
Table 1: Quantum software design patterns: Core algorithmic patterns, data-encoding strategies, hybrid algorithms, modular
software components, and NISQ execution strategies.
Name / Purpose Resource Footprint Classical Processing Topology Constraints Typical Applications Limitations Reference
Algorithm Core
Initialization Requires qubits for the problem
size; no gates for the all-zero
state (default for many SDKs).
Minimal depth if standard.
No classical overhead unless
advanced prep is used (classi-
cal data might define angles).
Not sensitive to hardware
connectivity if no entan-
gling gates.
Fundamental for most quan-
tum algorithms (simulation,
cryptography, etc.).
Gate overhead grows for non-
trivial states; prone to prep er-
rors on noisy devices.
(B
¨
uhler et al.,
2023; Leymann,
2019)
Uniform Super-
position
Needs as many qubits as
the input size; typically one
Hadamard per qubit. Depth
about one plus overhead.
No big classical overhead; op-
tional control for adaptive se-
quences.
Single-qubit operations
only, weakly dependent on
connectivity.
Common in Grover’s search,
amplitude amplification.
Phase errors may accumulate;
precise single-qubit calibrations
needed.
(B
¨
uhler et al.,
2023; Weigold
et al., 2022)
Entanglement At least two qubits; uses con-
trolled gates (CNOT, CZ).
Depth depends on pairs.
Usually no classical over-
head. Possibly some coordi-
nation in hybrid programs.
Important if qubits are not
directly connected; may re-
quire gate routing.
Central in teleportation, su-
perdense coding, error cor-
rection, EPR pairs.
Sensitive to decoherence and
cross-talk; higher error rates.
(Leymann,
2019; B
¨
uhler
et al., 2023)
Oracle Qubits depend on the function;
custom multi-qubit gates or se-
quences. Depth follows func-
tion complexity.
Classical pre-processing to
build the reversible circuit.
Post-processing to check ora-
cle results.
Routing needed if connec-
tivity is limited. Multi-
controls might need ancil-
las.
Key for search, Boolean
function evaluations, etc.
Large oracles consume re-
sources; mapping from classical
logic can be complex.
(Georg et al.,
2023)
Uncompute Often uses ancillas; same gate
count as forward subcircuit in
reverse. Depth roughly doubled.
No extra classical overhead;
purely quantum. Possibly
some logic for subcircuit
choice.
Constraints mirror the
original subcircuit.
Clears ancilla qubits (restor-
ing them to zero). Common
in arithmetic, phase estima-
tion.
Doubles depth, increasing over-
all error.
(B
¨
uhler et al.,
2023)
Amplitude Am-
plification
Depends on scale; oracle plus
diffuser repeated. Gate count
and depth scale with iterations.
Optional measurement at the
end. Feedback loops in adap-
tive variants.
Limited by multi-qubit
gate connectivity.
Used in Grover’s search,
combinatorial optimization.
Iterations grow as square root of
problem size; gate errors accu-
mulate.
(Bechtold et al.,
2023)
Data Encoding
Basis Encoding Uses ⌈log
2
(k)⌉ qubits for k
states; may need bit-flip gates or
none if already binary. Very low
depth.
Classical data in binary. Min-
imal post-processing unless
partial qubit measurement.
Few connectivity de-
mands; mostly single-qubit
or simple controls.
For categorical states, clas-
sification, simpler quantum
tasks.
Inefficient for large k; misses
amplitude-based advantages.
(Weigold et al.,
2022)
Amplitude
Encoding
⌈log
2
(M)⌉ qubits for M-dim
data. Potentially O(M) gates for
arbitrary loads.
Classical pre-processing to
get angles or normalize data.
Post-processing to check fi-
delity.
Can be connectivity-heavy
if multi-qubit gates are
needed.
Used in Quantum Machine
Learning, Principal Compo-
nent Analysis, or amplitude-
based speedups.
Large data = big gate count;
noise sensitivity.
(B
¨
uhler et al.,
2023)
Angle Encoding One qubit per feature; single-
qubit rotations. Depth is how
many rotations.
Feature values mapped to an-
gles. Post-processing checks
final correlations.
Low connectivity demands
if no entangling layers.
Popular in near-term QML,
classifiers, variational cir-
cuits.
Limited features per qubit; rota-
tion errors matter.
(B
¨
uhler et al.,
2023; Georg
et al., 2023)
Quantum Ran-
dom Access
Memory Encod-
ing
Needs log
2
(M) address qubits +
data qubits. Multi-controls can
grow depth.
Classical data must be or-
ganized for random access.
Post-processing reads out
lines.
Complex routing if con-
nectivity is limited; multi-
controls.
Enables large-scale QML or
database queries in superpo-
sition.
Building true QRAM is hard;
multi-controlled gates raise er-
ror.
(Georg et al.,
2023)
Quantum Asso-
ciative Memory
Qubit count scales with pattern
dimension. Summation of basis
states. Depth varies by retrieval
method.
Might need classical query
for retrieval. Post-processing
identifies matched pattern.
Controlled gates might be
required; connectivity can
matter.
Used in pattern match-
ing, content-addressable
searches, some QML.
Scalability uncertain; large cir-
cuits can be error-prone.
(Weigold et al.,
2022)
Hybrid Algorithms
Variational
Quantum
Algorithm
Problem-dependent qubits;
param. circuit layers (single-
/two-qubit gates). Depth
depends on layer count.
Classical optimizers update
gate params after measure-
ments. Pre-/post- steps for
param setup routines.
Needs mid-circuit mea-
surement or repeated runs.
Entangling layers may
need good connectivity.
Foundational for near-term
heuristics: QML, chemistry,
optimization.
Sensitive to noise, barren
plateaus, slow or stuck classical
optimization.
(Weigold et al.,
2021)
Variational
Quantum
Eigensolver/
Quantum
Approximate
Optimization
Algorithm
Qubits match system/graph.
Param. ansatz with single-/two-
qubit gates. Depth grows with
layering.
Needs iterative classical opti-
mization. Post-processing ob-
tains final params/energies.
Connectivity shapes
ansatz. Distant qubits may
need swaps.
VQE for ground-state ener-
gies, Quantum Approximate
Optimization Algorithm for
combinatorial tasks.
Excess depth undermines ad-
vantage; more layers raise gate
errors.
(Weigold et al.,
2021)
Warm-starting Same qubit/gate needs as main
approach, plus minor overhead
for classical solutions.
A classical solver seeds initial
parameters; post-processing
is standard.
No extra constraints be-
yond regular variational
circuits.
Speeds up hybrid tasks
(portfolio, max-cut) with
classical seeds.
Depends on seed quality; may
fail if guess is poor.
(Truger et al.,
2024)
Software Module
Quantum Mod-
ule
Qubits/gates depend on module
function. Depth varies with rou-
tines.
Classical inputs set params;
post-processing reads states
or outcomes.
Depends on module. Many
entangling gates can be
connectivity-heavy.
Reusable quantum logic
(e.g. arithmetic, oracles,
transformations).
Large modules can be resource-
heavy; must integrate carefully.
(B
¨
uhler et al.,
2023)
Hybrid Module Any size, combining quantum
subcircuits + classical routines.
Depth includes quantum + clas-
sical overhead.
Typically has quantum-
classical loops, measurements
feed classical logic.
Quantum portion needs
connectivity. Classical part
may add latency.
Used for end-to-end hybrid
solutions, iterative or data-
driven workflows.
Complex debugging/tuning; re-
peated hardware calls can be
slow.
(B
¨
uhler et al.,
2023)
Circuit Transla-
tor
Rewrites circuits without direct
qubit use. Gate count depends
on decomposition.
Uses classical logic to opti-
mize or rewrite gates.
Must match hardware cou-
pling, so connectivity is
key.
Enables cross-framework or
cross-hardware circuit com-
patibility.
Poor translations can increase
depth or gates, reducing fidelity.
(Georg et al.,
2023)
Execution and Noisy Intermediate-Scale Quantum (NISQ)
Standalone Exe-
cution
Follows final compiled circuit’s
qubits/gates. Depth per chosen
algorithm.
Minimal overhead, typically
just job submission and result
retrieval.
Compile-time connectivity
handling, no dynamic
feedback.
For quick prototyping of
small circuits without ad-
vanced mitigation.
Constrained by hardware coher-
ence/fidelity; no built-in mitiga-
tion.
(Piattini et al.,
2020)
Ad-hoc Hybrid Same as circuit, plus overhead
for repeated loop runs.
Host code runs pre-/post-
each quantum run for param-
eter/data adjustments.
No extra constraints, but
repeated calls are time-
consuming.
Prototyping or small-scale
hybrid demos in research
settings.
Inefficient for large param
sweeps; lacks advanced re-
source management.
(Weigold et al.,
2021)
Pre-deployed Supports any qubit/gate scale,
subject to practical limits. Re-
peated instantiation.
Classical logic routes jobs,
collects results, handles
scheduling.
Connectivity matters for
distributed or cloud hard-
ware.
Used by cloud-based
enterprise solutions and
repeated/persistent quantum
jobs.
Scheduling/queue overhead
adds latency; limited real-time
control or debugging.
(Georg et al.,
2023)
Circuit Cutting Splits large circuits into subcir-
cuits. Each subcircuit fits local
qubit limit.
Combines subcircuit mea-
surement results for global
outcome.
Connectivity matters in-
side subcircuits; classical
stitching logic is key.
Distributes large computa-
tions for resource-limited
hardware.
Post-processing grows with
cuts; noise accumulates.
(Bechtold et al.,
2023)
Next, examine the Resource Footprint column for
an overview of the qubit count, gate depth, and
other hardware demands each pattern may intro-
duce. Patterns with sparse multi-qubit operations
Guidelines for the Application of Hybrid Software Design Patterns
107