Quantum Circuit Obfuscation

Updated 11 November 2025

Quantum Circuit Obfuscation is the process of transforming a quantum circuit into a functionally equivalent form that hides its internal structure, preserving intellectual property and algorithmic secrets.
Techniques include cryptographic constructions like QFHE-based schemes, algebraic methods such as braid group normal forms, and low-level circuit deformations including dummy gate insertions and phase obfuscation.
Security analysis reveals that while generic, reusable black-box obfuscation is impossible under certain assumptions, tailored methods offer practical protection while balancing performance metrics and resource overhead.

Quantum Circuit Obfuscation (QCO) is the paper and engineering of transformations that take a quantum circuit (or quantum program) and produce a functionally equivalent object—circuit, state, or hybrid artifact—that conceals as much as possible of the implementation’s internal structure, enabling only black-box execution while hiding intellectual property, algorithmic secrets, and other proprietary details. QCO arises in contexts such as secure quantum cloud computing, IP protection against untrusted compilers, delegated quantum computation, and quantum cryptography. The design of QCO protocols draws on techniques from quantum information, cryptography, complexity theory, and practical quantum software engineering.

1. Definitions and Security Models

Formal security notions for QCO extend, refine, or reinterpret classical obfuscation definitions for the quantum regime. There are three main paradigms:

Virtual Black-Box (VBB) Obfuscation: A QCO is VBB-secure if, for any adversary given the obfuscated circuit (or state), there exists an efficient simulator with only black-box/oracle access to the original circuit that cannot be distinguished from the real adversary (up to negligible probability). This notion is unconditional in the information-theoretic variant and computational in the cryptographic variant (Alagic et al., 2016).
Indistinguishability Obfuscation (iO): A QCO is an iO if, for any two functionally equivalent circuits $C_0, C_1$ of equal size, the obfuscations $\mathcal{O}(C_0)$ and $\mathcal{O}(C_1)$ are indistinguishable to any quantum polynomial-time (QPT) adversary. Quantum variants relax this to classes such as pseudo-deterministic circuits or approximately unitary maps. Security can be perfect, statistical, or computational, and may be instantiated in the random-oracle or classical-oracle models (Broadbent et al., 2020, Zhang et al., 23 Jul 2025, Zhang et al., 19 Nov 2024, Bartusek et al., 2023, Bartusek et al., 18 Jan 2024, Huang et al., 16 Jul 2025).
Partial/Task-Oriented Obfuscation: In some settings, only specific equivalence relations (e.g., relations derived from a finite generative gate algebra or certain circuit rewriting rules) are hidden, yielding partial-indistinguishability obfuscation (Alagic et al., 2012).

The model parameters include the obfuscation target (reversible, unitary, or general CPTP circuits), output type (classical description, quantum state, or hybrid), assumed adversarial power (single-use, reusable, multi-copy, access to oracles or hardware), and functionality class (fully quantum versus pseudo-deterministic).

2. Obfuscation Methodologies and Constructions

QCO methodologies range from cryptographic to algorithmic and algebraic. Central approaches include:

Cryptographic Constructions: These leverage quantum-secure classical primitives such as Learning with Errors (LWE), quantum fully-homomorphic encryption (QFHE), and functional commitments.
- QFHE-based schemes: Encode the circuit as a QFHE ciphertext, together with classical obfuscated decryption/or verification routines, resulting in reusable, publicly-verifiable obfuscations for pseudo-deterministic circuits (Bartusek et al., 2023, Bartusek et al., 9 Oct 2025).
- Quantum Authentication Codes and Functional Commitments: Functional quantum authentication may facilitate simulation-based security, supporting access control to measurements and projections within authenticated quantum data (Huang et al., 16 Jul 2025).
- Quantum State Obfuscation: Quantum programs with auxiliary states and logic are encoded as quantum states plus classical oracles, attaining ideal iO in the classical-oracle model for both pseudo-deterministic functionality and (recently) unitary transformations (Bartusek et al., 18 Jan 2024, Huang et al., 16 Jul 2025).
Algebraic or Structural Obfuscation:
- Braid group–based partial obfuscation: Circuits are mapped to words in computationally universal groups (e.g., the braid group), and the normal forms serve as the obfuscated description. Indistinguishability follows only with respect to generating relations, not all semantic equivalences (Alagic et al., 2012).
- Path-Sum and Loop Insertion Techniques: Circuits are rewritten via insertion of identity or equivalent "loop" subpaths (i.e., subcircuits that yield the identity operator), scrambling the gate-level structure without affecting overall functionality. This is amenable to indistinguishability proofs via the Schwartz–Zippel lemma and hybrid quantum-oracle arguments (Zhang et al., 19 Nov 2024, Zhang et al., 23 Jul 2025).
Gate-Level and Logic Deformation Methods (primarily for NISQ/engineering settings):
- Obfuscation via Randomized Reversible Gates: Insert random reversible subcircuits to scramble output distributions, requiring an inverse operation for functional restoration (Das et al., 2023).
- Dummy/SWAP Insertion: Single or multiple dummy SWAP gates with metric-based selection (using features such as "depth-to-output") maximize output distribution corruption against reverse engineering. Recovery involves post-compilation removal (Suresh et al., 2021).
- Phase Obfuscation (OPAQUE): Encodes key bits as random shifts in single-qubit phase gates, with barriers to block compiler optimizations; achieves security-per-error advantages over prior gate-insertion (Rehman et al., 23 Feb 2025).
- Classical Post-Processing (Hybrid Methods): Random gates (state-flip, controlled NOTs, swaps) are inserted, and a classical decoder is used to map scrambled measurement results back to the real logical outputs, reducing quantum overhead and sidestepping the need for complex quantum reversal or barriers (Raj et al., 20 May 2025).
Automated Frameworks: Tools such as ObfusQate apply combinations of quantum-primitive-based circuit and code-level obfuscations, including identity insertions, composite blocks, non-intuitive gate decompositions, and quantum-controlled opaque predicates at the program logic level (Bartake et al., 31 Mar 2025).

The table below summarizes exemplary QCO methods and key attributes:

Approach	Obfuscation Type	Security Model / Application
QFHE + functional commitments	Quantum/classical hybrid	iO for pseudo-deterministic circuits (Bartusek et al., 2023, Bartusek et al., 9 Oct 2025)
Braid group normal-form	Algebraic (partial indistinguishability)	Word-problem equivalence, circuit hiding (Alagic et al., 2012)
Loop subpaths via path sums	Structural, path-integral-based	General QiO under random/oracle models (Zhang et al., 19 Nov 2024, Zhang et al., 23 Jul 2025)
Randomized reversible/dummy gates	Low-level circuit deformation	Output obfuscation, resource-aware hiding (Das et al., 2023, Suresh et al., 2021)
Phase obfuscation (OPAQUE)	Gate parameter obfuscation	Phase-key locking, high entropy, low error (Rehman et al., 23 Feb 2025)
Hybrid quantum-classical postprocessing	Structural plus classical key, compiler-agnostic	Scalable to NISQ regimes (Raj et al., 20 May 2025)

3. Security Analysis, Limitations, and Impossibility Results

Theoretical results establish both feasibility and hard limits for QCO:

Impossibility of Generic Black-Box Quantum Obfuscation: There is no reusable black-box (VBB) quantum circuit obfuscator (even outputting a quantum state) for all circuits and adversaries with two or more copies, if quantum-secure one-way functions exist. Statistical iO for all circuits would collapse PSPACE into QSZK, which is not believed to happen (Alagic et al., 2016).
Partial vs. Complete Indistinguishability: Algebraic approaches such as braid group normal forms only yield indistinguishability up to syntactic rewrite relations, not semantic equivalence, and are vulnerable to attacks exploiting relations outside the chosen generating set (Alagic et al., 2012).
Attack Models and Security Evaluation: Recent work demonstrates that “split compilation” approaches—which partition a circuit and hide the wire permutation at the boundary—offer only marginal security if the adversary has modest oracle access. The number of queries required for boundary reconstruction grows linearly rather than factorially with circuit or split size, as hierarchical block matching and reversible-gate invertibility dramatically reduce search space (Zhang et al., 6 Nov 2025). Thus, QCO techniques that do not account for adaptive, query-based attacks may be insufficient for high-stakes IP protection.

A recurring theme is the necessity of quantifying not only the total combinatoric search space an attacker faces, but also the practical query complexity under realistic adversary capabilities—especially when structural leakages and reversibility can be exploited.

4. Performance Metrics and Empirical Results

QCO protocols are evaluated using a range of correctness, security, and resource metrics:

Correctness: Measured by fidelity loss ( $\Delta F$ ) between original and de-obfuscated circuits, with high-performing schemes achieving average loss below 1–3% (Das et al., 2023, Zhang et al., 23 Jul 2025).
Statistical Obfuscation: Quantified via Total Variation Distance (TVD) between obfuscated and original output distributions, with values approaching or exceeding 0.7–1.9 considered strong hiding (Zhang et al., 23 Jul 2025, Raj et al., 20 May 2025, Zhang et al., 23 Jul 2025).
Structural Obfuscation: Normalized Graph Edit Distance (normGED) captures structural (DAG-level) differences, with empirically observed values as high as 0.88 (Zhang et al., 23 Jul 2025).
Resource Overhead: Measured in circuit depth, gate count, and classical/quantum runtime overhead. Several schemes keep added depth under 5% or per-dummy-gate, with overall circuit-level overhead depending on obfuscation strength (e.g., up to +43% time or +128 layers for heavy identity-insertion methods (Bartake et al., 31 Mar 2025)).
Empirical Security Evaluation: Automated tools and statistical metrics such as Degree of Functional Corruption (DFC) and resilience to reverse engineering (tested by oracle-guided pruning or feature-guided attacks) inform practical robustness (Raj et al., 20 May 2025, Zhang et al., 6 Nov 2025).

5. Applications, Use Cases, and Implementation Considerations

QCO has immediate significance in several areas:

Quantum IP Protection for Cloud Compilation: Obfuscation protocols ensure that proprietary algorithms sent to untrusted compilers do not reveal functional secrets or critical topologies, especially in cloud or third-party device workflows (Zhang et al., 23 Jul 2025, Raj et al., 20 May 2025).
Delegated Quantum Computation Security: Blindness, public verifiability, and succinctness are achieved by QFHE-based and commit-and-verify schemes, enabling classical verification of quantum computation for BQP with low client-side overhead (Bartusek et al., 9 Oct 2025).
Software Copy Protection: Quantum state obfuscation enables “unclonable software,” leveraging quantum state no-cloning for functionalities that are copy-protectable but not classically obfuscatable (Bartusek et al., 18 Jan 2024).
Quantum Logic Locking and Hardware Protection: Gate-insertion, phase, or random reversible hiding mechanisms serve as quantum logic locking approaches, analogous to hardware security in classical IP (Rehman et al., 23 Feb 2025, Suresh et al., 2021).
Offensive and Advanced Applications: ObfusQate demonstrates obfuscation of steganographic or malicious payloads for evasion of code analysis, indicating both potential for advanced security research and for adversarial countermeasures (Bartake et al., 31 Mar 2025).

Limitations include (i) scalability to circuits with large depth or bandwidth, (ii) sensitivity to noise models and realistic NISQ errors, and (iii) the difficulty of guaranteeing formal cryptographic security under practical constraints.

6. Open Problems, Research Directions, and Comparisons

Current research in QCO continues to face significant fundamental and engineering challenges:

Removing Classical-Oracle and Random-Oracle Assumptions: Most candidate iO or ideal QCO schemes circumvent impossibility via classical or quantum random oracles; eliminating or weakening these assumptions is a central open question (Huang et al., 16 Jul 2025, Bartusek et al., 18 Jan 2024).
Quantum-secure Classical Obfuscators: The construction of succinct, reusable, and fully quantum-secure obfuscators for general circuits without resorting to quantum state outputs remains unresolved (Bartusek et al., 9 Oct 2025).
Efficient Obfuscators for Arbitrary Quantum Circuits: Extending efficient constructions beyond pseudo-deterministic or Clifford-hierarchy classes to all unitaries or CPTP channels is an active area (Broadbent et al., 2020).
Resource and Overhead Optimization: Managing the trade-off between obfuscation strength and quantum overhead (depth, error) is especially salient for NISQ applications.
Noise and Device-Aware Obfuscation: Integration of decoupling pulse sequences into structural obfuscation (e.g., adaptive dynamical decoupling) is a practical line for matching physical-layer constraints and error mitigation (Zhang et al., 23 Jul 2025).
Formal Cryptographic Proofs: Many existing engineering methods (e.g., dummy-gate, randomized reversible insertions) lack rigorous security reductions. Stronger definitions using quantum random function theory and simulation-based security are under investigation (Bartusek et al., 18 Jan 2024, Huang et al., 16 Jul 2025).

Comparative analyses show that while classical obfuscation is unconditionally impossible for universal quantum circuits, quantum protocols enjoy unique advantages from no-cloning and quantum authentication, enabling possibilities such as uncloneable quantum software and cryptographic primitives unattainable classically (Alagic et al., 2016, Bartusek et al., 18 Jan 2024).

In summary, Quantum Circuit Obfuscation is a rapidly evolving field integrating quantum information, cryptography, and hardware-aware engineering to mitigate risks in quantum IP protection and secure delegated computation. While generic black-box obfuscation is ruled out even in the quantum setting, a tapestry of structural, cryptographic, and hybrid techniques—tailored for both theory and NISQ hardware—provide practical and provably secure alternatives within well-specified adversarial and circuit classes. Continuing research is directed at expanding the scope of secure obfuscation, optimizing practical resource requirements, and formalizing security in models capturing both quantum and classical realities.