For practical usage of quantum systems in solving real-world problems, large amounts of classical data are required to be transferred/encoded to the quantum domain. Arbitrary classical data is usually encoded onto quantum devices by synthesizing and initializing a corresponding quantum state. Current techniques of arbitrary state synthesis, however, produce deep and complex quantum circuits, leading to low state fidelity and possible violations of decoherence constraints. In this work, we propose an improved methodology and optimized circuits for synthesizing any arbitrary quantum state from given classical data. Compared to existing methods, the proposed methodology results in circuits with lower gate count, lower circuit depth, and high state fidelity. The proposed methods are evaluated by simulation in MATLAB and IBM qasm, and realistic implementation on an IBM quantum device. The experimental results show a reduction in gate count and circuit depth by a factor of two over existing methods.
For practical usage of quantum systems in solving real-world problems, large amounts of classical data are required to be transferred/encoded to the quantum domain. Arbitrary classical data is usually encoded onto quantum devices by synthesizing and initializing a corresponding quantum state. Current techniques of arbitrary state synthesis, however, produce deep and complex quantum circuits, leading to low state fidelity and possible violations of decoherence constraints. In this work, we propose an improved methodology and optimized circuits for synthesizing any arbitrary quantum state from given classical data. Compared to existing methods, the proposed methodology results in circuits with lower gate count, lower circuit depth, and high state fidelity. The proposed methods are evaluated by simulation in MATLAB and IBM qasm, and realistic implementation on an IBM quantum device. The experimental results show a reduction in gate count and circuit depth by a factor of two over existing methods.
The current phase of quantum computing is in the Noisy Intermediate-Scale Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much noisier than single-qubit gates, so it is essential to minimize their count. Quantum circuit synthesis is a process of decomposing an arbitrary unitary into a sequence of quantum gates, and can be used as an optimization tool to produce shorter circuits to improve overall circuit fidelity. However, the time-to-solution of synthesis grows exponentially with the number of qubits. As a result, synthesis is intractable for circuits on a large qubit scale. In this paper, we propose a hierarchical, block-by-block optimization framework, QGo, for quantum circuit optimization. Our approach allows an exponential cost optimization to scale to large circuits. QGo uses a combination of partitioning and synthesis: 1) partition the circuit into a sequence of independent circuit blocks; 2) re-generate and optimize each block using quantum synthesis; and 3) re-compose the final circuit by stitching all the blocks together. We perform our analysis and show the fidelity improvements in three different regimes: small-size circuits on real devices, medium-size circuits on noise simulations, and large-size circuits on analytical models. Using a set of NISQ benchmarks, we show that QGo can reduce the number of CNOT gates by 29.9% on average and up to 50% when compared with industrial compilers such as t|ket>. When executed on the IBM Athens system, shorter depth leads to higher circuit fidelity. We also demonstrate the scalability of our QGo technique to optimize circuits of 60+ qubits. Our technique is the first demonstration of successfully employing and scaling synthesis in the compilation toolchain for large circuits. Overall, our approach is robust for direct incorporation in production compiler toolchains.
Quantum circuit synthesis, the process of mapping logical operations onto a quantum hardware architecture, presents a significant bottleneck in the development of practical quantum computers. Traditional methods often suffer from exponential computational complexity, rendering them unsuitable for circuits of even moderate size. This work introduces a novel approach to quantum circuit synthesis leveraging topological optimization, a technique rooted in condensed matter physics. We represent quantum circuits as topological phases on a graph, where gate operations are encoded as transitions between these phases. An iterative optimization process then refines the graph structure, minimizing circuit complexity (represented as energy) while maintaining the desired quantum operations. The core of our method lies in the application of gradient-based optimization algorithms to this topological graph, driving the system towards a low-energy state representing an optimal quantum circuit. Preliminary results demonstrate the potential of this approach to significantly reduce gate count and improve fidelity compared to conventional synthesis methods. The proposed framework offers a scalable solution to the challenges inherent in quantum circuit design, paving the way for more efficient and reliable quantum computation.
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.
Quantum algorithms will likely play a key role in future high-performance-computing (HPC) environments. These algorithms are typically expressed as quantum circuits composed of arbitrary gates or as unitary matrices. Executing these on physical devices, however, requires translation to device-compatible circuits, in a process called quantum compilation or circuit synthesis, since these devices support a limited number of native gates. Moreover, these devices typically have specific qubit topologies, which constrain how and where gates can be applied. Consequently, logical qubits in input circuits and unitaries may need to be mapped to and routed between physical qubits. Furthermore, current Noisy Intermediate-Scale Quantum (NISQ) devices present additional constraints. They are vulnerable to errors during gate application and their short decoherence times lead to qubits rapidly succumbing to accumulated noise and possibly corrupting computations. Therefore, circuits synthesized for NISQ devices need to minimize gates and execution times. The problem of synthesizing device-compatible circuits, while optimizing for low gate count and short execution times, can be shown to be computationally intractable using analytical methods. Therefore, interest has grown towards heuristics-based synthesis techniques, which are able to produce approximations of the desired algorithm, while optimizing depth and gate-count. In this work, we investigate using genetic algorithms (GA)—a proven gradient-free optimization technique based on natural selection—for circuit synthesis. In particular, we formulate the quantum synthesis problem as a multi-objective optimization (MOO) problem, with the objectives of minimizing the approximation error, number of multi-qubit gates, and circuit depth. We also employ fuzzy logic for runtime parameter adaptation of GA to enhance search efficiency and solution quality in our proposed method.
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to be optimized as much as possible. To this end, an algorithm's description first has to be synthesized using the device's gate library. In this paper, we consider the optimal synthesis of Clifford circuits---an important subclass of quantum circuits, with various applications. Such techniques are essential to establish lower bounds for (heuristic) synthesis methods and gauging their performance. Due to the huge search space, existing optimal techniques are limited to a maximum of six qubits. The contribution of this work is twofold: First, we propose an optimal synthesis method for Clifford circuits based on encoding the task as a satisfiability (SAT) problem and solving it using a SAT solver in conjunction with a binary search scheme. The resulting tool is demonstrated to synthesize optimal circuits for up to 26 qubits---more than four times as many as the current state of the art. Second, we experimentally show that the overhead introduced by state-of-the-art heuristics exceeds the lower bound by 27 % on average. The resulting tool is publicly available at https://github.com/cda-tum/qmap.
The current phase of quantum computing is in the Noisy Intermediate-Scale Quantum (NISQ) era. On NISQ devices, two-qubit gates such as CNOTs are much noisier than single-qubit gates, so it is essential to minimize their count. Quantum circuit synthesis is a process of decomposing an arbitrary unitary into a sequence of quantum gates, and can be used as an optimization tool to produce shorter circuits to improve overall circuit fidelity. However, the time-to-solution of synthesis grows exponentially with the number of qubits. As a result, synthesis is intractable for circuits on a large qubit scale.
In this paper, we propose a hierarchical, block-by-block optimization framework, QGo, for quantum circuit optimization. Our approach allows an exponential cost optimization to scale to large circuits. QGo uses a combination of partitioning and synthesis: 1) partition the circuit into a sequence of independent circuit blocks; 2) re-generate and optimize each block using quantum synthesis; and 3) re-compose the final circuit by stitching all the blocks together. We perform our analysis and show the fidelity improvements in three different regimes: small-size circuits on real devices, medium-size circuits on noise simulations, and large-size circuits on analytical models. Using a set of NISQ benchmarks, we show that QGo can reduce the number of CNOT gates by 29.9% on average and up to 50% when compared with industrial compilers such as t|ket>. When executed on the IBM Athens system, shorter depth leads to higher circuit fidelity. We also demonstrate the scalability of our QGo technique to optimize circuits of 60+ qubits. Our technique is the first demonstration of successfully employing and scaling synthesis in the compilation toolchain for large circuits. Overall, our approach is robust for direct incorporation in production compiler toolchains.