons, two-qubit gates use resonance; the resonant energy levels determine whether iSWAP or CZ gates can be implemented.Source: Figure 15 · p. 12, Appendix B · p. 12

APPENDIX A EXAMPLE IDLE AND INTERACTION FREQUENCIES BY

  • ColorDynamic assigns idle frequencies in a high-low checkerboard and interaction frequencies for simultaneous two-qubit gates, using subgraph coloring and SMT solvers.The example keeps idle frequencies near the low sweet spot around 5 GHz and interaction frequencies near the high sweet spot around 7 GHz.Source: Appendix A · p. 11, Figure 14 · p. 12

APPENDIX B GATE ERRORS DUE TO CROSSTALK

  • State-of-the-art controls tune within 2 ns, while tunable-transmon iSWAP and CZ gates take around 50 ns with > 99.5% fidelity; fixed-frequency CR gates take around 160 ns.The text notes that control noise and pulse distortion remain present in tunable systems, and that sweet spots and limiting the number of colors are mitigation techniques.Source: Appendix B · p. 12

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