Circuit Reuse in Quantum and Electronic Design

• Circuit Reuse is a design principle where circuit resources such as qubits, wires, or PCB blocks are repurposed to reduce duplication while adhering to constraints like fidelity and type safety.
• Techniques such as graph coloring, CP-SAT formulation, and greedy heuristics schedule resource reuse, enabling dynamic measurement adjustments and optimal lifetime packing.
• Empirical benchmarks highlight significant reductions—up to 93%-95% in qubits and over 80% savings in PCB prototypes—while balancing trade-offs like increased circuit depth and reset overhead.

Searching arXiv for recent and foundational papers on “circuit reuse” across domains. Circuit reuse is a family of techniques in which a circuit-related resource is reused rather than recreated or dedicated permanently to a single logical role. In the literature, the reused object may be a quantum circuit wire or qubit, a random circuit instance in an experimental protocol, a cached intermediate state in noisy simulation, a reusable garbled circuit, a mechanistically identified transformer subcircuit, a typed PCB block, or a detachable electronic component assembly. Across these domains, the common objective is resource reduction under explicit constraints on correctness, fidelity, privacy, or type safety (Paler et al., 2016, Rovara et al., 27 Nov 2025, Harth-Kitzerow et al., 2022, Garza et al., 18 Sep 2025).

1. Scope and recurring structure

The technical literature uses the term in several distinct but structurally related ways. In quantum compilation, reuse means assigning non-overlapping logical qubit lifetimes to the same physical wire or qubit. In randomized quantum protocols, it means executing the same sampled circuit multiple times instead of resampling a fresh circuit. In secure computation, it means evaluating the same garbled object on many evaluator inputs. In mechanistic interpretability, it denotes the recurrence of the same causal subnetwork across tasks. In PCB workflows, it refers either to reusing typed circuit blocks during design or to reusing physical components during prototyping (Chen et al., 2024, Merullo et al., 2023, Yan et al., 2024).

Domain	Reused object	Principal constraint
Quantum compilation	Wires, qubits, subcircuits	Dependency, measurement, reset, depth
Experimental and simulation workflows	Sampled circuits, cached states	Variance, fidelity, memory
Secure computation and ML	Garbled circuits, learned circuits	Leakage, causal validity
Electronic design	PCB blocks, SMD assemblies	Type safety, contact reliability

A recurring formal pattern is the replacement of spatial duplication by temporal multiplexing. The resource is first represented by a dependency structure: a lifetime interval, a circuit DAG, a reuse candidate graph, a cost model $t(R)$, or a causal circuit extracted from model activations. Optimization then selects a reuse schedule subject to a domain-specific admissibility criterion. This suggests that “reuse” is less a single algorithm than a design principle instantiated by graph coloring, CP-SAT, SMT, ILP, greedy search, reinforcement learning, stochastic scheduling, or mechanical fixture design.

A common misconception is that circuit reuse is synonymous with simple reset-based recycling. The dynamic-circuit literature explicitly distinguishes static reuse, which only reorders measurements and inserts resets, from dynamic reuse, which also moves measurements and replaces quantum controls by classically controlled operations (Rovara et al., 27 Nov 2025). Conversely, in non-quantum settings, reuse may have no reset primitive at all: reusable garbled circuits rely on obfuscation and encoding rather than reinitialization, and PCB block reuse relies on typed composition rather than temporal scheduling (Harth-Kitzerow et al., 2022, Garza et al., 18 Sep 2025).

2. Static wire recycling and lifetime packing in quantum circuits

The earliest formulation in this corpus treats reuse as a wire-allocation problem. For a qubit $q$, the lifetime interval is defined as

$$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$

It can be decomposed into

$$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$

where only $\text{active}(q)$ contains entangling or single-qubit gates. Two qubits may share a wire only if their lifetimes do not overlap (Paler et al., 2016).

This condition yields an interference graph $G=(V,E)$ whose vertices are qubits and whose undirected edges connect pairs with overlapping lifetimes: $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$ Because $G$ is an interval graph, wire recycling reduces to graph coloring or interval scheduling. Sorting intervals by increasing $t_{\text{init}}(q)$ and assigning the smallest available color whose last-assigned interval ends before $t_{\text{init}}(q)$ gives an $q$0 coloring procedure for $q$1 qubits. The paper itself uses a more general causal-graph representation, repeatedly adding edges from an ancilla-measurement node $q$2 to a later ancilla-initialization node $q$3, provided that no directed path already forces $q$4, and then merging the two on the same wire (Paler et al., 2016).

Two heuristics are distinguished. In $q$5, ordered wires are assumed and ancilla outputs are scanned in ascending wire index. In $q$6, unordered wires are handled by a bidirectional breadth-first search in the causal graph that prefers forward edges and breaks ties by minimizing backward-edge traversals. The worst-case complexity is $q$7 for $q$8 operations, although the report notes that suitable data structures can drive this toward $q$9, and the empirical implementation ran in milliseconds for circuits with thousands of wires (Paler et al., 2016).

The experimental results establish the practical relevance of lifetime packing. On reversible circuits from RevLib, heuristic $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$0 achieved up to $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$1 wire reduction, with average savings of approximately $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$2–$$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$3; $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$4 still yielded $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$5–$$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$6 savings. On fault-tolerant ICM adder circuits derived from the Cuccaro adder, initial wire counts ranged from $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$7 to $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$8, and after $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$9 recycling the number of wires was approximately $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$0, i.e. more than $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$1 reduction, while $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$2 yielded approximately $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$3–$$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$4 reduction. The paper’s abstract summarizes the effect as a reduction by more than $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$5 compared to unoptimized quantum circuits (Paler et al., 2016).

These results are strongest for ancilla-rich constructions. The method does not recycle I/O qubits that span the full circuit, presumes a static circuit DAG, and therefore does not by itself cover dynamic circuits with mid-circuit measurement and classical control. Its significance lies in showing that wire count can be recast as a lifetime-allocation problem without altering algorithmic functionality or gate complexity.

3. Dynamic qubit reuse, measurement motion, and circuit resizing

Dynamic-circuit work generalizes static reuse by allowing mid-circuit measurement, reset, and classical feed-forward. A static quantum circuit is defined as one with only unitary gates, all measurements at the end, and no classical feedback. A dynamic circuit adds three primitives: mid-circuit measurement $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$6, reset $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$7, and classically controlled single-qubit gates such as $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$8 and $$\text{passive}_1(q),\quad \text{active}(q),\quad \text{passive}_2(q),$$9. In this model, measurements can be commuted leftward through suitable gates, controlled operations on measured qubits can be replaced by classically controlled gates, and liveness analysis can remove dead operations before reuse search remaps later operations onto a reset qubit (Rovara et al., 27 Nov 2025).

The transformation rules are explicit. Diagonal gates commute with measurement, bit-flip gates invert the measurement outcome under deferred classical update, and controlled gates on a measured control qubit can be rewritten by the deferred-measurement principle. After this rewrite, reuse is performed by scanning for qubit pairs with non-overlapping use-intervals, inserting $\text{active}(q)$0, and mapping subsequent gates on $\text{active}(q)$1 onto $\text{active}(q)$2. On benchmark families, the method reduced QPE circuits with $\text{active}(q)$3 up to $\text{active}(q)$4 to $\text{active}(q)$5 qubits, reduced QFT circuits with $\text{active}(q)$6 up to $\text{active}(q)$7 to $\text{active}(q)$8 qubit, reduced a hardware-efficient VQE “full” entanglement ansatz with $\text{active}(q)$9 up to $G=(V,E)$0 to $G=(V,E)$1 qubit, and achieved up to $G=(V,E)$2 fewer qubits on random sparse circuits. The same report notes a depth increase of approximately $G=(V,E)$3 at $G=(V,E)$4 for QPE, $G=(V,E)$5 for QFT, and more generally a depth increase by a factor $G=(V,E)$6–$G=(V,E)$7, sometimes $G=(V,E)$8 for highly serial circuits (Rovara et al., 27 Nov 2025).

Compiler-assisted reuse on IBM hardware predates this fuller dynamic formulation but already exposed the qubit–depth–fidelity trade-off. In one formulation, if an original circuit needs $G=(V,E)$9 logical qubits and $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$0 are selected for “measure-and-reset,” then

$\ell(q_1)\cap \ell(q_2)\neq \emptyset.$1

For Bernstein–Vazirani with $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$2, repeated reuse of the same work qubit yields

$\ell(q_1)\cap \ell(q_2)\neq \emptyset.$3

The same work showed that replacing the built-in reset primitive by “measure + controlled-X” reduced instruction duration from approximately $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$4 to approximately $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$5, where $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$6. It reported up to $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$7 qubit-usage reduction, over $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$8 SWAP reduction, and $\ell(q_1)\cap \ell(q_2)\neq \emptyset.$9–$G$0 improvements in TVD or success rate on representative applications; on IBM Mumbai, a BV case improved from $G$1 correct for a 5-qubit implementation with SWAP to $G$2 for a 4-qubit reuse version and $G$3 for a 3-qubit reuse version (Hua et al., 2022).

“Quantum Circuit Resizing” reformulates the same objective as segmentation. A circuit $G$4 on $G$5 logical qubits is partitioned into segments $G$6 with mappings $G$7 such that $G$8. The reuse score is

$G$9

where $t_{\text{init}}(q)$0 is the set of qubits that must be simultaneously present to execute $t_{\text{init}}(q)$1’s last gate. A greedy algorithm of complexity $t_{\text{init}}(q)$2 repeatedly selects the most reusable remaining dependency set, emits the corresponding subcircuit, and inserts middle measurement and middle reset when a qubit’s remaining gate count reaches zero. On a 27-qubit target, average PST rose from $t_{\text{init}}(q)$3 to $t_{\text{init}}(q)$4, i.e. a $t_{\text{init}}(q)$5 improvement, and gate count fell by approximately $t_{\text{init}}(q)$6 on average; on a 5-qubit target, circuits up to $t_{\text{init}}(q)$7 qubits became executable with average PST approximately $t_{\text{init}}(q)$8 across large benchmarks (Sadeghi et al., 2022).

The main technical point across these results is not merely that reuse saves qubits, but that dynamic measurement can alter the dependency structure itself. This is why dynamic reuse can succeed on QPE, QFT, and VQE cases where reorder-and-reset alone “cannot reuse any” or “no reuse before” is possible (Rovara et al., 27 Nov 2025). At the same time, the literature is explicit that more reuse is not automatically better, because depth, latency, and reset error can dominate when the original circuit already maps well or has few SWAPs.

4. Optimality, hardware-aware mapping, and integrated quantum workflows

Several works move from reuse as a local heuristic to reuse as a global optimization problem. One exact formulation is a CP-SAT model with binary variables $t_{\text{init}}(q)$9 for measurement time-slots, $t_{\text{init}}(q)$0 for liveness, and objective $t_{\text{init}}(q)$1, the peak number of simultaneously live qubits. Constraints enforce that every qubit is measured once, exactly one qubit is measured per time-slot, and causal-cone requirements are satisfied. A dual-circuit construction—swapping state preparations with measurements and reversing time—proves that optimal qubit-reuse compilation requires the same number of qubits for a circuit and its dual. Analytic compression results were given for several families, including $t_{\text{init}}(q)$2 qubits for a 1D $t_{\text{init}}(q)$3-layer brickwork circuit, $t_{\text{init}}(q)$4 for a depth-$t_{\text{init}}(q)$5 binary tree tensor network, $t_{\text{init}}(q)$6 for a depth-$t_{\text{init}}(q)$7 binary MERA or QCNN, and $t_{\text{init}}(q)$8 for Bernstein–Vazirani. The same paper reported an experimental realization of an 80-qubit QAOA MaxCut circuit on the 20-qubit Quantinuum H1-1 processor via qubit-reuse compilation (DeCross et al., 2022).

A more hardware-calibrated approach encodes reuse into SMT together with swap insertion. Here $t_{\text{init}}(q)$9 indicates whether a logical qubit is assigned at time $q$00, $q$01 indicates whether a reset is inserted immediately after measurement $q$02, $q$03 maps logical to physical qubits, and $q$04 represents SWAP insertion. The model can optimize depth, number of physical qubits used, or number of SWAPs. Crucially, it incorporates reset characterization. On ibmq_ehningen, measured reset fidelities ranged from $q$05 to $q$06, were state-dependent, and improved with a repeated reset up to a per-qubit optimum. The placement cost

$q$07

combines calibrated gate fidelities with reset fidelity including decoherence overhead. The reported empirical effect included up to $q$08–$q$09 ESP improvement on BV circuits and a Hellinger fidelity increase on BV$q$10 from $q$11 to $q$12, i.e. $q$13, while also showing that on circuits such as H-ladder reuse can worsen depth and fidelity if over-applied (Brandhofer et al., 2023).

Scalable heuristics have also become more graph-theoretic. GidNET represents a circuit as a DAG $q$14, derives a bipartite reachability graph between roots and terminals, forms a biadjacency matrix $q$15, and then computes the candidate matrix

$q$16

A reuse sequence is a chain of logical qubits mapped onto the same virtual qubit, and the algorithm repeatedly extracts such sequences over approximately $q$17 randomized trials. The overall worst-case runtime is

$q$18

where $q$19 is the number of reuse-sequence extractions. Compared with QNET, GidNET achieved a geometric-mean circuit-width reduction of $q$20, reaching up to $q$21 on larger circuits, with average execution time reduction of $q$22, i.e. $q$23 geometric-mean speedup, and up to $q$24, i.e. $q$25 speedup. Compared with Qiskit, it achieved an average circuit-width improvement of $q$26, with maximum reductions up to $q$27 in the largest tested circuits (Uchehara et al., 2024).

In modular architectures, reuse can be coupled directly to mapping and routing. QARMA-R inserts “measure→reset” pairs before DRL allocation whenever a qubit’s last operation precedes the first use of another qubit and the measured qubit does not carry coherent quantum information beyond that point. The reward trades off inter-core communication, total number of physical qubits in use, and reuse bonus. On a 10-core $q$28 grid with 10 physical qubits per core, QARMA-R achieved $q$29 elimination of inter-core transfers on $q$30 of benchmarks and $q$31 average reduction overall against Qiskit-O3; against QUBO mapping, it yielded a $q$32–$q$33 reduction in inter-core communications. In the sym9-146 case, QUBO required $q$34 transfers, Qiskit-O3 required $q$35, QARMA required $q$36, and QARMA-R required $q$37 (Sang et al., 11 Jun 2025).

Integrated workflows combine reuse with other circuit transformations. QRCC jointly optimizes qubit reuse, wire cutting, and gate cutting via an ILP that minimizes a linear surrogate for classical post-processing cost while respecting device-size constraints. The reported average effect was a $q$38 reduction in the number of cuts, with additional reduction when considering gate cuts. On IBM Lagos, a 7-qubit QAOA circuit run directly had expectation-value error approximately $q$39, i.e. $q$40 accuracy, whereas IQRC-B, using a 2-subcircuit partition onto 4 qubits plus post-processing, achieved $q$41 accuracy (Pawar et al., 2023).

5. Reuse across executions, simulations, privacy-preserving computation, and learned circuits

In randomized quantum-learning and benchmarking protocols, circuit reuse has a statistical meaning. One samples $q$42 independent circuits and executes each circuit $q$43 times, producing the estimator

$q$44

With fixed total cost $q$45, the variance becomes

$q$46

where $q$47 is the average within-circuit variance and $q$48 is the variance of circuit means. Under the constant-cost model $q$49, the optimal reuse factor is

$q$50

A near-optimal rule without prior circuit or noise knowledge is $q$51, with variance at most $q$52 in the constant-cost case. On a superconducting platform, the observed cost followed the batched model

$q$53

and the smallest empirical variance occurred at $q$54, contradicting the assumption of a simple linear relationship between $q$55 and cost (Chen et al., 2024).

Noisy simulation uses reuse computationally rather than physically. TQSim partitions a circuit into $q$56 subcircuits, builds a simulation tree whose nodes are cached statevectors, and reuses intermediate results across shots. If the baseline cost is $q$57, TQSim reduces gate-application work by applying each subcircuit only to the distinct cached parent states generated so far. On 48 benchmarks and $q$58 shots, it achieved speedups from $q$59 to $q$60, with average CPU speedup approximately $q$61 and average GPU speedup approximately $q$62, while keeping normalized-fidelity difference $q$63 and average approximately $q$64 (Wang et al., 2022).

In secure two-party computation, reuse takes the form of reusable garbled circuits. An RGC scheme consists of three PPT algorithms $q$65. Completely Reusable Garbled Circuits permit unbounded reuse of the same garbled object at the cost of bounded leakage $q$66, while Partially Reusable Garbled Circuits partition a circuit into reusable and non-reusable sections so that $q$67. The CRGC implementation was benchmarked against EMP SH2PC and TinyGarble2; evaluating a CRGC was up to twenty times faster, conversion to CRGC reached approximately $q$68 million gates per second, repeated evaluation reached approximately $q$69 million gates per second, and compressed CRGC file size was approximately $q$70 smaller than the unobfuscated Boolean circuit. The report further states that after $q$71–$q$72 repeated evaluations, CRGC plus compression beats sending a new garble via EMP or TinyGarble2 (Harth-Kitzerow et al., 2022).

Mechanistic interpretability uses “circuit reuse” in a different but technically precise sense: the same causal subnetwork can be redeployed across tasks. One study showed that the Indirect Object Identification circuit in GPT-2 small reappears in GPT-2 medium and is mostly reused for the Colored Objects task, with about a $q$73 overlap in in-circuit attention heads. By adjusting four attention heads in middle layers, the Colored Objects circuit was “repaired” to behave like the IOI circuit, increasing accuracy from $q$74 to $q$75 (Merullo et al., 2023). A complementary study of arithmetic transformers found that addition models converge on a common logical algorithm, that most addition-only models achieved $q$76 prediction accuracy, and that initialized mixed models reached $q$77 on $q$78 million add and $q$79 million subtraction test examples. It also introduced a reusable library of mechanistic interpretability tools—SubTask, NodeFinder, CircuitSpec, CircuitTester, and visualization modules—to locate and verify reusable arithmetic circuits across models (Quirke et al., 2024).

Taken together, these meanings of reuse show that the reused object need not be a physical component. It may be an experimental design point, a cached numerical state, a cryptographic object, or a causal computation embedded in a trained network. The shared idea is amortization: upfront construction or identification cost is paid once, then exploited repeatedly under a well-defined reuse model.

6. Electronic design, typed block composition, and reversible prototyping

In PCB design, reuse is often blocked not by hardware limits but by composition safety. TypedSchematics addresses this by representing schematic blocks with a minimal symbolic grammar for protocol and power interfaces,

$q$80

and by maintaining a typing context $q$81 with judgments $q$82. Expert users annotate blocks in a native tool such as Fusion 360, export the schematic and PCB as block files, and beginners compose them in a web front end with a 2D “Mats” canvas and a 3D PCB-block editor. Constraint checking is local and event-driven: on each connect or drop-on-mat event, TypedSchematics evaluates the corresponding typing rule in $q$83 time and overlays red-warning badges on violations. In a user study with $q$84 intermediate designers, Fusion 360 produced at least one error for $q$85 participants, whereas TypedSchematics produced $q$86 errors; mean completion time fell from $q$87 min to $q$88 min, a $q$89 speed-up, and $q$90 preferred Mats over Fusion 360’s graph model (Garza et al., 18 Sep 2025).

Reusable prototyping can also be made physical. SolderlessPCB uses detachable 3D-printed housings to mount SMD parts without soldering. The recommended material is a $q$91 weight ratio of “tough” and “flexible” UV resin, and screw-bolting is recommended over snap-fit, with $q$92 diameter bolts torqued to $q$93. For 0805 resistors, empirically supported flex-tab parameters include $q$94, $q$95, $q$96, $q$97, and $q$98, with tab stiffness

$q$99

Across 177 measurements, mean contact resistance was approximately $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$00 with $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$01; insertion-loss curves from $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$02 to $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$03 differed by less than $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$04 from soldered assemblies; tab housings were reassembled ten times, with contact resistance beginning to rise after the 7th cycle; and drop tests from $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$05 to $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$06 retained full functionality (Yan et al., 2024).

ProForm pursues the same objective through thermoforming rather than custom housings. It uses PETG with $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$07, $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$08, $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$09, and $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$10, together with anisotropic conductive film (“z-tape”). The evaluated PETG sheet thicknesses were $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$11, $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$12, and $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$13, with $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$14 selected as the optimal trade-off; reliable connections required $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$15, heating and hold were approximately $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$16, cooling approximately $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$17, and total thermoforming cycle approximately $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$18. A simplified retention model is

$$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$19

with target $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$20–$$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$21 per pin. Zero-ohm tests yielded $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$22 for 1206 and $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$23 for 0603; sine-wave tests showed insertion loss within $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$24 up to $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$25; a ProFormed PCB remained functional over $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$26 days of continuous power; and component reuse was demonstrated for at least $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$27 full attach/detach cycles with zero damage, with e-waste for a component stream dropping by $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$28 if each component is reused $$\ell(q) = [\,t_{\text{init}}(q),\,t_{\text{meas}}(q)\,].$$29 times rather than discarded (Pourjafarian et al., 28 Jul 2025).

The electronic-design literature therefore uses circuit reuse in two complementary senses. Typed block systems make previously authored circuit fragments composable without third-party engineering intervention, while reversible assembly methods make physical components recoverable across design iterations and obsolete prototypes. A plausible implication is that these two lines—typed logical composition and reversible physical assembly—address different layers of the same reuse problem: semantic correctness at design time and component recoverability at fabrication time.