Abstract The quantum approximate optimization algorithm (QAOA) is an approach for nearterm quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
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This content will become publicly available on June 6, 2024
Synthesizing QuantumCircuit Optimizers
Nearterm quantum computers are expected to work in an environment where each operation is noisy, with no error correction. Therefore, quantumcircuit optimizers are applied to minimize the number of noisy operations. Today, physicists are constantly experimenting with novel devices and architectures. For every new physical substrate and for every modification of a quantum computer, we need to modify or rewrite major pieces of the optimizer to run successful experiments. In this paper, we present QUESO, an efficient approach for automatically synthesizing a quantumcircuit optimizer for a given quantum device. For instance, in 1.2 minutes, QUESO can synthesize an optimizer with highprobability correctness guarantees for IBM computers that significantly outperforms leading compilers, such as IBM's Qiskit and TKET, on the majority (85%) of the circuits in a diverse benchmark suite. A number of theoretical and algorithmic insights underlie QUESO: (1) An algebraic approach for representing rewrite rules and their semantics. This facilitates reasoning about complex symbolic rewrite rules that are beyond the scope of existing techniques. (2) A fast approach for probabilistically verifying equivalence of quantum circuits by reducing the problem to a special form of polynomial identity testing . (3) A novel probabilistic data structure, called a polynomial identity filter (PIF), for efficiently synthesizing rewrite rules. (4) A beamsearchbased algorithm that efficiently applies the synthesized symbolic rewrite rules to optimize quantum circuits.
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 NSFPAR ID:
 10429347
 Date Published:
 Journal Name:
 Proceedings of the ACM on Programming Languages
 Volume:
 7
 Issue:
 PLDI
 ISSN:
 24751421
 Page Range / eLocation ID:
 835 to 859
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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