Detector-Conditioned Quantum Speed Limits for Trajectory-Independent Bounds on Open-System Dynamics

Existing quantum speed limits (QSLs) for dissipative dynamics generally require integrating the full state trajectory, limiting their predictive utility before simulation. We introduce a detector-conditioned framework to overcome this requirement. By projecting the adjoint Lindblad dissipator onto a target detector $\Pi_\omega$ and taking its operator norm, we obtain a single static number---the \emph{dissipative transition capacity} $\Gamma_\omega$ ---that caps the fidelity decay rate for any initial state, without requiring prior ODE integration. We demonstrate that within the specified class of trajectory-independent detector-conditioned bounds, $\Gamma_\omega$ provides a natural functional driven by spatial locality, provide algebraic saturation conditions, and delineate regimes where it provides tighter constraints than standard trajectory-dependent trace-norm bounds. An extensive many-body scaling law ( $\Gamma \le N\gamma$ for local baths) and subadditivity across orthogonal detectors follow from the triangle inequality, demonstrating an exponential $\mathcal{O}(2^N)$ separation from global geometric trajectory bounds under stated locality assumptions. We provide an operational interpretation in binary state discrimination and quantum error correction, and demonstrate a matrix-free runtime scaling advantage over differential equation integration.Existing quantum speed limits (QSLs) for dissipative dynamics generally require integrating the full state trajectory, limiting their predictive utility before simulation. We introduce a detector-conditioned framework to overcome this requirement. By projecting the adjoint Lindblad dissipator onto a target detector $\Pi_\omega$ and taking its operator norm, we obtain a single static number---the \emph{dissipative transition capacity} $\Gamma_\omega$---that caps the fidelity decay rate for any initial state, without requiring prior ODE integration. We demonstrate that within the specified class of trajectory-independent detector-conditioned bounds, $\Gamma_\omega$ provides a natural functional driven by spatial locality, provide algebraic saturation conditions, and delineate regimes where it provides tighter constraints than standard trajectory-dependent trace-norm bounds. An extensive many-body scaling law ($\Gamma \le N\gamma$ for local baths) and subadditivity across orthogonal detectors follow from the triangle inequality, demonstrating an exponential $\mathcal{O}(2^N)$ separation from global geometric trajectory bounds under stated locality assumptions. We provide an operational interpretation in binary state discrimination and quantum error correction, and demonstrate a matrix-free runtime scaling advantage over differential equation integration.

Jul 27, 20260 citations

Simulation of Lindbladian dynamics via adaptive variational quantum trajectory compression

Huan-Yu Liu, Cheng Xue, Yun-Jie Wang +5 more

Quantum simulation of open quantum systems in the noisy intermediate-scale quantum (NISQ) era is hindered by the non-unitary nature of dissipative dynamics and the limited quantum resources available on near-term quantum processors. In this work, we propose a resource-efficient algorithm for simulating Lindbladian dynamics on NISQ devices. For open quantum systems with Pauli dissipations, we first derive a compact and stable mixed-unitary adjoint channel that approximates the target dissipative dynamics and enables ancilla-free implementation through trajectory sampling. To further reduce the circuit depth required for implementing the sampled trajectories, we introduce an adaptive variational quantum trajectory compression framework. In this framework, a depth-adaptive parameterized quantum circuit is trained to approximate repeated Trotterized Hamiltonian simulation operators, which are then used to replace repeated unitary segments appearing in the sampled trajectories. Importantly, the training procedure can also be performed without auxiliary qubits. Numerical simulations of the dissipative quantum $XY$ model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.Quantum simulation of open quantum systems in the noisy intermediate-scale quantum (NISQ) era is hindered by the non-unitary nature of dissipative dynamics and the limited quantum resources available on near-term quantum processors. In this work, we propose a resource-efficient algorithm for simulating Lindbladian dynamics on NISQ devices. For open quantum systems with Pauli dissipations, we first derive a compact and stable mixed-unitary adjoint channel that approximates the target dissipative dynamics and enables ancilla-free implementation through trajectory sampling. To further reduce the circuit depth required for implementing the sampled trajectories, we introduce an adaptive variational quantum trajectory compression framework. In this framework, a depth-adaptive parameterized quantum circuit is trained to approximate repeated Trotterized Hamiltonian simulation operators, which are then used to replace repeated unitary segments appearing in the sampled trajectories. Importantly, the training procedure can also be performed without auxiliary qubits. Numerical simulations of the dissipative quantum $XY$ model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.

quant-pharXiv:2607.09051Jul 13, 20260 citations

TARGET-VARIANCE QUANTUM SPEED LIMITS FROM PROJECTIVE FIDELITY REDUCTION

Roy Surya Sekhar

Quantum state readout on many experimental platforms is performed through a single projective measurement channel rather than full quantum state tomography. We derive a detector-conditioned quantum speed limit that constrains the minimum time for the projective fidelity $F(t) = \langle\omega|\rho(t)|\omega\rangle$ to reach a prescribed discrimination threshold: $T \;\ge\; \frac{|\Theta(0) - \Theta_*|}{\Delta H_\omega},$ where $\Theta = \arccos\sqrt{F}$ is the Bures angle and $\Delta H_\omega$ is the energy standard deviation of the \emph{fixed target state}. This bound, valid for both pure and mixed states under unitary dynamics, expresses the speed constraint in terms of a time-independent quantity determined entirely by the Hamiltonian and the detector projector, rather than the evolving-state variance appearing in standard Mandelstam--Tamm-type bounds. We further show that the resulting bound is structurally distinct from standard Mandelstam--Tamm-type bounds based on evolving-state variance. The bound exhibits commuting-sector invariance, suppressing Hamiltonian components that are energetically large but detection-irrelevant. Exact diagonalization of the transverse-field Ising model for $N \le 12$ spins confirms asymptotic separation between the bounds in the strong-interaction regime. The framework provides a detector-conditioned lower bound for rank-1 projective detection dynamics, applicable to superconducting qubit readout, trapped-ion fluorescence detection, and stabilizer syndrome monitoring. The construction is particularly relevant for architectures in which experimentally accessible information is restricted to a small set of projective readout channels rather than full-state tomography. ## Results & Validation Below is the macro-level data extracted from the 156-qubit **ibm_fez** processor, confirming the asymptotic separation predicted by Theorem 5.2 as the many-body coupling strength scales extensively: [Quantum Speed Limit Validation Benchmark](qsl_validation_plot.png) ## Hardware Compilation Profile The transpiled circuit diagram below illustrates the native pulse-level gate routing on the IBM Quantum Heron architecture. By optimizing the physical register map, the compiler enforces a clean nearest-neighbor coupling loop with zero SWAP gate overhead: [Heron Chip Circuit Native Compilation](circuit-d8uhclsbp3hs73861d7g.png) ## Raw Measurement Diagnostics To evaluate the projective fidelity reduction threshold ( $F_* = 0.15$ ), raw binary distributions are unpacked and corrected using Matrix-Free Measurement Mitigation (M3). Below is a representative diagnostic histogram of single-outcome state frequencies sampled from the hardware backend: [Error Mitigated Hardware Measurement Histogram](job_d8uhc4ctqbtc73d1qdmg_results_c.png)Quantum state readout on many experimental platforms is performed through a single projective measurement channel rather than full quantum state tomography. We derive a detector-conditioned quantum speed limit that constrains the minimum time for the projective fidelity $F(t) = \langle\omega|\rho(t)|\omega\rangle$ to reach a prescribed discrimination threshold:\[T \;\ge\; \frac{|\Theta(0) - \Theta_*|}{\Delta H_\omega},\]where $\Theta = \arccos\sqrt{F}$ is the Bures angle and $\Delta H_\omega$ is the energy standard deviation of the \emph{fixed target state}. This bound, valid for both pure and mixed states under unitary dynamics, expresses the speed constraint in terms of a time-independent quantity determined entirely by the Hamiltonian and the detector projector, rather than the evolving-state variance appearing in standard Mandelstam--Tamm-type bounds. We further show that the resulting bound is structurally distinct from standard Mandelstam--Tamm-type bounds based on evolving-state variance. The bound exhibits commuting-sector invariance, suppressing Hamiltonian components that are energetically large but detection-irrelevant. Exact diagonalization of the transverse-field Ising model for $N \le 12$ spins confirms asymptotic separation between the bounds in the strong-interaction regime. The framework provides a detector-conditioned lower bound for rank-1 projective detection dynamics, applicable to superconducting qubit readout, trapped-ion fluorescence detection, and stabilizer syndrome monitoring. The construction is particularly relevant for architectures in which experimentally accessible information is restricted to a small set of projective readout channels rather than full-state tomography. ## Results & Validation Below is the macro-level data extracted from the 156-qubit **ibm_fez** processor, confirming the asymptotic separation predicted by Theorem 5.2 as the many-body coupling strength scales extensively: [Quantum Speed Limit Validation Benchmark](qsl_validation_plot.png) ## Hardware Compilation Profile The transpiled circuit diagram below illustrates the native pulse-level gate routing on the IBM Quantum Heron architecture. By optimizing the physical register map, the compiler enforces a clean nearest-neighbor coupling loop with zero SWAP gate overhead: [Heron Chip Circuit Native Compilation](circuit-d8uhclsbp3hs73861d7g.png) ## Raw Measurement Diagnostics To evaluate the projective fidelity reduction threshold ($F_* = 0.15$), raw binary distributions are unpacked and corrected using Matrix-Free Measurement Mitigation (M3). Below is a representative diagnostic histogram of single-outcome state frequencies sampled from the hardware backend: [Error Mitigated Hardware Measurement Histogram](job_d8uhc4ctqbtc73d1qdmg_results_c.png)

Jun 14, 20260 citations

Dissipation accelerates quantum and classical simulation of open-system dynamics

Armando Angrisani, Ricard Puig, Yanting Teng +1 more

Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, can ease quantum and classical simulation by exponentially suppressing high-weight components of Heisenberg-evolved observables. For bounded-degree Lindblad dynamics, this permits system-size-independent Trotter steps when estimating local observables. Combining this compression with Richardson extrapolation, we provide classical and quantum error bounds with respect to the 2-norm of the propagated observable. These give high-probability expectation-value guarantees for random input states or random Hamiltonians acting on a fixed state and control (out-of-time-order) correlators. Concretely, we show that expectation values of local observables at time $t$ can be estimated to accuracy $\varepsilon$ using circuits of maximum depth $O\!\left(\left[1+\left(t/γ\right)^{3/2}\right]\log^2(1/\varepsilon)\right)$ , independent of the system size $n$ . Classically, we show that sparse Pauli propagation runs in time polynomial in $n$ , $t$ and $1/\varepsilon$ for every fixed $γ>0$ , with polynomial degree $O(1/γ)$ in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, can ease quantum and classical simulation by exponentially suppressing high-weight components of Heisenberg-evolved observables. For bounded-degree Lindblad dynamics, this permits system-size-independent Trotter steps when estimating local observables. Combining this compression with Richardson extrapolation, we provide classical and quantum error bounds with respect to the 2-norm of the propagated observable. These give high-probability expectation-value guarantees for random input states or random Hamiltonians acting on a fixed state and control (out-of-time-order) correlators. Concretely, we show that expectation values of local observables at time $t$ can be estimated to accuracy $\varepsilon$ using circuits of maximum depth $O\!\left(\left[1+\left(t/γ\right)^{3/2}\right]\log^2(1/\varepsilon)\right)$, independent of the system size $n$. Classically, we show that sparse Pauli propagation runs in time polynomial in $n$, $t$ and $1/\varepsilon$ for every fixed $γ>0$, with polynomial degree $O(1/γ)$ in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.

quant-pharXiv:2609.40174Oct 1, 20260 citations

Trajectory-independent speed limits for controlled open quantum systems

James B. Larsen, Tameem Albash, Alicia B. Magann +1 more

Existing quantum speed limits for controlled open quantum systems depend on the specified trajectory. For example, lower bounds on quantum annealing times in the presence of dissipation depend explicitly on the chosen annealing schedule. Recently, schedule-independent speed limits have been derived for annealing in the closed quantum system setting (SciPost Phys. 18, 159 (2025)). In this work, we generalize these results to open quantum systems, deriving schedule-independent lower bounds for quantum annealing times in systems described by a Lindblad master equation. We analyze the interplay between coherent control and dissipation in single- and two-qubit examples, demonstrating that the derived lower bounds capture key scaling behavior with respect to the strength of the dissipator. Finally, we apply the bound to thermal state preparation and show that the bound matches the expected asymptotic behavior for an Ising model in the high temperature limit.Existing quantum speed limits for controlled open quantum systems depend on the specified trajectory. For example, lower bounds on quantum annealing times in the presence of dissipation depend explicitly on the chosen annealing schedule. Recently, schedule-independent speed limits have been derived for annealing in the closed quantum system setting (SciPost Phys. 18, 159 (2025)). In this work, we generalize these results to open quantum systems, deriving schedule-independent lower bounds for quantum annealing times in systems described by a Lindblad master equation. We analyze the interplay between coherent control and dissipation in single- and two-qubit examples, demonstrating that the derived lower bounds capture key scaling behavior with respect to the strength of the dissipator. Finally, we apply the bound to thermal state preparation and show that the bound matches the expected asymptotic behavior for an Ising model in the high temperature limit.

quant-pharXiv:2603.13090Physical Review AMar 16, 20260 citations

Computational regimes in matrix-product-state-based quantum trajectory simulations

Aaron Sander, Simon Cichy, Martin Eigel +4 more

Efficient simulation of open quantum systems is central to modeling noisy quantum hardware and many-body dynamics. In trajectory-based tensor network methods, cost is often associated with trajectory-level quantities such as entanglement growth or bond dimension. However, the total cost of a fixed-accuracy simulation also depends on statistical sampling, and the interplay between per-trajectory complexity and sampling effort remains poorly understood. Here we introduce a cost-resolved framework for matrix product state (MPS)-based quantum trajectory simulations that decomposes total cost into memory per trajectory, runtime per trajectory, and sampling effort. We show that physically equivalent stochastic unravelings of the same Lindblad dynamics do not necessarily reduce total cost, but instead redistribute cost between trajectory complexity and statistical convergence. This trade-off is quantified by two dimensionless inflation factors: a bond dimension inflation $α$ and a sampling inflation $κ$ , which together determine the preferred unraveling under hardware-dependent memory and parallelism constraints. We provide a practical protocol for extracting $(α,κ)$ from modest pilot simulations and demonstrate it using benchmarks across multiple noise channels. The resulting decision maps show that the computationally favorable unraveling can change with noise strength, time-step resolution, system size, and available parallelism. These results establish unraveling choice as a hardware-aware simulation design problem rather than an intrinsic optimization of trajectory entanglement alone.Efficient simulation of open quantum systems is central to modeling noisy quantum hardware and many-body dynamics. In trajectory-based tensor network methods, cost is often associated with trajectory-level quantities such as entanglement growth or bond dimension. However, the total cost of a fixed-accuracy simulation also depends on statistical sampling, and the interplay between per-trajectory complexity and sampling effort remains poorly understood. Here we introduce a cost-resolved framework for matrix product state (MPS)-based quantum trajectory simulations that decomposes total cost into memory per trajectory, runtime per trajectory, and sampling effort. We show that physically equivalent stochastic unravelings of the same Lindblad dynamics do not necessarily reduce total cost, but instead redistribute cost between trajectory complexity and statistical convergence. This trade-off is quantified by two dimensionless inflation factors: a bond dimension inflation $α$ and a sampling inflation $κ$, which together determine the preferred unraveling under hardware-dependent memory and parallelism constraints. We provide a practical protocol for extracting $(α,κ)$ from modest pilot simulations and demonstrate it using benchmarks across multiple noise channels. The resulting decision maps show that the computationally favorable unraveling can change with noise strength, time-step resolution, system size, and available parallelism. These results establish unraveling choice as a hardware-aware simulation design problem rather than an intrinsic optimization of trajectory entanglement alone.

quant-pharXiv:2606.13779Jun 15, 20260 citations

\Pi_\omega

and taking its operator norm, we obtain a single static number---the \emph{dissipative transition capacity}

\Gamma_\omega

---that caps the fidelity decay rate for any initial state, without requiring prior ODE integration. We demonstrate that within the specified class of trajectory-independent detector-conditioned bounds,

\Gamma_\omega

provides a natural functional driven by spatial locality, provide algebraic saturation conditions, and delineate regimes where it provides tighter constraints than standard trajectory-dependent trace-norm bounds. An extensive many-body scaling law (

\Gamma \le N\gamma

for local baths) and subadditivity across orthogonal detectors follow from the triangle inequality, demonstrating an exponential

\mathcal{O}(2^N)

separation from global geometric trajectory bounds under stated locality assumptions. We provide an operational interpretation in binary state discrimination and quantum error correction, and demonstrate a matrix-free runtime scaling advantage over differential equation integration.

XY

model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.

F(t) = \langle\omega|\rho(t)|\omega\rangle

to reach a prescribed discrimination threshold:

T \;\ge\; \frac{|\Theta(0) - \Theta_*|}{\Delta H_\omega},

where

\Theta = \arccos\sqrt{F}

is the Bures angle and

\Delta H_\omega

is the energy standard deviation of the \emph{fixed target state}. This bound, valid for both pure and mixed states under unitary dynamics, expresses the speed constraint in terms of a time-independent quantity determined entirely by the Hamiltonian and the detector projector, rather than the evolving-state variance appearing in standard Mandelstam--Tamm-type bounds. We further show that the resulting bound is structurally distinct from standard Mandelstam--Tamm-type bounds based on evolving-state variance. The bound exhibits commuting-sector invariance, suppressing Hamiltonian components that are energetically large but detection-irrelevant. Exact diagonalization of the transverse-field Ising model for

N \le 12

spins confirms asymptotic separation between the bounds in the strong-interaction regime. The framework provides a detector-conditioned lower bound for rank-1 projective detection dynamics, applicable to superconducting qubit readout, trapped-ion fluorescence detection, and stabilizer syndrome monitoring. The construction is particularly relevant for architectures in which experimentally accessible information is restricted to a small set of projective readout channels rather than full-state tomography. ## Results & Validation Below is the macro-level data extracted from the 156-qubit **ibm_fez** processor, confirming the asymptotic separation predicted by Theorem 5.2 as the many-body coupling strength scales extensively: [Quantum Speed Limit Validation Benchmark](qsl_validation_plot.png) ## Hardware Compilation Profile The transpiled circuit diagram below illustrates the native pulse-level gate routing on the IBM Quantum Heron architecture. By optimizing the physical register map, the compiler enforces a clean nearest-neighbor coupling loop with zero SWAP gate overhead: [Heron Chip Circuit Native Compilation](circuit-d8uhclsbp3hs73861d7g.png) ## Raw Measurement Diagnostics To evaluate the projective fidelity reduction threshold (

F_* = 0.15

), raw binary distributions are unpacked and corrected using Matrix-Free Measurement Mitigation (M3). Below is a representative diagnostic histogram of single-outcome state frequencies sampled from the hardware backend: [Error Mitigated Hardware Measurement Histogram](job_d8uhc4ctqbtc73d1qdmg_results_c.png)

t

can be estimated to accuracy

\varepsilon

using circuits of maximum depth

O\!\left(\left[1+\left(t/γ\right)^{3/2}\right]\log^2(1/\varepsilon)\right)

, independent of the system size

n

. Classically, we show that sparse Pauli propagation runs in time polynomial in

n

t

and

1/\varepsilon

for every fixed

γ>0

, with polynomial degree

O(1/γ)

in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.

α

and a sampling inflation

κ

, which together determine the preferred unraveling under hardware-dependent memory and parallelism constraints. We provide a practical protocol for extracting

(α,κ)

from modest pilot simulations and demonstrate it using benchmarks across multiple noise channels. The resulting decision maps show that the computationally favorable unraveling can change with noise strength, time-step resolution, system size, and available parallelism. These results establish unraveling choice as a hardware-aware simulation design problem rather than an intrinsic optimization of trajectory entanglement alone.