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arXiv:2609.13379

Handling Imperfections in Subcircuit Compilation for Linear Optical Quantum Computing

Tobias Forster, Yannick Stade, Andreas Fyrillas, Jean Senellart, Lukas Burgholzer, Robert Wille

quant-phcs.ETSubmitted Sep 11, 2026• Announced Sep 15, 2026• 0 citations
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Abstract

Linear Optical Quantum Computing (LOQC) is emerging as a promising technology in large-scale quantum computing. Corresponding devices, including linear optical circuits, are rapidly growing in size and fabrication precision. However, even with improved quality, the circuits still exhibit imperfections leading to photon loss or phase noise that vary across the circuit. Already small deficiencies can have a vast impact on both accuracy and efficiency. For computations that do not require the entire linear optical circuit, so-called subcircuits, one can choose where to perform the computation, opening optimization opportunities that are addressed by subcircuit compilation. Current compilers spread the subcircuit's computation across the entire circuit, connecting the same input and output ports, thereby failing to fully exploit the optimization opportunities. However, given the subcircuit's reduced size compared to the entire circuit, one can keep its implementation localized and intentionally route photons to connect good input and output ports. This, however, is a highly non-trivial task, as numerous options must be weighed against one another, and the quality of the solution is influenced by a wide range of hardware parameters. In particular, the reflectivities of imperfect beam splitters can lead to photon losses during routing, which must be traded off against losses at the input and output ports due to imperfect transmission rates. Since current compilers do not account for these effects, we propose the first efficient subcircuit compilation method that optimizes for the coincidence rate, the probability of successfully measuring all desired photons, by handling hardware imperfections. Our evaluations demonstrate significant improvement over existing methods in robustness against phase noise and significantly increased coincidence rates across all benchmarks of up to plus 33.2%.

Related papers

Resource Costs for Fault-Tolerant Linear Optical Quantum Computing

Ying Li, Peter C. Humphreys, Gabriel J. Mendoza +1 more

Linear optical quantum computing (LOQC) seems attractively simple: Information is borne entirely by light and processed by components such as beam splitters, phase shifters, and detectors.However, this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads.Here, we quantify the resource costs for full-scale LOQC by proposing a specific protocol based on the surface code.With the caveat that our protocol can be further optimized, we report that the required number of physical components is at least 5 orders of magnitude greater than in comparable matter-based systems.Moreover, the resource requirements grow further if the per-component photon-loss rate is worse than 10 -3 or the per-component noise rate is worse than 10 -5 .We identify the performance of switches in the network as the single most influential factor influencing resource scaling.

arXiv:1504.02457•Physical Review X•Oct 14, 2015•114 citations

Mitigating photon loss in linear optical quantum circuits

James Mills, Rawad Mezher

Photon loss rates set an effective upper limit on the size of computations that can be run on current linear optical quantum devices. We present a family of techniques designed to mitigate the effects of photon loss on both output probabilities and expectation values derived from noisy linear optical circuits composed of an input of n photons, an m --mode interferometer, and m single photon detectors. Central to these techniques is the construction recycled probabilities . Recycled probabilities are constructed from output statistics affected by loss, and are designed to amplify the signal of the ideal (lossless) probabilities. Classical postprocessing techniques then take recycled probabilities as input and output a set of loss-mitigated probabilities, or expectation values. Our postprocessing methods result in biased estimators of the lossless probabilities. Nevertheless, we provide both analytical and numerical evidence that these methods can be applied, up to large sample sizes, to produce output probabilities with lower combined bias and statistical errors than the statistical errors of the output probabilities obtained from postselection. Therefore, these methods can outperform postselection - currently the standard method of coping with photon loss when sampling from discrete variable linear optical quantum circuits. In contrast, we provide evidence that the popular zero-noise extrapolation technique cannot improve on the performance of postselection for any photon loss rate.

arXiv:2405.02278•Quantum•Mar 16, 2026•2 citations

Efficient circuit compression by multiqudit entangling gates in linear optical quantum computation

Apurav Tehri, Jaskaran Singh

Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit compression schemes mitigate this issue by encoding multiple qubits onto qudits. However, these schemes become inefficient when only a subset of the encoded qubits is required to participate in the non-local entangling gate, leading to an exponential increase in the number of non-local gates. In this Letter, we address this bottleneck by demonstrating the existence of multi-level control-Z (CZ) gates for qudits encoded in multiple spatial modes in LOQC. Unlike conventional two-level CZ gates, which act only on a single pair of modes, multi-level CZ gates impart a conditional phase shift for an arbitrarily chosen subset of the spatial modes. We present two explicit linear optical schemes that realize such operations, illustrating a fundamental trade-off between prior information about the input quantum state and the physical resources required. The first scheme is realized with a constant success probability of $1/8$ independent of the qudit dimension using a single non-local entangling gate, at the cost of state dependence, which is significantly better than the current success probability of $1/9$. Our second scheme provides a fully state independent realization reducing the number of non-local gates to $\mathcal{O}(2^{r_1}+2^{r_2})$ as compared to the existing bound of $\mathcal{O}(2^{r_1+r_2})$ where $r_1$ and $r_2$ are the number of qubits to be removed as control in the qudits. The success probability of the realization is $\frac{1}{2} \left(\frac{1}{8}\right)^{2^{r_1}+2^{r_2}}$. When combined with qudit circuit compression schemes, our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.

quant-pharXiv:2602.08394•Physical Review A•Feb 10, 2026•0 citations

Reducing Maximum Subcircuits Depth in Quantum Circuit Cutting

Milad Eslaminia, Sébastien Le Beux

Noisy intermediate-scale quantum (NISQ) devices with limited qubit count and connectivity limit the scale of quantum circuits that can be executed. Circuit cutting methods simulate larger quantum computers by decomposing large circuits into small subcircuits that can be executed on NISQ hardware. Existing circuit cutting methods only consider the qubit count of the target hardware for finding the locations of cuts on the circuits. This can result in deeper subcircuits after mapping on the hardware. Fidelity decays exponentially with circuit depth and diminishes the quality of execution. We propose a circuit-cutting framework that reduces variance in the depth of subcircuits after mapping to the hardware. Our method formulates the initial circuit cutting as a multi-objective optimization problem based on an evolutionary search method with the number of cuts and the maximum depth of individual routed subcircuits as fitness objectives. This method is implemented as an extension to the existing Qiskit Circuit Cutting Addon, which allows for integration in existing flows. Our approach achieves reductions in routed subcircuit depth of up to 9.9% across benchmark circuits compared with baseline methods.

IEEE Transactions on Quantum Engineering•Jan 1, 2026•0 citations

Improving Quantum Computation by Optimized Qubit Routing

Friedrich Wagner, Andreas Bärmann, Frauke Liers +1 more

Abstract In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms formulated in the circuit model of computation onto specific quantum hardware. Our approach decomposes the routing problem into an allocation subproblem and a set of token swapping problems. This allows us to tackle the allocation part and the token swapping part separately. Extracting the allocation part from the qubit routing model of Nannicini et al. (Optimal qubit assignment and routing via integer programming, 2021, http://arxiv.org/abs/2106.06446 ), we formulate the allocation subproblem as a binary linear program. Herein, we employ a cost function that is a lower bound on the overall routing problem objective. We strengthen the linear relaxation by novel valid inequalities. For the token swapping part we develop an exact branch-and-bound algorithm. In this context, we improve upon known lower bounds on the token swapping problem. Furthermore, we enhance an existing approximation algorithm which runs much faster than the exact approach and typically is able to determine solutions close to the optimum. We present numerical results for the fully integrated allocation and token swapping problem. Obtained solutions may not be globally optimal due to the decomposition and the usage of an approximation algorithm. However, the solutions are obtained fast and are typically close to optimal. In addition, there is a significant reduction in the number of artificial gates and output circuit depth when compared to various state-of-the-art heuristics. Reducing these figures is crucial for minimizing noise when running quantum algorithms on near-term hardware. As a consequence, using the novel decomposition approach leads to compiled algorithms with improved quality. Indeed, when compiled with the novel routing procedure and executed on real hardware, our experimental results for quantum approximate optimization algorithms show an significant increase in solution quality in comparison to standard routing methods.

arXiv:2206.01294•Journal of Optimization Theory and Applications•May 4, 2023•24 citations

Linear optics quantum computing - construction of small networks and asymptotic scaling

Konrad Kieling

In the paradigm of linear optics, quantum states of optical field modes are manipulated by means of photon sources, beam splitters, and photodetectors. This restriction of the allowed interactions introduces non-unit success probabilities into every non-trivial computation irrevocably. The resulting probabilistic nature of this architecture opens up questions about scalability of this approach as well as about basic limitations like optimal resource consumption and the construction of optical networks for given tasks. The scalability question is addressed within the framework of cluster state computing which allows to shift the problem towards the problem of scalable state production. Several schemes with different constraints, resulting in different experimental feasibility, are shown to exhibit optimal scaling behaviour. These schemes include restrictions to certain easy-to-implement gate sets, and the banning of re-routing, which is a major obstacle in optical quantum computing. In the small-scale regime various methods for constructing and analysing linear optics networks are presented. Rather than constructing the gates in the general quantum gate model, a direct construction from linear optics’ basic elements – beam splitters and phase shifters – will be considered. This can result in higher success probabilities and smaller resource consumption. Due to the complexity of the problems, these techniques are applicable only to quantum gates which involve a small number of optical modes and photons. A couple of examples ranging from state preparation over quantum gates to state discrimination are used to illustrate these tools. LOQC – construction of small networks and asymptotic scaling 2

•Jan 1, 2008•5 citations
Linear Optical Quantum Computing (LOQC) is emerging as a promising technology in large-scale quantum computing. Corresponding devices, including linear optical circuits, are rapidly growing in size and fabrication precision. However, even with improved quality, the circuits still exhibit imperfections leading to photon loss or phase noise that vary across the circuit. Already small deficiencies can have a vast impact on both accuracy and efficiency. For computations that do not require the entire linear optical circuit, so-called subcircuits, one can choose where to perform the computation, opening optimization opportunities that are addressed by subcircuit compilation. Current compilers spread the subcircuit's computation across the entire circuit, connecting the same input and output ports, thereby failing to fully exploit the optimization opportunities. However, given the subcircuit's reduced size compared to the entire circuit, one can keep its implementation localized and intentionally route photons to connect good input and output ports. This, however, is a highly non-trivial task, as numerous options must be weighed against one another, and the quality of the solution is influenced by a wide range of hardware parameters. In particular, the reflectivities of imperfect beam splitters can lead to photon losses during routing, which must be traded off against losses at the input and output ports due to imperfect transmission rates. Since current compilers do not account for these effects, we propose the first efficient subcircuit compilation method that optimizes for the coincidence rate, the probability of successfully measuring all desired photons, by handling hardware imperfections. Our evaluations demonstrate significant improvement over existing methods in robustness against phase noise and significantly increased coincidence rates across all benchmarks of up to plus 33.2%.
Linear optical quantum computing (LOQC) seems attractively simple: Information is borne entirely by light and processed by components such as beam splitters, phase shifters, and detectors.However, this very simplicity leads to limitations, such as the lack of deterministic entangling operations, which are compensated for by using substantial hardware overheads.Here, we quantify the resource costs for full-scale LOQC by proposing a specific protocol based on the surface code.With the caveat that our protocol can be further optimized, we report that the required number of physical components is at least 5 orders of magnitude greater than in comparable matter-based systems.Moreover, the resource requirements grow further if the per-component photon-loss rate is worse than 10 -3 or the per-component noise rate is worse than 10 -5 .We identify the performance of switches in the network as the single most influential factor influencing resource scaling.
Photon loss rates set an effective upper limit on the size of computations that can be run on current linear optical quantum devices. We present a family of techniques designed to mitigate the effects of photon loss on both output probabilities and expectation values derived from noisy linear optical circuits composed of an input of n photons, an m --mode interferometer, and m single photon detectors. Central to these techniques is the construction recycled probabilities . Recycled probabilities are constructed from output statistics affected by loss, and are designed to amplify the signal of the ideal (lossless) probabilities. Classical postprocessing techniques then take recycled probabilities as input and output a set of loss-mitigated probabilities, or expectation values. Our postprocessing methods result in biased estimators of the lossless probabilities. Nevertheless, we provide both analytical and numerical evidence that these methods can be applied, up to large sample sizes, to produce output probabilities with lower combined bias and statistical errors than the statistical errors of the output probabilities obtained from postselection. Therefore, these methods can outperform postselection - currently the standard method of coping with photon loss when sampling from discrete variable linear optical quantum circuits. In contrast, we provide evidence that the popular zero-noise extrapolation technique cannot improve on the performance of postselection for any photon loss rate.
Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit compression schemes mitigate this issue by encoding multiple qubits onto qudits. However, these schemes become inefficient when only a subset of the encoded qubits is required to participate in the non-local entangling gate, leading to an exponential increase in the number of non-local gates. In this Letter, we address this bottleneck by demonstrating the existence of multi-level control-Z (CZ) gates for qudits encoded in multiple spatial modes in LOQC. Unlike conventional two-level CZ gates, which act only on a single pair of modes, multi-level CZ gates impart a conditional phase shift for an arbitrarily chosen subset of the spatial modes. We present two explicit linear optical schemes that realize such operations, illustrating a fundamental trade-off between prior information about the input quantum state and the physical resources required. The first scheme is realized with a constant success probability of 1/81/81/8 independent of the qudit dimension using a single non-local entangling gate, at the cost of state dependence, which is significantly better than the current success probability of 1/91/91/9. Our second scheme provides a fully state independent realization reducing the number of non-local gates to O(2r1+2r2)\mathcal{O}(2^{r_1}+2^{r_2})O(2r1​+2r2​) as compared to the existing bound of O(2r1+r2)\mathcal{O}(2^{r_1+r_2})O(2r1​+r2​) where r1r_1r1​ and r2r_2r2​ are the number of qubits to be removed as control in the qudits. The success probability of the realization is 12(18)2r1+2r2\frac{1}{2} \left(\frac{1}{8}\right)^{2^{r_1}+2^{r_2}}21​(81​)2r1​+2r2​. When combined with qudit circuit compression schemes, our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.
Noisy intermediate-scale quantum (NISQ) devices with limited qubit count and connectivity limit the scale of quantum circuits that can be executed. Circuit cutting methods simulate larger quantum computers by decomposing large circuits into small subcircuits that can be executed on NISQ hardware. Existing circuit cutting methods only consider the qubit count of the target hardware for finding the locations of cuts on the circuits. This can result in deeper subcircuits after mapping on the hardware. Fidelity decays exponentially with circuit depth and diminishes the quality of execution. We propose a circuit-cutting framework that reduces variance in the depth of subcircuits after mapping to the hardware. Our method formulates the initial circuit cutting as a multi-objective optimization problem based on an evolutionary search method with the number of cuts and the maximum depth of individual routed subcircuits as fitness objectives. This method is implemented as an extension to the existing Qiskit Circuit Cutting Addon, which allows for integration in existing flows. Our approach achieves reductions in routed subcircuit depth of up to 9.9% across benchmark circuits compared with baseline methods.
Abstract In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms formulated in the circuit model of computation onto specific quantum hardware. Our approach decomposes the routing problem into an allocation subproblem and a set of token swapping problems. This allows us to tackle the allocation part and the token swapping part separately. Extracting the allocation part from the qubit routing model of Nannicini et al. (Optimal qubit assignment and routing via integer programming, 2021, http://arxiv.org/abs/2106.06446 ), we formulate the allocation subproblem as a binary linear program. Herein, we employ a cost function that is a lower bound on the overall routing problem objective. We strengthen the linear relaxation by novel valid inequalities. For the token swapping part we develop an exact branch-and-bound algorithm. In this context, we improve upon known lower bounds on the token swapping problem. Furthermore, we enhance an existing approximation algorithm which runs much faster than the exact approach and typically is able to determine solutions close to the optimum. We present numerical results for the fully integrated allocation and token swapping problem. Obtained solutions may not be globally optimal due to the decomposition and the usage of an approximation algorithm. However, the solutions are obtained fast and are typically close to optimal. In addition, there is a significant reduction in the number of artificial gates and output circuit depth when compared to various state-of-the-art heuristics. Reducing these figures is crucial for minimizing noise when running quantum algorithms on near-term hardware. As a consequence, using the novel decomposition approach leads to compiled algorithms with improved quality. Indeed, when compiled with the novel routing procedure and executed on real hardware, our experimental results for quantum approximate optimization algorithms show an significant increase in solution quality in comparison to standard routing methods.
In the paradigm of linear optics, quantum states of optical field modes are manipulated by means of photon sources, beam splitters, and photodetectors. This restriction of the allowed interactions introduces non-unit success probabilities into every non-trivial computation irrevocably. The resulting probabilistic nature of this architecture opens up questions about scalability of this approach as well as about basic limitations like optimal resource consumption and the construction of optical networks for given tasks. The scalability question is addressed within the framework of cluster state computing which allows to shift the problem towards the problem of scalable state production. Several schemes with different constraints, resulting in different experimental feasibility, are shown to exhibit optimal scaling behaviour. These schemes include restrictions to certain easy-to-implement gate sets, and the banning of re-routing, which is a major obstacle in optical quantum computing. In the small-scale regime various methods for constructing and analysing linear optics networks are presented. Rather than constructing the gates in the general quantum gate model, a direct construction from linear optics’ basic elements – beam splitters and phase shifters – will be considered. This can result in higher success probabilities and smaller resource consumption. Due to the complexity of the problems, these techniques are applicable only to quantum gates which involve a small number of optical modes and photons. A couple of examples ranging from state preparation over quantum gates to state discrimination are used to illustrate these tools. LOQC – construction of small networks and asymptotic scaling 2