Bruno Schmitt’s research while affiliated with Integrated Laboratory Systems, Inc. and other places

... Like other QAOA approaches, the Hamiltonian unitary usually leads to huge circuit complexity after decomposition, making it challenging to deploy on NISQ devices. Typically, existing decomposition methods show exponential complexity to approximate the unitary [12], [43], and often exhibit high approximation error [46]. For example, trotter decomposition [36] approximates the unitary e −iβH d by dividing it into a series of small unitaries e −iβH d /N . ...

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Choco-Q: Commute Hamiltonian-based QAOA for Constrained Binary Optimization

... We cover these issues in Sections 6.2 and 6.3. Section 6.4 then describes how Asdf uses Tweedledum to synthesize QCircuit dialect code from classical circuit descriptions [40]. Section 6.5 concludes by describing optimizations we perform in the QCircuit dialect. ...

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ASDF: A Compiler for Qwerty, a Basis-Oriented Quantum Programming Language

... Due to their frequent utilization in quantum circuits, optimizing the overall cost of oracles has become a significant focus. Various synthesis and optimization methods for oracles have been proposed in recent years [1], [3], [4], [5]. In particular, oracle synthesis functionality has been integrated into quantum software platforms such as Qiskit [6] and Q# [7]. ...

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A Divide-And-Conquer Pebbling Strategy for Oracle Synthesis in Quantum Computing

... This AST is then converted to a classical logic network in the mockturtle library [52]. After running some classical optimizations provided by mockturtle, Asdf passes this classical circuit to tweedledum [40], which generates a Bennett embedding | ⟩ | ⟩ = | ⟩ | ⊕ ( )⟩ for the corresponding classical function [5,31,41]. The result is expressed in tweedledum Circuit IR, which we transpile to QCircuit IR. ...

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ASDF: A Compiler for Qwerty, a Basis-Oriented Quantum Programming Language

... [5,26,19,7,11,15,24,32]). Algorithms and heuristics for the token swapping problem have also undergone experimental evaluation [23,27]. ...

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Improved Hardness-of-Approximation for Token Swapping

... [78] and [23], as well as additional works such as Refs. [86,100,103]. Together, these describe software for everything from quantum compilation to mapping to verification. It is therefore important to emphasize that the goal of MustangQ is not to replace the many sophisticated quantum software design tools that already exist (especially those with thousands of users, such as Qiskit, PyTket, and Cirq), but rather to complement them. ...

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Automated Synthesis of Quantum Subcircuits

... The Boolean satisfiability (SAT) problem [55] asks whether there exists a solution that satisfies all constraints in a given set of Boolean constraints. This fundamental problem holds immense significance in computer science with applications spanning combinatorial optimization [25], software verification [57], probabilistic inference [10], mathematical conjecture proving [23], machine learning [28], and quantum computing [52,56]. While SAT is known to be NPcomplete, recent decades have witnessed remarkable advances in SAT solver technology [55] for both CDCL-based complete solvers [51,4] and heuristic-search incomplete solvers [50]. ...

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Thinking Out of the Box: Hybrid SAT Solving by Unconstrained Continuous Optimization

... For all these reasons, in the last decades several algorithms have been proposed for exact and heuristic minimization of ESOP forms [26], [28], [29], [30], [32], [36], with the aim of reducing the overall costs of their hardware realizations and software implementations. Heuristic methods focus on finding small (but not necessarily minimum) ESOP forms; they are fast, but only examine a subset of the possible search space. ...

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XOR-AND-XOR Logic Forms for Autosymmetric Functions and Applications to Quantum Computing

... For an arbitrary k-input single-target function, G(x 1 , . . . , x k ) an optimal ESOP form can be obtained employing techniques like [12] and then using (3) the corresponding ESOP forms for the auxiliary variable p realizing G or ¬G can be derived. Thus, quantum circuit interpretation of these ESOP-based SAT clauses for each auxiliary variable requires no more than one additional qubit and the implementation can be claimed optimal provided inexpensive ESOP form of G is employed. ...

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qSAT: Design of an Efficient Quantum Satisfiability Solver for Hardware Equivalence Checking

... From (12), we can conclude that the overall phase-depth ZD ESO P of the ESOP-based reversible circuit is less compared to the ZD Exact circuit on decomposition into fault-tolerant architecture as because of lesser literals [42]. Each MCT-gate can be linearly decomposed into fault-tolerant structure in linear-depth (4). ...

Reference:

Synthesis Techniques for Fault-tolerant Quantum Circuit Implementation using the Clifford+Z_N-group