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Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits
Bibek Pokharel, Namit Anand, Benjamin Fortman, Daniel Lidar
TL;DR
Decoherence limits small superconducting quantum computers, motivating methods that suppress errors without encoding overhead. This paper evaluates dynamical decoupling on IBM and Rigetti platforms and finds substantial unconditional fidelity gains for single-qubit evolution, with smaller benefits for entangled states and evidence that dephasing dominates spontaneous emission.
Problem
Cloud-based superconducting quantum computers require decoherence suppression, but unconditional demonstrations of such improvement on these noisy platforms were limited.
Method
The paper applies dynamical-decoupling pulse sequences on IBM and Rigetti superconducting-qubit platforms, including sequences tailored to dephasing and spontaneous emission.
Results
DD substantially improves single-qubit fidelity, slows entanglement loss to a lesser degree, and specialized sequences show that dephasing errors dominate spontaneous-emission errors.
Takeaways & Limitations
Unconditional dynamical decoupling can suppress inherent decoherence on prototype cloud quantum computers despite imperfect pulse implementation.
Abstract
from arXiv · showhide
Quantum computers must be able to function in the presence of decoherence. The simplest strategy for decoherence reduction is dynamical decoupling (DD), which requires no encoding overhead and works by converting quantum gates into decoupling pulses. Here, using the IBM and Rigetti platforms, we demonstrate that the DD method is suitable for implementation in today's relatively noisy and small-scale cloud based quantum computers. Using DD, we achieve substantial fidelity gains relative to unprotected, free evolution of individual superconducting transmon qubits. To a lesser degree, DD is also capable of protecting entangled two-qubit states. We show that dephasing and spontaneous emission errors are dominant in these systems, and that different DD sequences are capable of mitigating both effects. Unlike previous work demonstrating the use of quantum error correcting codes on the same platforms, we make no use of post-selection and hence report unconditional fidelity improvements against natural decoherence.
Appendix F):
Appendix F examines fidelity scaling and entangled-state protection under dynamical decoupling on IBMQX5 and Acorn. DD slows entanglement loss and decay toward the fully mixed state, while finite pulse and preparation errors limit fidelity.
- Fidelity-scaling analysis: For IBMQX5, the measured infidelity-scaling slope is below the ideal-pulse upper bound and becomes negative for N ≳ 200.The negative slope indicates decreasing infidelity with increasing pulse interval at fixed pulse number, contrary to the positive-slope bound interpretation.
- Protection of two-qubit entangled states: Bell-state preparation itself introduces substantial errors, including readout and CNOT-gate errors that bias the measured populations.These initialization imperfections contaminate computational-basis outcomes before the subsequent evolution is assessed.
- Protection of two-qubit entangled states: Spontaneous emission drives a sharp increase in p00 during free evolution, whereas DD suppresses this ground-state dominance.The comparison uses computational-basis probabilities after Bell-state preparation and evolution under free or dynamically decoupled conditions.
- Protection of two-qubit entangled states: Acorn shows stronger DD slowing of decay toward the fully mixed state than IBMQX5.On IBMQX5, complete scrambling occurs after approximately 20 pulses, while the corresponding Acorn behavior occurs after approximately 30 pulses.
- Protection of two-qubit entangled states: DD preserves entangled Bell-state populations better than free evolution, although entanglement is still rapidly lost.The decay toward the fully mixed state is slowed, with the original population ratio retained on Acorn for up to approximately 50 pulses.
Appendix A: Overview of existing QEC implementations on the IBM Quantum Experience
Existing IBM Quantum Experience studies explored error correction, fault tolerance, encoded memories, and post-selected fidelity improvements, but several implementations had important scope or methodology limitations.
- Fault-tolerance demonstrations used repetition or small encoded circuits, with results depending on circuit conditions and not always satisfying the proposed criterion.
- Encoded-memory fidelities were lower than those of physical qubits when testing artificial bit-flip and phase-flip errors with a three-qubit code.
- Post-selection increased [[4,2,2]] memory fidelity from 0.62±0.03 to 0.75±0.04, with an average retained-data yield of 54±2%.
- Randomized benchmarking reported 5.8% unencoded infidelity versus 0.6% encoded infidelity, but post-selection retained approximately 40% of data.
- Critiques of the randomized-benchmarking study included skipped logical-state preparation, testing only inherently robust ground-state-related conditions, and bypassing noisy multi-qubit gates.
Appendix B: Machine Specifications
The IBMQX5 and Rigetti Acorn platforms had broadly similar reported hardware figures of merit, while their physical parameters varied over time.
- IBMQX5 and Rigetti Acorn had similar T1 and T2 times, single-qubit gate errors, and readout errors.The paper notes that these parameters fluctuate daily and reports access dates with the hardware details.
1. IBMQX5
The IBMQX5 experiments used a 16-qubit superconducting-transmon chip with cloud-executed circuits, 90 ns single-qubit pulses, and characterization of physical gate performance.
- IBMQX5 is a 16-qubit superconducting-transmon chip whose qubits are coupled via coplanar waveguides.
- The platform specification table summarizes single-qubit pulse times, qubit counts, and shots per experiment for IBMQX5 and 19Q-Acorn.
- Each single-qubit pulse lasted 90 ns, experiments used 8192 repetitions, and single-qubit gate and readout errors were approximately 10^-3.
2. IBMQX4
The IBMQX4 experiments used a five-qubit superconducting platform and found that XY4 dynamical decoupling produced qualitatively consistent improvements relative to IBMQX5.
- IBMQX4 is a five-qubit chip with a specified qubit connectivity graph.
- The IBMQX4 physical-parameter table reports minimum, average, and maximum CNOT fidelities of 0.8738, 0.9441, and 0.9774.
- XY4 produced a nearly threefold increase in λ, from 44.7 ± 2.8 under free evolution to 128.0 ± 0.8 under DD.
- The free-evolution and DD curves intersected at t_int = 216±16, twice the IBMQX5 gate depth where DD improved average fidelity.
3. Rigetti Acorn
The Rigetti Acorn experiments used a 19-qubit superconducting chip, but device failures and performance variability constrained analyses to 15 active qubits. Results were collected across changing device conditions and compared with IBMQX4 connectivity and fidelity measurements.
- Platform and access: Acorn contains fixed-frequency and tunable transmon qubits accessed remotely through Rigetti’s Forest, Quil, and pyQuil.The chip’s layout combines capacitive-coupled qubits with different frequency tunability.
- Platform limitations: Qubit 3 was disabled for performance issues, while qubits 2, 12, 15, and 18 were excluded because their performance varied substantially or was too noisy.The excluded qubits reduced the analyzed device set to 15 active qubits.
- Baseline characteristics: Acorn and IBM chips both had microsecond-scale relaxation times and single-qubit fidelities greater than 0.98.The IBMQX5 relaxation times were longer than Acorn’s, while readout error was reported at a similar level.
- Comparison setup: IBMQX4 fidelity results under DD were compared with free evolution after averaging over 36 initial conditions and all five qubits.The comparison used the IBMQX4 device’s qubit set and aggregated initial-state conditions.
- Platform limitations: The Acorn chip experienced a cryogenic-system failure and thermal cycle that degraded performance and affected multiple two-qubit gates.The chip was out of service from 4/17/18 onward, and later measurements showed reduced final fidelity.
Appendix C: Statistical methods
The appendices describe averaging, bootstrapping, and fitted-curve procedures used to estimate fidelity statistics and intersection-time uncertainties across qubits, dates, and initial conditions.
- Averaging and uncertainty: DD experiments were run in parallel across qubits or qubit pairs, with reported means and error bars obtained by averaging and bootstrapping.This aggregation was applied to both single-qubit and entanglement experiments.
- Date comparisons: Figure 12 reports Acorn mean fidelity averages across 36 initial conditions and 15 active qubits for different measurement dates.The date comparison captures changing device performance.
- Averaging and uncertainty: Bootstrapping repeatedly resampled the data with replacement to calculate means, standard deviations, and confidence intervals.The IBMQX5 analysis used 5000 resamples of 576 observations from 36 initial conditions and 16 qubits.
- Fitted intersection times: Intersection-time uncertainties were estimated by sampling fitted parameters from their Gaussian error distributions and recalculating the intersection time.The reported result is the mean intersection time with 2σ error bars.
- Fitted intersection times: The Acorn fit summarized mean fidelities for 15 active qubits, while IBMQX4 results were fitted using the same model.These fits correspond to the mean fidelities shown in Figure 12.
- Averaging and uncertainty: Figure 13 contrasts the original fidelity frequency distribution with its bootstrapped samples used for estimating the mean and confidence intervals.The example uses IBMQX5 data from 36 type-1 initial conditions and 16 qubits.
Appendix D: DD vs free evolution correlation plots, as a function of initial state
The correlation analysis shows that DD’s benefit depends strongly on the initial state: it can reduce fidelity near the ground state but improve superposition and excited-state preparations relative to free evolution.
- Initial-state dependence: For states near |0⟩, DD is worse than free evolution, whereas near-equal superpositions generally benefit from DD, especially on Acorn.The superposition regime is identified as susceptible to dephasing.
- Initial-state dependence: For states near |1⟩, DD improves fidelity at intermediate N on IBMQX5 and at all N on Acorn.These excited-state preparations are associated with susceptibility to spontaneous emission.
- Correlation pattern: Most near-ground-state points fall below the DD-versus-free-evolution diagonal, while points farther from |0⟩ mostly lie above it.On IBMQX5 the improvement tends to disappear with time, whereas Acorn retains it.
- Pulse-scaling analysis: The infidelity-scaling analysis examines how infidelity varies with τ for different pulse counts N.This provides a separate view of pulse-number and interval dependence.
Appendix E: DD tailored for dephasing and spontaneous emission
The appendix compares DD sequences tailored to dephasing and spontaneous emission with the universal XY4 sequence. Pure-dephasing suppression performs better, indicating that dephasing dominates spontaneous emission in the tested system.
- Noise-specific sequences: The experiments tested DD sequences tailored separately to dephasing and spontaneous-emission errors.Both error sources were identified as important contributors to free-evolution infidelity.
- Dephasing suppression: (XI)N and (YI)N suppress pure dephasing because σz anticommutes with X and Y pulses.Pure dephasing is represented by a σz ⊗ B system-bath interaction.
- Spontaneous-emission suppression: (ZI)N suppresses spontaneous emission by targeting the σ− ⊗ B interaction.The spontaneous-emission operator is written as σ− = |0⟩⟨1|.
- Performance comparison: The specialized sequences underperform universal XY4, but (XI)N and (YI)N achieve nearly 90% of XY4’s initial-decay-time λ value.The comparison is reported for the IBMQX5 performance summary.
- Performance comparison: Better performance after pure-dephasing suppression indicates that dephasing errors dominate spontaneous-emission errors in the tested system.This conclusion follows from the relative performance of the specialized sequences.
Appendix F: Infidelity as a function of pulse spacing
The appendix analyzes how infidelity scales with pulse spacing and pulse count, connecting theoretical DD bounds to fitted experimental scaling results.
- Theoretical scaling: For ideal DD pulses, the distance between free and dynamically decoupled states is bounded by an expression involving total evolution time, pulse count, and a bath-dependent constant.The bound is then related to Uhlmann fidelity after substituting T = τN.
- Theoretical scaling: D(ρ,σ) denotes half the trace-norm distance between quantum states.
- Experimental scaling: Figure 15 presents infidelity scaling, while straight-line fit slopes and offsets are extracted for additional τ and N values and used in main-text Fig. 5.
Appendix G: Higher order sequences based on genetic algorithms
This appendix introduces higher-order DD sequences generated by genetic algorithms and compares them experimentally with XY4 and free evolution. GA16a slightly outperforms XY4, whereas GA32a is similar to XY4 and GA8a performs slightly worse.
- Motivation: Genetic-algorithm sequences form a hierarchy predicted numerically to improve performance at fixed pulse interval and duration, but had not previously been experimentally tested.
- Sequence construction: The sequences are constructed from pulse unitaries P_j interleaved with free-evolution unitaries f_τ = e^−iHτ.
- Sequence construction: GA8a is an eight-pulse sequence built from alternating P1 and P2 operations with intervening free-evolution periods.
- Sequence construction: Choosing P1 = X and P2 = Y gives GA4 = XY4, while choosing P1 = X and P2 = Z gives GA8a.
- Experimental comparison: GA16a is the best tested sequence, slightly outperforming XY4; GA32a performs similarly to GA4, and GA8a performs slightly worse.
- Experimental comparison: Figure 16 compares GA8a, GA16a, and GA32a with XY4 and free evolution on IBMQX5.