Abstract Existing quantum compilers focus on mapping a logical quantum circuit to a quantum device and its native quantum gates. Only simple circuit identities are used to optimize the quantum circuit during the compilation process. This approach misses more complex circuit identities, which could be used to optimize the quantum circuit further. We propose Quanto, the first quantum optimizer that automatically generates circuit identities. Quanto takes as input a gate set and generates provably correct circuit identities for the gate set. Quanto’s automatic generation of circuit identities includes single-qubit and two-qubit gates, which leads to a new database of circuit identities, some of which are novel to the best of our knowledge. In addition to the generation of new circuit identities, Quanto’s optimizer applies such circuit identities to quantum circuits and finds optimized quantum circuits that have not been discovered by other quantum compilers, including IBM Qiskit and Cambridge Quantum Computing Tket. Quanto’s database of circuit identities could be applied to improve existing quantum compilers and Quanto can be used to generate identity databases for new gate sets.
Abstract Existing quantum compilers focus on mapping a logical quantum circuit to a quantum device and its native quantum gates. Only simple circuit identities are used to optimize the quantum circuit during the compilation process. This approach misses more complex circuit identities, which could be used to optimize the quantum circuit further. We propose Quanto, the first quantum optimizer that automatically generates circuit identities. Quanto takes as input a gate set and generates provably correct circuit identities for the gate set. Quanto’s automatic generation of circuit identities includes single-qubit and two-qubit gates, which leads to a new database of circuit identities, some of which are novel to the best of our knowledge. In addition to the generation of new circuit identities, Quanto’s optimizer applies such circuit identities to quantum circuits and finds optimized quantum circuits that have not been discovered by other quantum compilers, including IBM Qiskit and Cambridge Quantum Computing Tket. Quanto’s database of circuit identities could be applied to improve existing quantum compilers and Quanto can be used to generate identity databases for new gate sets.
Near-term quantum computers are expected to work in an environment where each operation is noisy, with no error correction. Therefore, quantum-circuit 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 quantum-circuit optimizer for a given quantum device. For instance, in 1.2 minutes, QUESO can synthesize an optimizer with high-probability 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 beam-search-based algorithm that efficiently applies the synthesized symbolic rewrite rules to optimize quantum circuits.
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices, which use different gate sets, and can miss optimizations that are hard to find manually. We propose Quartz, a quantum circuit superoptimizer that automatically generates and verifies circuit transformations for arbitrary quantum gate sets. For a given gate set, Quartz generates candidate circuit transformations by systematically exploring small circuits and verifies the discovered transformations using an automated theorem prover. To optimize a quantum circuit, Quartz uses a cost-based backtracking search that applies the verified transformations to the circuit. Our evaluation on three popular gate sets shows that Quartz can effectively generate and verify transformations for different gate sets. The generated transformations cover manually designed transformations used by existing optimizers and also include new transformations. Quartz is therefore able to optimize a broad range of circuits for diverse gate sets, outperforming or matching the performance of hand-tuned circuit optimizers.
Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices, which use different gate sets, and can miss optimizations that are hard to find manually. We propose Quartz, a quantum circuit superoptimizer that automatically generates and verifies circuit transformations for arbitrary quantum gate sets. For a given gate set, Quartz generates candidate circuit transformations by systematically exploring small circuits and verifies the discovered transformations using an automated theorem prover. To optimize a quantum circuit, Quartz uses a cost-based backtracking search that applies the verified transformations to the circuit. Our evaluation on three popular gate sets shows that Quartz can effectively generate and verify transformations for different gate sets. The generated transformations cover manually designed transformations used by existing optimizers and also include new transformations. Quartz is therefore able to optimize a broad range of circuits for diverse gate sets, outperforming or matching the performance of hand-tuned circuit optimizers.
Quantum circuit compilation is a multi-stage process that translates a high-level quantum circuit representation into a sequence of quantum gates that can be directly executed by a quantum machine. One of the core steps in quantum compilation is mapping, a procedure that transforms a quantum circuit into a semantically equivalent circuit while inserting additional gates to comply with the architectural constraints of the underlying quantum hardware. Current mapping techniques exhibit significant performance degradation—in terms of circuit depth and gate count—when applied to large-scale circuits containing hundreds of thousands of gates or more. In this work, we propose a novel methodology to enhance quantum compiler capabilities by adapting general principles from classical Electronic Design Automation. We model the quantum hardware as being composed of standard cells, onto which portions of the circuit are mapped using a floorplanning-based technique. This contrasts with current state-of-the-art solutions, which perform mapping at the gate level without considering any form of hierarchical abstraction. We use the ChaCha20 stream cipher as a running example to validate and explain our strategy. We evaluate our methodology using two well-known, industrial-grade quantum compilers: IBM Qiskit and Quantinuum TKET. Compared to these compilers, our approach achieves an average circuit depth reduction of 59.78% and 68.85%, respectively, and a gate count reduction of 4.07 % and 6.20 %, respectively. These results are obtained across a large set of randomly generated quantum circuit descriptions in the range of millions of gates, with varying input and output connectivity for each block in the circuit.
Parameterized circuit instantiation is a common technique encountered in the generation of circuits for a large class of hybrid quantum-classical algorithms. Despite being supported by popular quantum compilation infrastructures such as IBM Qiskit and Google Cirq, instantiation has not been extensively considered in the context of circuit compilation and optimization pipelines. In this work, we describe algorithms to apply instantiation during two common compilation steps: circuit optimization and gate-set transpilation. When placed in a compilation workflow, our circuit optimization algorithm produces circuits with an average of 13% fewer gates than other optimizing compilers. Our gate-set transpilation algorithm can target any gate-set, even sets with multiple two-qubit gates, and produces circuits with an average of 12% fewer two-qubit gates than other compilers. Overall, we show how instantiation can be incorporated into a compiler workflow to improve circuit quality and enhance portability, all while maintaining a reasonably low compile time overhead.
Abstract Quantum circuit optimizers use rewrite rules from circuit equivalences, yet prior work has identified thousands of such identities, creating substantial challenges for their storage, management, and effective application. For many widely used unitary gate sets, including Clifford+T, this apparent complexity is largely redundant, raising a fundamental question: How many quantum circuit identities are actually needed to generate all others? In this work, we provide strong evidence that a small pruned set of identities suffices to generate all circuit equivalences of bounded depth. Surprisingly, for circuits on up to nine qubits in which each side of an equality has depth at most ten, fewer than twenty identities are sufficient to derive all others, and for circuits on up to five qubits with depth at most ten, only 17 rules–each involving at most three qubits–are enough. These results enable significantly more compact and efficient rewriting systems for quantum compiler optimization and reveal underlying algebraic structure in common gate sets, showing that the vast majority of known circuit identities are consequences of a small foundational basis.