Optimized Quantum Compilation for Near-Term Algorithms with OpenPulse

1. INTRODUCTION

• The motivation is to optimize across the algorithm-to-device stack for near-term applications on noisy hardware.The cited examples span molecular chemistry [1], combinatorial optimization [2], and adversarial machine learning [3].Source: §1 · p. 1
• The compiler targets near-term algorithms on hardware-agnostic user code by augmenting basis gates to match the hardware and optimizing pulse schedules.The approach is presented as applicable to any quantum computer.Source: Figure 1 · p. 1, §1 · p. 1
• The compiler was exercised on IBM hardware through OpenPulse, with 11.4 million experimental shots and 4 million presented as concrete research outcomes.The work describes this as the first experimental demonstration of OpenPulse for optimized quantum-program compilation.Source: §1 · pp. 1–2
• Pulse-level control enables direct single-qubit rotations, cross-gate pulse cancellation, and two-qubit decompositions into hardware-implemented interactions.These are the first three optimizations identified in the introduction.Source: §1 · p. 2
• Pulse control also enables d-level qudit operations beyond the two-level qubit subspace.The introduction identifies this as a fourth compiler optimization.Source: §1 · p. 2

2.1 The Qubit

• A qubit can occupy superpositions of |0⟩ and |1⟩, with its state represented by latitude and longitude on the Bloch sphere.Upon measurement, it collapses to |0⟩ or |1⟩ with probabilities dependent only on latitude.Source: §2.1 · p. 2

2.2 Quantum Gates

• Single-qubit gates correspond to Bloch-sphere rotations, while multi-qubit operations can be decomposed into single-qubit rotations and an entangling gate such as CNOT.The pulse-backed layer provides a richer, overcomplete gate set than the standard interface.Source: §2.2 · p. 2

2.3 Gate Calibration

• Routine calibrations account for experimental drift; two-qubit gate calibration also calibrates Rx(180°) pulses on each qubit, which the paper exploits.RZ(θ) gates are implemented in software and typically do not require calibration.Source: §2.3 · p. 2

2.4 Experimental Setup

• Experiments used IBM’s 20-qubit Almaden device, with mean T1 and T2 lifetimes of 94 and 88 µs and mean single- and two-qubit error rates of 0.14% and 1.78%.Measurement error was 3.8%; the study used mitigation for biased measurement errors and also reports later Figure 13 results from Armonk.Source: §2.4 · pp. 2–3

3. COMPILER FLOW

• The compiler’s alternative flow augments the basis-gate set and produces a more optimized pulse schedule across the four compilation stages.The stages are programming language, assembly, basis gates, and pulse schedule.Source: §3 · p. 3

3.1.1 Programming Language

• Quantum programming languages provide user-facing control flow, debugging tools, and abstraction from underlying hardware.Examples include Qiskit, Cirq, and PyQuil [26].Source: §3.1.1 · p. 3

3.1.2 Assembly

• Quantum assembly is close to hardware but generally remains device-agnostic, with instructions usually acting on one or two qubits.Examples include OpenQASM [6], pyQuil [26], and cQASM [33].Source: §3.1.2 · p. 3

3.1.3 Basis Gates

• Basis gates express operations using the gate set implemented by hardware, but existing basis-gate implementations remain too far from pulse-level primitives.A Controlled-Z instruction, for example, can be rewritten as H and CNOT gates.Source: §3.1.3 · p. 3

3.1.4 Pulse Schedule

• A pulse schedule is a multi-channel sequence of complex-valued analog pulses, with hardware channels driven by an Arbitrary Waveform Generator.The cited experimental AWG produces a new complex number every 0.22 ns.Source: §3.1.4 · p. 3

3.2 Motivation for Different Basis Gates

• The compiler targets gaps between standard basis gates and pulse-level hardware primitives, where alternative gates can reduce operation costs.Table 2 compares two-qubit operation costs by native gate; its costs count the number of two-qubit gates.Source: §3.2 · pp. 3–4, Table 2 · p. 4
• Because several native-gate columns have identical costs to CNOT, compilers can treat them as equivalent despite distinct optimization opportunities.Quantum algorithms are usually written in terms of CNOTs, which contributes to the lack of an obvious reason to deviate from those basis gates.Source: §3.2 · p. 4
• Half-iSWAP uses a damped standard iSWAP pulse, halving each row’s cost relative to full iSWAP.The CNOT and SWAP decompositions are known, while the authors say the ZZ Interaction and Fermionic Simulation decompositions were not previously known.Source: §3.2 · p. 4
• A parametrized CR(θ) gate makes the ZZ Interaction 2x cheaper than standard CR(90◦), under a 99.9+% fidelity decomposition constraint.The ZZ Interaction is described as the most common two-qubit operation in near-term algorithms.Source: §3.2 · p. 4

3.3 Design of Our Compiler

• Figure 3 depicts the compiler passes for commutativity detection and augmented basis gate detection.The passes perform the pattern matching used to optimize quantum assembly.Source: Figure 3 · p. 5, §3.3 · p. 5
• The compiler augments Qiskit’s basis gates and adds cmd_def translations that convert them into pulse schedules.Its framework is designed to target any underlying quantum hardware, although the experiments used IBM hardware.Source: §3.3 · pp. 4–5
• Transpiler passes pattern-match gate sequences that reduce to augmented basis gates, including patterns obscured by false dependencies through commutativity detection.The passes preserve write-once, target-all behavior so user code can remain hardware agnostic.Source: §3.3 · p. 5

3.4 Compiler Design Tradeoffs

• QOC-designed pulses can accumulate substantial error when the device Hamiltonian is inaccurate.The authors identify perfect characterization of the underlying physics as a QOC requirement.Source: §3.4 · p. 5
• Experimental QOC also faces bounded-amplitude and smooth-derivative constraints, which diminish its potential advantage and reliable convergence.Evaluating fidelity partial derivatives is extremely difficult with noisy experimental measurements.Source: §3.4 · p. 5
• Prior experimental QOC work mostly focused on state preparation and often incurred substantial Hamiltonian tomography or calibration overhead.The authors note that superconducting-qubit Hamiltonians drift over time and that experimental QOC there is rarer.Source: §3.4 · p. 5
• The authors’ approach re-scales pre-calibrated basis-gate pulses, avoiding device-Hamiltonian requirements and producing simple, interpretable pulses.The calibrations are already performed daily; the passage says pulse simplicity minimizes the possibility of control errors.Source: §3.4 · p. 5

4.2 Direct partial rotation about the X axis

• DirectRx(θ) scales the amplitude of a pre-calibrated Rx(180◦) pulse by θ/180◦, requiring no additional calibration.The approach directly realizes partial X-axis rotations rather than invoking two discrete Rx(90◦) pulses.Source: §4.2 · p. 6

4.1 Direct X gates

• DirectX takes 35.6 ns versus 71.1 ns for the standard X gate, using a pre-calibrated Rx(180◦) pulse instead of two Rx(90◦) pulses.The compared pulse schedules have the same absolute area-under-curve.Source: Figure 4 · p. 6, §4.1 · p. 6

4.3 Optimizing generic rotations

• Any single-qubit gate can be expressed using direct Rx(θ) rotations sandwiched by Rz frame changes, which have zero duration and perfect fidelity.This extends the direct-rotation approach from X-axis rotations to generic single-qubit gates.Source: §4.3 · p. 6

4.4 Compiler implications

• The compiler uses simulations and experiments to characterize rotation errors across angles and inform pulse-substitution choices.The experiments measure final-state X, Y, and Z components for scaled pulses; Figure 6 presents simulation results and Figure 7 presents experimental results.Source: §4.4 · p. 6, Figure 6 · p. 7, Figure 7 · p. 7

4.2 Direct partial rotation about the X axis

• 2x faster and 16% lower error on average, DirectRx(θ) rotations bypass the gate abstraction compared with standard gate-compiled rotations.Figure 5 shows the single-pulse path and the tomography-based fidelity comparison.Source: §4.2 · p. 6, Figure 5 · p. 7

4.4 Compiler implications

• Experiments show X-component deviations from simulation are shifted right and larger, and empirical phase correction can compensate using the measured dephasing at each θ.The simulation shows small, sinusoidal deviations from the Prime Meridian, with no dephasing at 0◦, 90◦, and 180◦.Source: §4.4 · p. 7

5. OPTIMIZATION 2: CROSS-GATE PULSE CANCELLATION

• Standard basis gates are not atomic; augmenting them with hardware primitives reveals cancellation opportunities that yield 24% speedups for common operations.The compiler adds CR(±45°) basis gates and uses gate cancellation; the echoed Cross-Resonance pulse itself includes two pulses separated by an X gate.Source: §5 · p. 8, §5.1 · p. 8

5.2 Application

• For open-CNOT, the first control X cancels the internal X in the CNOT decomposition, illustrating a cancellation invisible at standard gate granularity.The open-CNOT applies X to the target only when the control is |0⟩.Source: §5.2 · p. 8
• 24% shorter open-CNOT duration—from 1984 dt to 1504 dt—after pulse-level X cancellation.In the experiment, success probability changed from 87.1(9)% to 87.3(9)% over 16k shots.Source: Figure 8 · p. 8, §5.2 · p. 8

6.1 Theory

• CR(θ), the IBM pulse-level hardware primitive, can be added as a basis gate after its experimental behavior closely tracks the ideal curve.The compiler derives CR(90°) from the CNOT pulse schedule and stretches it horizontally to implement arbitrary θ, guided by the active cancellation echo implementation.Source: §6.1 · pp. 8–9

6.2 Application

• A single CR(θ) implements the ZZ Interaction, whereas the textbook standard-basis implementation requires two CNOTs.The decomposition was discovered computationally using the compiler’s optimization procedure.Source: §6.2 · p. 9
• 60% average reduction in state-infidelity error for the ZZ Interaction using optimized compilation.Figure 10 reports fidelities of 98.4% for standard compilation and 99.0% for optimized compilation; the ZZ Interaction is the most frequent two-qubit operation in near-term algorithms and a dominant source of benchmark improvements.Source: Figure 10 · p. 9, §6.2 · p. 9

7.1 Theory

• Frequency-shifting pulse schedules can target transitions beyond |0⟩ to |1⟩, including the |1⟩ to |2⟩ subspace.The |1⟩ to |2⟩ transition has energy gap f12 = f01 + α; applying the described frequency-shifting pulse changes the effective local-oscillator frequency.Source: §7.1 · pp. 9–10

7. OPTIMIZATION 4: QUDIT OPERATIONS

• Using higher energy levels one at a time realizes a base-d counter, with potential use in modulo-d parity checks and leakage detection.The passage also identifies possible applications beyond near-term computing, including speeding up function-evaluation oracles.Source: §7.2 · p. 10

7.2 Application

• The counter uses microwave control of two transitions inaccessible to standard basis gates: f12 and f02/2.The two-photon |0⟩ to |2⟩ transition is suppressed and requires greater drive power than a single-photon |0⟩ to |1⟩ X gate.Source: §7.2 · p. 10
• A single qutrit completed 60 counter cycles, or 180 increments, before dropout exceeded 40%.The authors describe this as high-fidelity control and note that a single qubit cannot model a base-3 counter.Source: §7 · p. 9, §7.2 · p. 10

8.1 Benchmarks

• The benchmarks use Hellinger error to compare actual and target outcome distributions, rather than relying on QAOA probability of success.The authors explain that QAOA targets a distribution of outcomes, so probability of success alone may not reflect error appropriately.Source: §8.1 · pp. 10–11

8.2 Results

• 1.55x average error reduction across all six benchmarks; 5 Qubit QAOA error fell from 33.7% to 14.5%, a 2.32x reduction.Figure 12 presents benchmark error reductions; the benchmarks cover VQE, QAOA, and Hamiltonian dynamics.Source: §8.1 · p. 10, §8.2 · p. 11, Figure 12 · p. 11
• The qutrit incrementer completed 60 cycles, or 180 increment operations, before dropout exceeded 40%, without a standard qubit comparison.A single qubit cannot model a base-3 counter.Source: §8.2 · p. 11

8.3 Source of Fidelity Improvements

• Shorter pulses, reduced susceptibility to calibration error, and smaller pulse amplitudes are identified as sources of fidelity improvement.Randomized benchmarking estimates that shorter pulses account for 70% of the improvement, while reduced calibration susceptibility and smaller amplitudes account for the remaining 30%.Source: §8.3 · p. 11

• 2.88 million total shots were used for a randomized-benchmarking-style experiment fitted to exponential decay.For each K, the experiment randomized 5 sequences of unitary operations.Source: Figure 13 · p. 12
• 1.6x error reductions and 2x speedups for near-term algorithms result from augmenting basis gates with pulse-backed hardware primitives bootstrapped from existing calibrations.Source: §9 · pp. 11–12
• The technique bypasses experimental barriers to quantum optimal control by not relying on knowledge of the system Hamiltonian, and is available immediately through software.Source: §9 · p. 12