Quantum Circuit Repair by Gate Prioritisation

Quantum Circuit Repair by Gate Prioritisation E ˜ naut Mendiluze Usandizaga ∗ † , Thomas Laurent ‡ , Paolo Arcaini § , and Shaukat Ali ∗ † ∗ Simula Research Laboratory , Oslo, Norway † Oslo Metropolitan Univ ersity , Oslo, Norway ‡ T rinity College Dublin, School of Computer Science and Statistics, Dublin, Ireland § National Institute of Informatics, T ok yo, Japan Abstract —Repairing faulty quantum cir cuits is challenging and requir es automated solutions. W e present QRep , an automated repair approach that iteratively identifies and repairs faults in a cir cuit. QRep uniformly applies patches across the cir cuit and assigns each gate a suspiciousness score, reflecting its likelihood of being faulty . It then narrows the search space by prioritising the most suspicious gates in subsequent iterations, increasing the repair efficiency . W e evaluated QRep on 40 (real and synthetic) faulty circuits. QRep completely r epaired 70% of them, and for the remaining circuits, the actual faulty gate was ranked within the top 44% most suspicious gates, demonstrating the effectiveness of QRep in fault localisation. Compared with two baseline approaches, QRep scales to larger and more complex circuits, up to 13 qubits. Index T erms —A utomatic Program Repair , Fault Localisation, Quantum Circuits, Quantum Software Engineering I . I N T RO D U C T I O N Quantum software testing has become an acti ve area of research with several techniques proposed to detect faults [1]– [14]. Howe ver , little attention has been paid to quantum circuit repair , despite the need for automated and scalable approaches to fix faults in increasingly complex quantum circuits. Some approaches have been proposed for quantum circuit repair . HornBro [15] simplifies circuits to Clif ford gates and frames repair as parameter tuning, while UnitAR [16] generates unitary operator patches from a black-box algebraic model. Both face scalability challenges: HornBro adds many new gates, causing scalability issues and potentially failing to fully con vert the circuit in Clifford gates, and UnitAR cannot handle more than fiv e qubits. Guo et al. [17] explore semi- automatic repair with ChatGPT , but it relies on human input and struggles to generalise beyond its training circuits. T o address key limitations in the current literature regarding practicality and usability , we propose QRep , a quantum circuit repair approach that combines fault localisation with quantum circuit repair via gate-based modifications. As shown by Ishi- moto et al. [18], quantum gate-based modifications are more effecti ve at identifying quantum faults than classical mutations. Building on this insight, QRep automatically repairs circuits and, when it does not fully repair the circuit, it assists users in localising the faults and generating patches that can guide manual repair . E. Mendiluze Usandizaga is supported by Simula’ s internal strategic project on quantum software engineering. P . Arcaini is supported by the ASPIRE grant No. JPMJ AP2301, JST . S. Ali is supported by the Qu-T est project (Project #299827) funded by the Research Council of Norw ay and Oslo Metropolitan Univ ersity’ s Quantum Hub. QRep has two phases. First, it localises faulty gates by assigning a suspiciousness scor e to each gate. Second, this score guides the prioritisation of repair patches, focusing on the most suspicious gates. This strategy reduces the search space and av oids unnecessary patch attempts. W e performed a preliminary empirical ev aluation with 40 faulty quantum circuits. Results show that QRep can repair circuits of up to 13 qubits, compared to existing methods that typically handle up to 4 qubits. Even when a circuit is not fully repaired, QRep improv es it, and ranks the most suspicious gates, reducing the search space for manual repairs. I I . B A C K G RO U N D Quantum software presents unique challenges as it utilises phenomena from quantum mechanics, such as superposition and entanglement , to perform computations [19]. Superpo- sition allows a qubit (or quantum bit ) to be in multiple states simultaneously , meaning that, in contrast to a classical bit, it can exist in both 0 and 1 states at the same time. Entanglement is the phenomenon where two or more qubits are correlated, regardless of their distance. These and other quantum phenomena enable quantum computers to process large amounts of data very efficiently , theoretically allo wing them to solve problems that classical computers cannot handle. Fig. 1: Quantum circuit and patch example. Qubits: q [0] and q [1] ; group c 2 of tw o classical bits. Quantum software is typically imple- mented as a quantum cir cuit , which con- sists of a set of qubits and quantum gates that are applied to alter their states. Quantum gates serve as the quantum equiv alent of logic gates in the classi- cal domain. These gates can change the state of single qubits or multiple qubits simultaneously . Each gate in the circuit affects a qubit’ s state in a specific way . Fig. 1 sho ws a two-qubit entanglement circuit, with a Hadamard gate H applied to the first qubit, creating a superposition state, and a CNO T multi-qubit conditional gate, illustrated as a dot and a cross. At the end of the circuit, two measurement operations translate the quantum state into a classical state. I I I . QR E P – P RO P O S E D R E P A I R A P P R OAC H Alg. 1 shows an ov ervie w of QRep . Its inputs are: (i) a faulty quantum circuit C init to be repaired, (ii) a failing test suite TS , i.e, a test suite with at least one failing test case tc , Algorithm 1: QRep Automated Repair Overview Input: Faulty quantum circuit C init ; failing test suite TS ; total time budget B ; number of iterations I Output: Best patches, gate suspiciousness ranking // Initialization 1 Evaluate C init on TS and compute initial fitness as in Eq. 1; // Fault Localisation (see Sect. III-A) 2 for gate g in C init do 3 Remove gate g from C init obtaining ˜ C ; 4 Evaluate candidate circuit ˜ C over TS ; 5 if TS passes over ˜ C then 6 return ˜ C as completely repaired circuit; 7 Compute fitness fit ( ˜ C ) as in Eq. 1; 8 Update gate suspiciousness sus ( g ) as in Eq. 2; // Patch Generation (see Sect. III-B) 9 Generate candidate patches CandPatches ; 10 Distribute patches CandPatches ; // Repair (see Sect. III-C) 11 Calculate remaining time: B r = B − fault localisation time; 12 Calculate iteration time budget B i = B r / I ; 13 for i in I do 14 init timer ; 15 while timer < B i AND patches exist in CandPatches do 16 Apply patch p from CandPatches to C init obtaining ˜ C ; 17 Evaluate candidate circuit ˜ C ; 18 if TS passes over ˜ C then 19 return repaired quantum circuit ˜ C ; 20 Compute fitness fit ( ˜ C ) as in Eq. 1; 21 Update gate suspiciousness sus ( g ) as in Eq. 2; 22 Keep in CandPatches the most suspicious gates (top  1 − i I  % ) ; 23 return best patches, gate suspiciousness ranking; (iii) a time b udget B for the entire repair process, and (iv) the number of iterations I the repair process must go through. QRep uses an iterativ e process that prioritises the most suspicious gates in each iteration. Between iterations, the least suspicious gates are discarded, progressively reducing the search space, while prioritising the most suspicious gates. In Line 1, QRep ex ecutes the test suite TS on the faulty cir- cuit C init . Then, it computes an initial fitness score fit ( C init ) , calculated based on the number of failed test cases # tc fail , and the total Hellinger distance H of all test cases from the ideal distribution. Formally , the fitness function that must be minimised is defined as: fit ( C ) = # tc fail + | TS | X i =1 H ( tc i ) (1) The Hellinger distance quantifies the similarity between two probability distributions, from 0 (identical) to 1 (totally different) [20]. In our context, it quantifies how far the measured quantum state is from the expected state, helping identify faults and guide fitness impro vement while prioritising test case reduction. A. F ault Localisation In this step, QRep assesses the suspiciousness of the gates by removing one gate at a time from C init and e valuating the effect of its removal (Lines 3-4). If a modified circuit ˜ C passes the test suite TS , QRep e xits and reports ˜ C as the completely repaired circuit (Lines 5-6). Instead, if any test case fails, the process continues until all gate removals hav e been ev aluated. After each ev aluation, the fitness score of ˜ C is computed (Line 7) and the suspiciousness score of the gate g that has been removed in ˜ C is updated (Line 8); the score considers the change in fitness caused by the circuit modification: sus ( g ) = sus ( g ) +  fit ( C ) − fit ( ˜ C )  (2) All gates are initialised with sus ( g ) = 0 . The score may become ne gative if modifying a gate increases the fitness. This process assumes that if a modified gate is neither the faulty one nor related to the fault, then introducing a new modification will act as a second fault, leading to more failed test cases or greater test case failure distance, thus increasing the fitness. Instead, we assume that removing the faulty gate will reduce the effect of the fault, thereby decreasing the fitness. Over multiple modifications, gates that consistently decrease the fitness value accumulate higher suspiciousness scores, whereas gates that increase the fitness score may acquire negati ve scores, making them less suspicious. B. P atch Generation In Line 9, QRep starts the patch generation by generating the list of all possible patches CandPatches av ailable for the faulty circuit C . This patch list contains gate-based modifi- cations to apply to the circuit. As pre viously proposed in the literature [18], we can either add a new gate to the quantum circuit or replace a gate with another gate. Every possible modification will be treated as a ne w candidate patch. Fig. 1 shows an example of adding a new gate to the circuit. The generated patches are then distrib uted uniformly across the circuit to ensure early cov erage of the circuit’ s gates (Line 10). The uniform distribution is achieved by selecting one patch at each position in the circuit, alternating between adding and replacing gates. Also, the approach ensures that a variety of Qiskit-supported gates are used, cov ering different quantum gates throughout the process. This approach ensures that different gates are targeted in each iteration, enabling broad exploration of potential patches while maintaining bal- anced cov erage across the entire circuit. C. Repair Once all possible patches are generated, the iterati ve process begins. In Line 12, the approach sets a time budget B i for each iteration, which is determined by distributing the remaining time B r for the ov erall approach (computed at Line 11) across the desired number of iterations I . In each iteration’ s inner loop (Line 15), for each patch p , the modification is applied to the faulty circuit C init and remov ed from the patch list CandPatches , generating a candidate circuit ˜ C incorporating the modification (Line 16) that is further ev aluated with the test suite TS (Line 17). If a parametrised gate is introduced, the COBYLA optimiser (widely used in quantum computing) is employed to find the best parameter values. Any patch passing TS is considered successful, marking the circuit as repaired, and terminating the process (Lines 18-19). After the execution of TS , the fitness of ˜ C is calculated using Eq. 1 (Line 20). Then, in Line 21, the suspiciousness score of the related gate g is updated using Eq. 2. If the iteration concludes without finding a successful patch and not all patches have been executed, the process proceeds to the next iteration. During this transition, the gate suspicious- ness list and the current iteration i will be used to select the most suspicious gates (Line 22), and only patches linked to these gates will proceed to the next iteration. If, after an iteration, no more patches are av ailable in CandPatches or the budget has expired, the circuit will be considered as “Not Fixed”, and QRep will report the best patches identified throughout the ev aluation, along with the gate suspiciousness ranking (Line 23). These patches are the most effecti ve modifications to the circuit for addressing the faults and can facilitate future manual repair . I V . E X P E R I M E N T D E S I G N W e here describe the experiment design. The implementa- tion and all results are av ailable in our repository [21]. Research questions: T o assess the effecti veness of QRep , we address the following research questions: RQ1 : How effective is QRep in r epairing quantum cir cuits? RQ2 : In the non-r epair ed quantum cir cuits, what is the par- tial repair effectiveness and how accurate is the fault localisation? Subject Systems: W e used 4 real faulty benchmarks from Bugs4Q [22] and used to ev aluate UnitAR by Li et al. [16], with qubits ranging from 2 to 4, depths from 4 to 11, and gates from 3 to 14. These faulty benchmarks originate from small quantum circuits in terms of qubit size and complexity , which is usually measured by the circuit’ s depth and the number of gates. Therefore, we chose to utilise two quantum mutation tools currently av ailable in the literature, Muskit [23] and QMutPy [24], to create additional faulty circuits. W e selected a set of 12 quantum circuits 1 , each with a different number of qubits (2-13), gates (14-50) and depth (7-38). These circuits were sourced from MQT Bench [25], a widely recognised benchmark suite for quantum circuits. The selection of these circuits was guided by the grouping methodology outlined in [26], which categorises quantum algorithms based on their building blocks. W e generated all possible mutants using both tools and merged the mutant sets by comparing them to av oid duplication. The mutants were then grouped by mutation operator . For each algorithm, we randomly selected a mutant from each group, resulting in three mutants per algorithm. This process resulted in a benchmark set of 36 faulty circuits. Baseline approaches: W e compare QRep with two base- line repair approaches to provide a fair assessment of its ef fec- tiv eness. First, we compare it to a random search strategy ( RS ): this strategy randomly generates patches without guidance on 1 Amplitude Estimation (ae); Deutsch-Jozsa (dj); Greenberger-Horne- Zeilinger State (ghz); Graph State (graphstate); Grover Search(grover); Quan- tum Approximate Optimization Algorithm (qaoa); Quantum Fourier T rans- form (qft); Quantum Phase Estimation Exact (qpeexact); Quantum W alk (qwalk); V ariational Quantum Eigensolver (vqe); W -State (wstate). suspiciousness or any patch selection strategy . Since QRep includes an optimisation algorithm for parametric gates, we allocate the same number of ev aluations used for the optimiser to RS as the budget for assessing them. Next, we compared QRep with a well-established approach from the literature called UnitAR [16]. This approach of fers strong theoretical foundations for patch generation based on al- gebraic models of unitarity operations. In this comparison, we adhered to the parameters and b udget specified in UnitAR ’ s documentation and translated those to our approach. Each approach was executed with a budget of 2 hours per faulty quantum circuit, and for UnitAR , a unitary matrix budget of 100,000, as in the original study . T est Suite: For each faulty circuit C init , we construct a test suite TS based on the input coverage proposed by W ang et al. [13], where we generate all possible classical input initialisations of the qubits. Since a quantum circuit can be measured in multiple bases, we create test cases for each major measurement bases, X , Y and Z . Therefore, the total number of tests in TS is 2 # qubits × 3 , where # qubits is the number of qubits of C init . Note that, for ex ecution in UnitAR , the provided implementation did not support multiple base measurements, so we ran UnitAR using the default Z base measurements. The differences in the test suite may lead UnitAR to consider some of the generated faults as equiv alent, since the faults might not be apparent in only the Z -basis. W e chose to proceed by running QRep alongside RS across the three bases, as we believ e this of fers a more comprehensiv e view of the faults and actual repairs. In the case of UnitAR , the faults may not hav e been completely repaired; they simply may not be visible in the Z -basis. 2 T o determine whether a test case passes or fails, we used an oracle-based assessment method [26]. A test case is considered failed in either of the following cases: (i) the observed output is not among the expected ones, indicating incorrect program behaviour , or (ii) the output probabilities deviate significantly from the expected probabilities. Experimental Setup: The experimental environment con- sisted of a W indows machine with 20 CPUs and 64 GB of RAM. All circuits are written in QASM 2, and we used Qiskit ver . 1.1.0 to load and modify the circuit. T o execute the quantum circuits, we used Qulacs ver . 0.6.10 as the simulator . T o enhance consistency and reproducibility , a fixed random seed was used during the simulations. T o address the uncer- tainty in quantum computing, we performed a number of shots proportional to the number of qubits, calculated as 2 # qubits × 2 , that should allow us to cov er all output states if necessary . V . R E S U LT S A N D A NA LY S I S RQ1 (Repair Effectiveness): T ab. I presents the results. Each column sho ws the repair rate for each approach, indicat- ing the number of circuits completely repaired out of the total number of faulty quantum circuits. 2 Note that this fa vours UnitAR in the comparison with QRep . Therefore, it does not affect the soundness of our experiments. T ABLE I: RQ1 – Number of faulty quantum circuits repaired by approach ( R ep air e dCir cuits / T otalF aultyCir cuits ). Quantum Circuit # Qubits Appr oach UnitAR RS QRep Bugs4Q-id25 3 1/1 0/1 0/1 Bugs4Q-id26 2 1/1 1/1 1/1 Bugs4Q-id27 3 0/1 1/1 1/1 Bugs4Q-id39 4 0/1 0/1 0/1 QNN 2 0/3 2/3 3/3 AE 3 0/3* 1/3 3/3 Grover 4 0/3* 1/3 3/3 Qwalk 5 0/3* 0/3 3/3 QA OA 6 0/3* 0/3 1/3 VQE 7 0/3* 0/3 3/3 QPE 8 0/3* 0/3 2/3 QFT 9 0/3* 0/3 2/3 W -state 10 0/3* 0/3 2/3 DJ 11 0/3* 0/3 2/3 Graphstate 12 0/3 † 0/3 1/3 GHZ 13 0/3* 0/3 1/3 T otal - 2/40 6/40 28/40 *No unitary matrixes found, † Equivalent program (Only Z basis measurements) All three approaches achieve the same effecti veness in repairing real faults from Bugs4Q, each repairing 2 out of 4. Howe ver , there is a slight dif ference in terms of which faults are repaired. All three approaches successfully repair the id26 faulty circuit, but UnitAR also repairs id25, while QRep and RS repair id27. None of the approaches can repair the id39 fault, highlighting a possible scalability issue in quantum circuit repair , as it inv olves a higher qubit count. When considering the generated faulty circuits, we note that scalability is a key challenge. The artificially generated faults originate from larger , more complex circuits, resulting in a significant decrease in complete repairs for both baselines. In contrast, QRep successfully repairs 26 out of the 36 artificially generated faults, bringing the total number of repaired faults to 28 out of 40, representing a 70% complete repair rate. Results show the weakness of UnitAR , as it is unable to repair any of the generated faults within the provided budget. For the largest circuits, this limitation prevents e ven selecting unitary matrix operations, as scaling becomes increasingly challenging with the number of qubits and gates. RQ2 (Partial Repair & Fault Localization): For the non- repaired circuits, QRep provides a list of best patches and a rank of gates by suspiciousness. Thus, we analyse the partial repair of the best patch by measuring the improv ement in fitness, and we ev aluate ho w well QRep localises faults by reporting the faulty gate’ s rank in the gate suspiciousness list. T ab. II sho ws the results obtained for the circuits that were not completely repaired. The second column sho ws the percentage improv ement in circuit fitness. The last column indicates the final rank of the faulty gate within the suspiciousness list: 0% corresponds to the top of the list (most suspicious) and 100% to the bottom (least suspicious). W e observe that although the faults were not fully repaired, all cases e xcept one sho w at least some improv ement in fitness. Some cases showed a significant repair rate, up to 99%. In the T ABLE II: RQ2 – Fitness improvement and faulty gate loca- tion in avg across non-repaired faults from the same circuit. Quantum Circuit #Faults Improv ement % Location (T op %) Bugs4Q-id25 1 3.6% 50% Bugs4Q-id39 1 10.6% 0% QA OA 2 99.3% 40.5% QPE 1 33.7% 58.2% QFT 1 83.6% 0% W -state 1 52.8% 25% DJ 1 0.0% 37.2% Graphstate 2 15.8% 29.7% GHZ 2 40.2% 62.9% case where the fitness was not reduced, the faulty gate was ranked in the top 37% of the most suspicious g ates. This means that if a user checks the gates in order of their suspiciousness, they could significantly reduce the search space or the time required to locate the fault by more than half. Some cases located the gate at the top of the suspiciousness list 0%, meaning QRep was able to identify the faulty gate as the most suspicious. Even in the worst result, the faulty gate is still 62% from the top, indicating that it can also help reduce the search space to some extent. T ogether with the provided partial repair rates, this significantly reduces the manual work required to repair the quantum circuit. V I . D I S C U S S I O N A N D F U T U R E W O R K QRep sho ws promise for repairing and localising faults in quantum circuits. Howe ver , it supports only one modification at a time. Thus, further work is required to in vestigate QRep ’ s effecti veness for circuits with multiple faults and potential improv ements with multiple modifications. In our case, the correctness of the repaired circuit is ev alu- ated using the provided test suite, as QRep considers a fault repaired once the circuit passes all test cases in the test suite. Howe ver , there may be test cases outside the test suite in which the repaired circuit fails. Regarding empirical e valuation, we ev aluated the QRep on 40 faulty quantum circuits, 36 of which were artificially generated. In the future, we aim to e valuate our approach with a broader benchmark of real faults. V I I . 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