PaperlayerView exact revision on arXiv

Source-linked AI summary

A Hardware-Native Trapped-Ion Hybrid Qudit-Oscillator Instruction Set

Masoud Hakimi Heris, Yuan Liu, Frank Mueller

arXiv:2610.13843v1quant-phcs.ARcs.ET

TL;DR

Trapped-ion scaling remains challenging, motivating use of each ion’s internal levels alongside native bosonic modes. The paper introduces a hardware-native hybrid qudit–oscillator instruction set whose three operation families suffice for multimode Hamiltonian generation. For the three-chromophore benchmark, a qudit step is projected to be 10.5 times faster under the stated sequential timing model.

  • Problem

    Scaling trapped-ion processors by adding ions remains challenging, motivating complementary ways to enlarge the computational space within each ion.

    Source: §I · p. 1

  • Method

    The paper introduces a hardware-native qudit–oscillator instruction set in which XE, Zd, and CΠzD generate arbitrary qudit operators tensored with polynomial functions of mode quadratures.

    Source: §XI · p. 17, §8 · p. 20

  • Results

    A projected 10.5 speedup for one Trotter step on the qudit versus the qubit reference is reported under the sequential timing model.

    Source: §X · p. 16

  • Takeaways & Limitations

    When the electronic manifold fits in one qudit, electronic couplings become intra-ion transitions and the lab-frame Hamiltonian compiles without a displaced-frame transformation.

    Source: §X · p. 16

    Single-ion compression applies when Nc + 2 ≤ deff; beyond that, the manifold is spread over multiple ions.

    Source: §XI · p. 17

Abstract

from arXiv · show

Scaling trapped-ion processors by adding ions remains challenging. A complementary route exploits the multilevel internal structure of each ion to increase the computational Hilbert space per ion. We introduce a hardware-native hybrid qudit-oscillator instruction set for a general d-level internal register coupled to bosonic modes and prove that three of its native operation families suffice for universality of one qudit coupled to several modes. Adding an entangling operation between ions extends universality to a connected register of several qudits. The architecture natively supports both phase-space and sideband instruction sets and is implemented in the open-source framework HybridLane. As a representative application, we reproduce the dissipative vibronic dynamics of a three-chromophore complex previously simulated on a hybrid qubit-oscillator superconducting platform. Moving from a one-qubit-per-state register to a single qudit stores the entire electronic manifold in one ion, so every electronic coupling becomes a local intra-ion transition and the lab-frame Hamiltonian compiles directly into the ISA. Under the stated sequential timing model from a 40Ca+ qudit processor, one Trotter step is projected to run about ten times faster on the qudit, with an average RMSE of approximately 1.1 percent against the published reference.

I. INTRODUCTION

Trapped-ion scaling can also come from using each ion’s internal levels, while hybrid processors keep bosonic modes native. This work combines qudit control with motional modes as computational registers in a hardware-native instruction set.

I. INTRODUCTION

  • Trapped-ion scaling remains challenging, while hybrid processors keep bosonic modes native and qudit control enlarges the discrete register within each ion.Molecular and spin-boson problems pair a small discrete manifold with many bosonic modes, and qubit-only encodings require truncating and digitally encoding those modes.Source: §I · p. 1

II. A NATIVE HYBRID QUDIT–OSCILLATOR INSTRUCTION SET

  • The instruction set treats a d-level qudit and its motional modes as computational registers, with level-selective couplings and a universality guarantee.The five native primitives comprise qudit phase shifts, transitions, and three qudit–mode interactions; the architecture also includes a synthesized beam splitter.Source: Figure 1 · p. 2, §I · p. 2, §II · p. 3
  • The architecture includes the phase-space instruction set and makes sideband operations native, while retaining native SU(d) control of the discrete register.The conditional displacement realizes the phase-space entangling primitive, and the transition-conditioned displacement makes the sideband model native.Source: §II · p. 3

B. Zd: Qudit Phase Shift

  • A qudit is a d-level register, a qumode is a bosonic mode, and Zd applies a controllable phase to one selected qudit level.The Zd projectors span the diagonal sector of u(d), while their traceless differences span that of su(d).Source: A. Background · p. 3, B. Zd: Qudit Phase Shift · p. 3

C. XE: Qudit Transition

The native operations provide selective control of qudit transitions and level-conditioned mode motion. Together, they support both phase-space and sideband interactions.

C. XE: Qudit Transition

  • XE drives a Rabi rotation on a selected pair of qudit levels while leaving the other levels untouched.The transition is selected by drive frequency, and rotation angle and phase are controlled by its tone; noncommuting shared-level drives require a synthesized sequential unitary.Source: C. XE: Qudit Transition · p. 4

D. CΠzD: Level-Conditioned Displacement

  • CΠzD displaces a mode conditioned on a selected qudit level and supplies the non-Gaussian resource used in the universality construction.For a specific multilevel encoding, exact single-level projector selectivity may require a calibrated combination of level-selective controls.Source: D. CΠzD: Level-Conditioned Displacement · p. 4

E. CΠR: Level-Conditioned Mode Rotation

  • CΠR rotates a mode conditioned on a selected qudit level and directly compiles the vibronic Hamiltonian’s dispersive terms.Its physical basis is the phonon-number-dependent dispersive shift from a far-detuned motional sideband; exact projector selectivity may require calibrated controls.Source: E. CΠR: Level-Conditioned Mode Rotation · pp. 4–5

F. CΠxD: Transition-Conditioned Displacement

  • CΠxD couples a qudit transition to a mode, combining red and blue sidebands for a quantum Rabi interaction and enabling sideband operations within the native instruction set.Driving only the red sideband yields the excitation-conserving Jaynes–Cummings interaction.Source: F. CΠxD: Transition-Conditioned… · p. 5

G. The Synthesized Beam Splitter

The trapped-ion architecture uses native qudit–motion controls and a synthesized beam splitter, with a two-ion exchange for manifolds spanning ions. Its vibronic benchmark maps term by term to the instruction set.

G. The Synthesized Beam Splitter

  • A beam splitter is synthesized from spin-dependent forces on two modes, with a mediator ancilla carrying the conditioning while leaving the computational register undisturbed.It provides efficient Gaussian mode mixing and allows programs written for the phase-space set to run without modification.Source: G. The Synthesized Beam Splitter · p. 5

H. The Two-Ion Exchange

  • When an electronic manifold spans multiple ions, a two-qudit Mølmer–Sørensen interaction moves excitation between ions through a selected level pair.This native trapped-ion operation is not used in the single-ion circuits.Source: H. The Two-Ion Exchange · p. 5

A. Register and Encoding

  • The hybrid register pairs one trapped-ion qudit with collective motional modes, which directly interact through the shared motional bus.This avoids SWAP operations used to mediate interactions on nearest-neighbor architectures.Source: A. Register and Encoding · p. 5

B. Qudit Platforms Across Ion Species

  • The 40Ca+ encoding uses an auxiliary level for projector-conditioned mode operations, and the three-chromophore electronic manifold fits within one ion.The usable qudit dimension depends on levels that can be coherently initialized, selectively addressed, coupled to modes, and read out; when Nc + 2 exceeds deff, the manifold spans several ions.Source: A. Register and Encoding · p. 6, B. Qudit Platforms Across Ion Species · p. 6

C. The Vibronic Benchmark

  • The benchmark is a three-chromophore vibronic model with localized vibrational modes and a low-frequency link mode coupled to chromophore A.The model follows Vu et al..Source: C. The Vibronic Benchmark · p. 6
  • Each lab-frame Hamiltonian term maps exactly to an instruction-set primitive, so compilation introduces no frame or operator approximation.The numerical evolution still uses Trotterization and a finite Fock cutoff.Source: C. The Vibronic Benchmark · pp. 6–7

IV. UNIVERSALITY

Three native operation types suffice for Hamiltonian generation over a qudit and multiple modes. Qudit control and level-conditioned displacements generate the polynomial Hamiltonians of the joint system.

IV. UNIVERSALITY

  • XE, Zd, and CΠzD generate Hamiltonians formed from arbitrary qudit operators tensored with polynomial functions of all mode quadratures.Cross-mode terms arise from commutators of conditional-displacement generators, so no mode-coupling primitive is required.Source: §IV · p. 7

A. Pillar 1: Qudit Control from XE and Zd

  • XE transitions on a connected graph, together with Zd phase control, generate su(d) through commutation.This permits full qudit control without directly addressing every level pair.Source: A. Pillar 1: Qudit Control from XE and… · p. 7
  • Commutators of conditional displacements with qudit rotations raise quadrature-polynomial degree, extending the generated algebra beyond Gaussian operations.The construction extends from su(2) to su(d) and arbitrary polynomial degree.Source: B. Pillar 2: Universal Single-Mode… · p. 7
  • For Fock cutoffs N = 6, 8, and 10, the generated algebra has the same ranks through iterations 0–3, while unconditional displacements retain bandwidth one.The truncated matrices reach u(4N) at iteration 4; this is a consistency check, not the universality proof, which is analytical.Source: B. Pillar 2: Universal Single-Mode… · p. 8

C. Multimode Coupling Without a Beam Splitter

The native primitives generate multimode qudit–oscillator Hamiltonians without requiring a beam splitter, while a synthesized beam splitter and direct cross-compilation support both phase-space and sideband models. The framework is applied to dissipative vibronic dynamics in a three-chromophore benchmark.

C. Multimode Coupling Without a Beam Splitter

  • XE, Zd, and CΠzD generate arbitrary joint polynomials across oscillator modes, making the multimode register universal without a beam splitter.The construction uses cross-mode commutators of generators acting on different modes.Source: C. Multimode Coupling Without a Beam… · p. 8

D. The Synthesized Beam Splitter

  • The unconditional beam splitter is not needed for universality, but provides Gaussian mode mixing and compatibility with the phase-space instruction set.A mediator ancilla ion carries the conditioning when this operation is invoked; the vibronic circuits do not use it.Source: D. The Synthesized Beam Splitter · p. 8

E. Closure

  • The three native primitives generate arbitrary qudit operators tensored with polynomials in all mode quadratures, establishing universality in Hamiltonian generation.The closure follows from single-qudit generators, per-mode generators, and their cross-mode commutators.Source: E. Closure · p. 8

V. CROSS-COMPILATION BETWEEN PHASE-SPACE AND SIDEBAND MODELS

  • The same trapped-ion architecture supports phase-space and sideband instruction sets, with circuits rewritable between them using native primitives.The choice between models is an algorithmic decision within one architecture, not a constraint imposed by heterogeneous hardware.Source: §V · pp. 8–9

VI. HYBRIDLANE IMPLEMENTATION

  • HybridLane is extended from hybrid oscillator–qubit circuits to native qudit–oscillator circuits, with five level-parameterized primitives implemented on its bosonic backend.The extension is parameterized by addressed level or level pair, making it independent of qudit dimension.Source: §VI · p. 9

VII. APPLICATION: DISSIPATIVE VIBRONIC DYNAMICS

  • The application validates the architecture on dissipative energy transfer among three chromophores coupled to multiple vibrational modes and an environment.The benchmark model is specified with published parameters for reproducibility.Source: §VII · p. 9

A. Qudit Compilation

The qudit compilation maps the lab-frame vibronic Hamiltonian directly to native operations, while the qubit reference compiles the displaced-frame model on the same backend. Under the stated compilation, the qudit step uses fewer timed pulses than the qubit step.

A. Qudit Compilation

  • The four-level qudit and four qumodes compile the lab-frame Hamiltonian's six pieces directly into native operations, without intermediate qubit compilation or SWAP/CNOT synthesis.Each sub-Hamiltonian maps directly to ISA operations, making the decomposition an architectural property rather than a compiler artifact.Source: A. Qudit Compilation · pp. 9–10

C. Simulation

  • 27 timed pulses for the qudit versus 58 for the qubit; separately, the multitone schedule uses 27 control blocks versus 34 reference ISA operations and reproduces that reference to machine precision.The 27-control-block schedule is an extension; the paper uses 34 reference ISA operations for bookkeeping.Source: B. Qubit Reference · p. 10, A. Qudit Compilation · p. 10, Figure 3 · p. 11

B. Qubit Reference

  • The qubit reference compiles the displaced-frame Hamiltonian on three qubits alongside the same four qumodes, representing the formulation used in Ref..A logical symmetric step has 32 ISA operations, 20 of them entangling.Source: B. Qubit Reference · p. 10

C. Simulation

  • Matched initial states, Trotter step sizes, and cutoffs support comparison; populations are checked against direct Hlab integration and Ref., with dissipation cross-checked using a Stinespring channel.Closed-system dynamics use QuTiP, while dissipative dynamics use a continuous Lindblad master equation.Source: C. Simulation · p. 10

VIII. RESULTS

The qudit compilation reproduces the dissipative reference closely overall, while closed-system Trotter error is negligible at the chosen step size. Resource comparisons distinguish register compression and locality from platform-level savings and depend on the counting model.

A. Closed-System Dynamics

  • The qudit compilation matches exact lab-frame evolution to an RMSE of order 10−4, while the qubit compilation reproduces the published reference to 0.031%.The compiled models differ by 1.6%; the residual is between the lab-frame and displaced-frame representations, with much smaller Trotter error.Source: A. Closed-System Dynamics · p. 11, Figure 4 · p. 12

B. Dissipative Dynamics

  • At Fock cutoff N = 4, displaced-frame Hcqed using the level-encoded Kraus builder reproduces the reference to 1.03% RMSE, while qudit gives 1.09%; they agree to 0.30%.Table II averages population-trajectory RMSE over eight panels; its rows represent independently validated implementations, not a controlled Fock-cutoff sweep.Source: B. Dissipative Dynamics · p. 11, Table II · p. 12
  • The strongly dephased panel departs from the published curve by ∼6%, although the lab-frame and displaced-frame compilations agree to 0.7%.The residual is between the calculations and the published reference, not between the encodings.Source: B. Dissipative Dynamics · p. 11

C. Convergence

  • At τ = 5 fs, mean population RMSE is 0.0062% for the qudit compilation and 0.0044% for the qubit reference; both show second-order Suzuki scaling.Over τ ≥5 fs, fitted slopes are 1.981 for the qudit and 2.027 for the qubit reference; N = 8 is the working Fock cutoff.Source: C. Convergence · pp. 11–12, Figure 8 · p. 14

IX. RESOURCE SCALING AND ARCHITECTURAL TRADEOFFS

  • The qudit applies Hlab directly, whereas the qubit reference follows the displaced-frame Hcqed formulation; the comparison therefore does not isolate encoding alone.The one-hot register can also represent Hlab within its code space.Source: §IX · p. 13
  • The qudit register compresses the discrete manifold and makes electronic exchanges local, but trapped-ion implementations still require the motional modes and use a different counting convention from the superconducting estimate.The trapped-ion register must supply 2Nc −2 spectrally resolvable motional modes; the superconducting layout estimate is context only, not a like-for-like gate-count comparison.Source: §IX · pp. 13–14

A. Computational-Register Footprint

When the electronic manifold fits within one qudit, the encoding reduces computational-ion count and turns electronic exchanges into intra-ion transitions. Its resource advantage is conditional on the available multilevel controls and comes with spectral-control complexity.

A. Computational-Register Footprint

  • For three chromophores, the qubit representation uses three computational qubits, while one ququart ion stores the full four-state manifold.These counts refer to ions carrying the discrete computational register, not necessarily the total ions in the trap.Source: A. Computational-Register Footprint · p. 14

B. Interaction Locality

  • When the manifold fits within one qudit, electronic coupling-graph edges become local transitions; both A ↔B and A ↔C are local XE operations in the benchmark.The corresponding qubit encoding uses interactions between different qubits.Source: B. Interaction Locality · p. 14

C. ISA Operation Counts

  • At Nc = 3, the timed-pulse counts are 27 for the qudit circuit and 58 for the qubit reference, while entangling counts are 16 and 20, respectively.Logical counts are 34 versus 32; these resource benefits are specific to the benchmark circuit and its pricing model.Source: Table III · p. 15, C. ISA Operation Counts · p. 15

D. Architectural Tradeoff

  • The qudit trades spatial register complexity for multilevel-control complexity, with useful operating points set by hardware-dependent spectral resolution, calibration, and leakage constraints.The number of internal levels and spectrally resolved controls grows with Nc.Source: D. Architectural Tradeoff · p. 15

E. Projected Runtime

The qudit architecture projects a 10.5× runtime advantage for the three-chromophore benchmark under the stated sequential timing model. Its structural benefit depends on how much of the discrete manifold fits within each ion; large-dimension fidelity scaling remains experimentally unestablished.

E. Projected Runtime

  • At Nc = 3, one Trotter step is projected at 210 µs on the qudit versus 2208 µs on the qubit reference, a 10.5 ratio under sequential timing.The projection uses stated pulse parameters and is not a pulse-by-pulse simulation of the full circuit.Source: E. Projected Runtime · p. 15

F. Scaling Beyond One Ion

  • When Nc ≤ K, no bond crosses ions and S grows with Nc; for long chains, S approaches a value between one and K, and S ≥ 1 for all Nc.The crossing bond adds cout at Nc = K + 1; the long-chain limit depends on the per-chromophore growth of T0 and the costs of inside and crossing bonds.Source: F. Scaling Beyond One Ion · p. 16
  • For the three-chromophore benchmark, reducing capacity to K = 2 raises projected step time from 210 µs to 1209 µs and lowers S from 10.5 to 1.8.With K = 5, five chromophores fit in one ion at S = 12.8; six, eight, and twelve require two, two, and three ions, with S = 4.2, 4.7, and 4.1.Source: F. Scaling Beyond One Ion · p. 16

X. DISCUSSION

  • The architecture’s principal benefit is structural: when the manifold fits in one qudit, electronic couplings become intra-ion transitions and the lab-frame vibronic Hamiltonian compiles without a displaced-frame transformation.Generalized multilevel controls also reduce the number of scheduled control blocks.Source: §X · p. 16, §XI · p. 17
  • For the three-chromophore benchmark, the qudit circuit uses 27 timed pulses versus 58 for the qubit reference, but the projected speedup is not a demonstrated fidelity improvement.The speedup is an estimate under the stated pulse parameters.Source: §X · p. 16
  • The operating regime depends on multilevel-control cost and fidelity; at large d, spectral-control requirements increase while fidelity scaling of native qudit–oscillator interactions remains experimentally unestablished.The experimentally usable qudit dimension deff sets how large a manifold can fit within one ion.Source: §X · p. 16

XI. CONCLUSION

  • The instruction set and universality result extend beyond molecular simulation to hybrid problems coupling multilevel discrete systems with bosonic modes.The conclusion identifies XE, Zd, and CΠzD as sufficient to generate arbitrary qudit operators tensored with polynomials in the quadratures of all modes.Source: §X · p. 16, §XI · p. 17
  • When Nc + 2 ≤ deff, Nc computational qubit ions can be represented by one multilevel ion; beyond that capacity, the manifold spreads across ⌈Nc/K⌉ ions and compression is constant per ion.Larger d increases spectral-addressing and calibration burdens, and fidelity scaling remains hardware dependent.Source: §XI · p. 17

Appendix A: Proof of Universality

The proof starts from full qudit control and conditional-displacement generators, then uses commutators to build mode polynomials. An induction extends the construction to every polynomial degree.

2. Step 1: All Paulis at Degree One

  • Full qudit control rotates the displacement seeds to produce each of the three embedded Pauli operators tensored with x̂ or p̂.The construction uses real and imaginary displacement amplitudes.Source: §1 · p. 18, §2 · p. 19

1. Setup and Notation

  • The generated Lie algebra is defined from all su(d) qudit generators and the two conditional-displacement seed generators, with the goal of obtaining qudit operators tensored with mode polynomials and mode-only polynomials.The proof’s conclusion is that XE, Zd, and CΠzD generate arbitrary qudit operators tensored with polynomials in all mode quadratures, without requiring a mode-coupling primitive.Source: §1 · p. 18, Appendix A · p. 18

3. Step 2: Degree Two, and Why Conditional Displacements Alone Do Not Suffice

  • Two conditional displacements with the same Pauli factor yield only an identity term, whereas commutators using different Pauli factors generate quadratic mode monomials.Rotating the Pauli factor then supplies the quadratic monomials with any of the three Pauli operators.Source: §3 · p. 19

4. Step 3: Induction on Polynomial Degree

  • Induction on polynomial degree uses anticommutators with x̂ or p̂ to generate the next-degree monomials, while lower-degree commutator corrections are removed using the inductive hypothesis.The lemma establishes σk ⊗ Q in the Lie algebra for every polynomial Q and each Pauli index k.Source: §4 · p. 19

5. Step 4: From su(2) to su(d)

Commutator closure extends the construction from su(2) to su(d) and from one mode to several, including the identity sector, yielding polynomial Hamiltonians for the joint qudit–oscillator system.

5. Step 4: From su(2) to su(d)

  • Repeated commutators with su(d) generators span every qudit operator tensored with an arbitrary oscillator polynomial.The adjoint action of su(d) is irreducible because su(d) is simple.Source: §5 · p. 19

6. Step 5: Several Modes from CΠzD Alone

  • The construction extends mode by mode: conditional displacement alone generates arbitrary multimode polynomials, without a mode-coupling primitive.Commutators combine quadratures from different modes, then induction raises total polynomial degree.Source: §6 · p. 19

7. Step 6: The Identity Sector

  • Summing level-pair projector terms supplies the identity sector, completing the span of all qudit operators tensored with multimode polynomials.The identity-sector construction applies for arbitrary d ≥ 2.Source: §7 · p. 20

8. Conclusion

  • The resulting algebra establishes universality as Hamiltonian generation, spanning arbitrary qudit operators tensored with finite polynomials in all mode quadratures.The ququart numerical check reaches bandwidth three by iteration 3, certifying non-Gaussian operators of at least degree three; finite-cutoff saturation remains only a consistency check.Source: §8 · p. 20

Appendix B: Qubit Reference Compilation

The appendix compiles a second-order qubit-reference step for trapped ions, then expands its logical operations into timed pulses. Finite-shot execution agrees with exact integration for both qubit and qudit encodings.

1. From the published circuit to 32 logical operations

  • The qubit reference is a 32-operation second-order Trotter step on three qubits and four modes, grouped from 22 Hamiltonian terms.The shared motional bus removes the superconducting circuit's ancilla and SWAP routing; one half-step uses 15 operations, with two link-modulated exchanges at the center.Source: §1 · p. 21, Table IV · p. 21

2. From 32 logical to 58 timed pulses

  • 58 timed pulses and 12 virtual updates realize the qubit step, while the qudit circuit requires 27 pulses under the same counting rule.The two exchange classes account for the decompositions: J splits exactly into XX and YY windows, while each Jl uses a pulse sandwich; counting each CNOT as one pulse makes 58 a lower bound.Source: §2 · p. 21

3. Executed circuit

  • With 104 shots at 41 time points, qudit and qubit trajectories agree with exact integration to 0.40–0.42% and 0.35–0.43% RMSE, respectively.These executions validate circuit logic, not pulse cost.Source: §3 · p. 21

Appendix C: Pulse-Level Parameters

The appendix specifies pulse realizations and hardware parameters for the ISA primitives, distinguishing physical-drive replay from optimizer self-consistency. It also evaluates a chosen dispersive detuning operating point.

Appendix C: Pulse-Level Parameters

  • Physical replay, rather than optimizer self-consistency, is the relevant fidelity measure; physical replay is unavailable for CD and CR, so the paper makes no physical-fidelity claim for them.The pulse simulations mostly use Fock cutoff 8 and 200 time slots per pulse; the CΠR replay uses 400 slots and the two-transition CΠxD run uses 20,000.Source: Appendix C · p. 21

1. Hardware parameters

  • Hardware parameters are labeled measured, derived, or assumed, so operating-point choices are distinguishable from values measured on the 40Ca+ processor.The carrier Rabi frequency is derived from the measured sideband Rabi frequency and Lamb–Dicke factor.Source: §1 · p. 22, Table V · p. 22

2. Method per gate

  • At the circuit angle, CΠzD's physical replay reaches 1−F = 5×10^-6 with leakage 2×10^-4, while CΠR uses a 25.000 µs detuning-period pulse.CΠxD requires at least half a motional period for quadrature selection; its large-angle flat pulse fails, but the vibronic circuit uses small angles. XE's multitone block assumes a 2–5 MHz Zeeman-splitting window because Ref. does not report those splittings.Source: §2 · p. 23

3. Choice of the CΠR detuning

  • The chosen CΠR detuning is 40 kHz, with Ωsb/δ = 0.1 and δ/ν = 0.05; the sequential runtime ratio at Nc = 3 rises across the detuning sweep.The detuning is bounded by the dispersive condition and the need to remain within one sideband; the full-crystal mode spectrum is not anchored, so ν serves as the upper-bound stand-in.Source: §3 · p. 23

1. Rules

Under the stated sequential timing model, the projected qudit step is about ten times faster than the qubit reference at Nc = 3. The comparison is driven by local qudit carrier pulses replacing two-ion exchange windows.

1. Rules

  • The timing model sums per-instance gate times sequentially; shared-ion exchange gates cannot be parallelized under its disjoint-pair scheduling assumption.Mode rotations are charged on both sides, and each qubit J is priced as two Mølmer–Sørensen windows while each Jl is priced as one.Source: §1 · p. 24

2. Results

  • The ratio increases from 10.5 at Nc = 3 to 14.6 at Nc = 12, but rows beyond Nc = 5 assume deff ≥ Nc + 2 and are not 40Ca+ predictions.If the manifold is split across several ions, the ratio drops.Source: §2 · p. 25, Table X · p. 27
  • At Nc = 3, the projected ratio ranges from 6.5 at 20 kHz to 15.7 at 80 kHz across the chosen CΠR detuning window.The high-detuning end requires about twice the measured sideband amplitude.Source: §2 · p. 25
  • At Nc = 3, one qudit step is projected at 210 µs versus 2208 µs for the qubit reference, a ratio of 10.5.The table assumes the manifold fits in one ion; its larger-Nc entries are projections, not compiled circuits.Source: §2 · p. 25, Table X · p. 27
Loading 2610.13843v1…