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Register a new userLEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach
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While showing great promise, circuit synthesis techniques that combine numerical optimization with search over circuit structures face scalability challenges due to large number of parameters, exponential search spaces, and complex objective functions. The LEAP algorithm improves scaling across these dimensions using iterative circuit synthesis, incremental reoptimization, dimensionality reduction, and improved numerical optimization. LEAP draws on the design of the optimal synthesis algorithm QSearch by extending it with an incremental approach to determine constant prefix solutions for a circuit. By narrowing the search space, LEAP improves scalability from four to six qubit circuits. LEAP was evaluated with known quantum circuits such as QFT and physical simulation circuits like the VQE, TFIM and QITE. LEAP is able to compile four qubit unitaries up to $59times$ faster than QSearch and five and six qubit unitaries with up to $1.2times$ fewer CNOTs compared to the advanced QFAST package. LEAP is able to reduce the CNOT count by up to $48times$, or $11times$ on average, compared to the IBM Qiskit compiler. Although employing heuristics, LEAP has generated optimal depth circuits for all test cases where a solution is known a priori. The techniques introduced by LEAP are applicable to other numerical optimization based synthesis approaches.
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Real-world multiobjective optimization problems usually involve conflicting objectives that change over time, which requires the optimization algorithms to quickly track the Pareto optimal front (POF) when the environment changes. In recent years, evolutionary algorithms based on prediction models have been considered promising. However, most existing approaches only make predictions based on the linear correlation between a finite number of optimal solutions in two or three previous environments. These incomplete information extraction strategies may lead to low prediction accuracy in some instances. In this paper, a novel prediction algorithm based on incremental support vector machine (ISVM) is proposed, called ISVM-DMOEA. We treat the solving of dynamic multiobjective optimization problems (DMOPs) as an online learning process, using the continuously obtained optimal solution to update an incremental support vector machine without discarding the solution information at earlier time. ISVM is then used to filter random solutions and generate an initial population for the next moment. To overcome the obstacle of insufficient training samples, a synthetic minority oversampling strategy is implemented before the training of ISVM. The advantage of this approach is that the nonlinear correlation between solutions can be explored online by ISVM, and the information contained in all historical optimal solutions can be exploited to a greater extent. The experimental results and comparison with chosen state-of-the-art algorithms demonstrate that the proposed algorithm can effectively tackle dynamic multiobjective optimization problems.
Reconfigurable Intelligent Surfaces (RISs), comprising large numbers of low-cost and passive metamaterials with tunable reflection properties, have been recently proposed as an enabler for programmable radio propagation environments. However, the role of the channel conditions near the RISs on their optimizability has not been analyzed adequately. In this paper, we present an asymptotic closed-form expression for the mutual information of a multi-antenna transmitter-receiver pair in the presence of multiple RISs, in the large-antenna limit, using the random matrix and replica theories. Under mild assumptions, asymptotic expressions for the eigenvalues and the eigenvectors of the channel covariance matrices are derived. We find that, when the channel close to an RIS is correlated, for instance due to small angle spread, the communication link benefits significantly from the RIS optimization, resulting in gains that are surprisingly higher than the nearly uncorrelated case. Furthermore, when the desired reflection from the RIS departs significantly from geometrical optics, the surface can be optimized to provide robust communication links. Building on the properties of the eigenvectors of the covariance matrices, we are able to find the optimal response of the RISs in closed form, bypassing the need for brute-force optimization.
We present a quantum synthesis algorithm designed to produce short circuits and to scale well in practice. The main contribution is a novel representation of circuits able to encode placement and topology using generic gates, which allows the QFAST algorithm to replace expensive searches over circuit structures with few steps of numerical optimization. When compared against optimal depth, search based state-of-the-art techniques, QFAST produces comparable results: 1.19x longer circuits up to four qubits, with an increase in compilation speed of 3.6x. In addition, QFAST scales up to seven qubits. When compared with the state-of-the-art rule based decomposition techniques in Qiskit, QFAST produces circuits shorter by up to two orders of magnitude (331x), albeit 5.6x slower. We also demonstrate the composability with other techniques and the tunability of our formulation in terms of circuit depth and running time.
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.
Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set. These approximation algorithms find asymptotically optimal approximations in probabilistic polynomial time, in some cases even finding the optimal solution in probabilistic polynomial time given access to an oracle for factoring integers. In this paper, we present a common mathematical structure underlying all results related to the exact synthesis of qubit unitaries known to date, including Clifford+T, Clifford-cyclotomic and V-basis gate sets, as well as gates sets induced by the braiding of Fibonacci anyons in topological quantum computing. The framework presented here also provides a means to answer questions related to the exact synthesis of unitaries for wide classes of other gate sets, such as Clifford+T+V and SU(2) level k anyons.
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