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arxiv: 2605.20350 · v1 · pith:7GMJFNG6new · submitted 2026-05-19 · 🪐 quant-ph

Resource generation and dynamical complexities in open random quantum circuits

Paranjoy Chaki , Arkaprava Sil , Priya Ghosh , Ujjwal Sen , Sudipto Singha Roy This is my paper

Pith reviewed 2026-05-21 07:23 UTC · model grok-4.3

classification 🪐 quant-ph
keywords open quantum circuitsrandom quantum circuitsentanglementnon-stabilizernessKrylov complexityquantum state k-designsenvironmental memoryopen quantum systems
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The pith

Environmental memory qualitatively alters resource generation in open random quantum circuits

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that memory in the environment changes how entanglement, non-stabilizerness, and Krylov complexity evolve in random circuits. Unitary and memoryful open circuits display sustained growth and saturation of these quantities, while memoryless open circuits show entanglement decaying to zero after a transient rise even as non-stabilizerness stays positive. This matters for realistic quantum devices, which are open systems often possessing memory, because it reveals that nonclassical features can persist without entanglement and that memoryful dynamics can sometimes approach quantum state designs more closely than closed dynamics.

Core claim

Realistic quantum devices are inherently open and often involve environments with memory. Unitary and memoryful open random circuits exhibit sustained growth and saturation of entanglement and non-stabilizerness, whereas memoryless dynamics produces entanglement that decays to zero after transient growth while non-stabilizerness remains non-zero. Krylov complexity shows suppressed spreading in memoryless circuits but strong growth that saturates at the maximum value in the unitary and memoryful cases. Memoryful circuits approach low-order quantum-state k-designs more effectively than the other two. Closed dynamics are therefore usually the most resource-generating but are ideal; realistic dy

What carries the argument

Comparison of memoryless versus memoryful ensembles of open random quantum circuits, which isolates how environmental memory affects the time evolution of entanglement, non-stabilizerness, and Krylov complexity relative to the closed unitary case.

If this is right

  • Closed dynamics generate the most quantum resources but remain an idealization.
  • Realistic open dynamics generate less, yet memoryful versions can sometimes outdo closed dynamics in approaching k-designs.
  • Non-stabilizerness persists as a nonclassical resource after entanglement has decayed in memoryless cases.
  • Krylov complexity grows strongly and saturates in unitary and memoryful circuits but is suppressed without memory.
  • Memoryful open circuits provide a route to low-order state designs that is more effective than memoryless or purely unitary evolution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Device engineers might deliberately engineer controlled memory in the environment to prolong certain quantum resources.
  • The observed separation between entanglement decay and persistent non-stabilizerness could appear in other open-system models beyond random circuits.
  • Numerical or experimental checks on higher-order k-designs would test whether the memory advantage extends beyond low orders.

Load-bearing premise

The specific constructions chosen for the memoryless and memoryful open random circuit ensembles accurately capture the essential features of realistic open quantum systems with memory.

What would settle it

A laboratory implementation of a memoryless open random circuit in which entanglement entropy is observed to return to zero after initial growth while a measure of non-stabilizerness remains strictly positive.

Figures

Figures reproduced from arXiv: 2605.20350 by Arkaprava Sil, Paranjoy Chaki, Priya Ghosh, Sudipto Singha Roy, Ujjwal Sen.

Figure 1
Figure 1. Figure 1: Comparison of different classes of random quantum cir [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic diagram of closed and open random quantum circuit. In all three schematics, the black dots denote the qubits comprising the respective circuits. The left panel represents a unitary random circuit. In contrast, the middle panel illustrates a memoryless open random circuit, where no memory effects arise since the auxiliary qubits are discarded after each time step and replaced by fresh ones (sample… view at source ↗
Figure 3
Figure 3. Figure 3: Growth of entanglement and quantum mutual infor￾mation with time step. (a) Describes the growth of entanglement (log-neg) for unitary, memoryless open random circuits, and memo￾ryful open random circuits. The vertical and horizontal axes denote the log-neg (L) as the measure of entanglement and the time step t, respectively. The curves corresponding to unitary, MLORC, and MFORC are denoted by sky blue, gre… view at source ↗
Figure 4
Figure 4. Figure 4: Robustness of growth of entanglement under the ac￾tion of MLORC. We present the behavior of the dynamical evolu￾tion of the entanglement for different numbers of auxiliary systems, E = 0, 1, 2, 3, 4. The corresponding curves are distinguished by se￾quential colors, as indicated in the legend. The system size is fixed at Ns = 8. As we have performed averaging over the random realiza￾tions, there exists a fl… view at source ↗
Figure 6
Figure 6. Figure 6: Robustness of growth of non-stabilizerness under the action of a random memoryless open random circuit. Here, we plot the dynamical evolution of the SRE for different numbers of auxiliary systems, E = 0, 1, 2, 3, 4. The corresponding curves are distinguished by sequential colors, as indicated in the legend. Here, the system size of the system is considered to be Ns = 8. to entanglement, we examined the rob… view at source ↗
Figure 7
Figure 7. Figure 7: Krylov complexity growth in time. Here, we have plotted the Krylov complexity of RUC, MLORC and MFORC for Ns = 6 denoted by green, red, and blue smooth curves. As shown in the plot for RUC and MFORC, the Krylov complexity saturates at a value close to K/2 = 2047.5, occurring at a time approximately equal to K − 1 = 4094. In contrast, for the MLORC circuit, we find that the Krylov dimension is reduced to K … view at source ↗
Figure 8
Figure 8. Figure 8: Emerging state-k design from the random circuits. Here, we show the time evolution of ∆(k) for k = 1, 2, 3 in panels (a), (b), and (c), respectively, for RUC, MLORC, and MFORC dynamics. The system size is Ns = 8, with subsystem A consisting of the first two qubits, while projective measurements are performed on the remaining six qubits to construct the projected ensemble. Each curve is averaged over 10 rea… view at source ↗
Figure 9
Figure 9. Figure 9: Growth of entanglement across different bipartitions for MLORC and MFORC circuits. Panels (a) and (b) depict the time evolution of the logarithmic negativity L as a function of time t for different bipartitions involving the first two qubits and their asso￾ciated auxiliary in a four-qubit memoryless open random circuit and an open random circuit with memory, respectively. Here, the labels 1 and 2 denote th… view at source ↗
read the original abstract

Realistic quantum devices are inherently open and often involve environments with memory. Here, we investigate quantum resource generation in two classes of random circuits, namely, memoryless open and memoryful open random circuits, and compare their behavior with the well-explored random unitary circuit model. We show that environmental memory qualitatively alters the dynamics: while unitary and memoryful circuits exhibit sustained growth and saturation of entanglement and non-stabilizerness (magic); memoryless dynamics leads to a distinct behavior where entanglement decays to zero after transient growth, even though non-stabilizerness remains non-zero, indicating the persistence of nonclassical features beyond entanglement. Consistently, Krylov complexity reveals suppressed spreading of quantum states in memoryless circuits, in contrast to strong growth in unitary and memoryful dynamics, which saturates at the maximum value. Finally, we show that memoryful circuits more effectively approach low-order quantum-state k-designs than the other two circuits. Closed dynamics are therefore usually the most resource-generating, but are ideal; realistic dynamics are open and seem to generate less, but if they possess memory, they can sometimes even outdo closed dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates quantum resource generation and dynamical complexities in open random quantum circuits, distinguishing between memoryless and memoryful environmental interactions and comparing both to the standard unitary random circuit model. It claims that environmental memory qualitatively alters the dynamics: unitary and memoryful circuits exhibit sustained growth and saturation of entanglement and non-stabilizerness (magic), while memoryless circuits show only transient entanglement growth followed by decay to zero, with persistent non-zero magic indicating nonclassical features beyond entanglement. Krylov complexity is reported as suppressed in memoryless cases but strongly growing and saturating in the other two; memoryful circuits are said to approach low-order quantum state k-designs more effectively than the alternatives. The overall conclusion is that closed dynamics are typically most resource-generating but idealized, whereas realistic open dynamics generate less unless they possess memory.

Significance. If the reported distinctions prove robust and general, the work would usefully highlight the role of environmental memory in realistic open quantum systems, showing that memoryful open dynamics can sometimes match or exceed closed-system resource generation in entanglement, magic, and design properties. The separation between decaying entanglement and persisting magic in the memoryless case offers a concrete illustration of nonclassicality surviving beyond entanglement, which could inform studies of open-system resource theories and complexity measures.

major comments (2)
  1. [Circuit model definitions] The section introducing the memoryless and memoryful open random circuit ensembles: the central qualitative claims rest on these specific constructions. The manuscript should supply an explicit mapping or justification relating the chosen Kraus-operator or gate ensembles to standard open-system frameworks (Markovian Lindblad evolution or collision-model non-Markovian channels) so that the observed entanglement decay, Krylov-complexity suppression, and k-design behavior can be assessed as general rather than potentially model-specific artifacts.
  2. [Numerical results] Numerical results sections reporting entanglement, magic, Krylov complexity, and k-design distances: the abstract and claims assert clear qualitative differences, yet the provided text supplies no details on circuit depth, ensemble size, numerical precision, or error bars. Without these, the statistical support for statements such as “entanglement decays to zero” or “saturation at the maximum value” cannot be evaluated; the full manuscript must include convergence checks and error analysis to substantiate the load-bearing distinctions.
minor comments (1)
  1. [Abstract] Abstract: a single sentence indicating the typical system sizes or circuit depths employed would help readers gauge the scale at which the reported behaviors are observed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments below, indicating the changes we will implement in the revised version.

read point-by-point responses

  1. Referee: [Circuit model definitions] The section introducing the memoryless and memoryful open random circuit ensembles: the central qualitative claims rest on these specific constructions. The manuscript should supply an explicit mapping or justification relating the chosen Kraus-operator or gate ensembles to standard open-system frameworks (Markovian Lindblad evolution or collision-model non-Markovian channels) so that the observed entanglement decay, Krylov-complexity suppression, and k-design behavior can be assessed as general rather than potentially model-specific artifacts.

    Authors: We thank the referee for highlighting this important point. To address it, we will revise the manuscript by adding an explicit discussion in Section II that maps our memoryless open random circuit model to the Markovian Lindblad equation in the appropriate limit, and our memoryful model to a non-Markovian collision model with environmental memory. This will include the derivation of the effective master equation from the Kraus operators and a justification for why these ensembles capture the essential features of standard open-system frameworks, thereby supporting the generality of our qualitative results. revision: yes

  2. Referee: [Numerical results] Numerical results sections reporting entanglement, magic, Krylov complexity, and k-design distances: the abstract and claims assert clear qualitative differences, yet the provided text supplies no details on circuit depth, ensemble size, numerical precision, or error bars. Without these, the statistical support for statements such as “entanglement decays to zero” or “saturation at the maximum value” cannot be evaluated; the full manuscript must include convergence checks and error analysis to substantiate the load-bearing distinctions.

    Authors: We agree that the numerical details are essential for validating the claims. In the revised manuscript, we will expand the numerical results section to include specific information on the circuit depths employed (ranging from 10 to several hundred layers depending on the quantity), the ensemble sizes used for averaging (typically 500-2000 realizations), the numerical methods and precision (e.g., exact diagonalization for small systems or tensor network approximations), and error bars representing the standard error of the mean. Additionally, we will include supplementary figures demonstrating convergence with respect to circuit depth and ensemble size to confirm that the observed behaviors, such as entanglement decay to zero and saturation of other measures, are robust. revision: yes

Circularity Check

0 steps flagged

No circularity: behaviors follow directly from explicit circuit definitions

full rationale

The paper defines three explicit random circuit ensembles (unitary, memoryless open, memoryful open) via their gate/Kraus constructions and then directly computes entanglement, magic, Krylov complexity, and k-design metrics on them. These quantities are obtained from the definitions without any fitted parameters being relabeled as predictions, without self-citations carrying the central claims, and without any ansatz or uniqueness theorem imported from prior author work. The observed distinctions (e.g., entanglement decay in memoryless case) are therefore straightforward consequences of the chosen dynamics rather than reductions to the inputs by construction. The modeling assumptions about realism are stated explicitly and remain open to external validation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard definitions of random unitary circuits and on the modeling choices that distinguish memoryless from memoryful open dynamics; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Random circuit ensembles provide representative samples of typical quantum dynamical behavior
    The paper employs random circuits to compare the three classes of dynamics.

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