Quantum state preparation initializes the quantum registers and is essential for running quantum algorithms. Designing state preparation circuits that entangle qubits efficiently with fewer two-qubit gates enhances accuracy and alleviates coupling constraints on devices. Existing methods synthesize an initial circuit and leverage compilers to reduce the circuit's gate count while preserving the unitary equivalency. In this study, we identify numerous conditions within the quantum circuit where breaking local unitary equivalences does not alter the overall outcome of the state preparation (i.e., don't cares). We introduce a peephole optimization algorithm that identifies such unitaries for replacement in the original circuit. Exploiting these don't care conditions, our algorithm achieves a 36% reduction in the number of two-qubit gates compared to prior methods.
Quantum state preparation initializes the quantum registers and is essential for running quantum algorithms. Designing state preparation circuits that entangle qubits efficiently with fewer two-qubit gates enhances accuracy and alleviates coupling constraints on devices. Existing methods synthesize an initial circuit and leverage compilers to reduce the circuit's gate count while preserving the unitary equivalency. In this study, we identify numerous conditions within the quantum circuit where breaking local unitary equivalences does not alter the overall outcome of the state preparation (i.e., don't cares). We introduce a peephole optimization algorithm that identifies such unitaries for replacement in the original circuit. Exploiting these don't care conditions, our algorithm achieves a 36% reduction in the number of two-qubit gates compared to prior methods.
Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most automated optimization techniques focus on transforming circuits into equivalent ones that implement the same unitary, we show that substantial new opportunities for resource reduction can be achieved by (1) allowing approximate local transformations and (2) employing mixed quantum channels to approximate pure circuits. Our novel automated protocol for approximate circuit rewriting is a refined evolution of automated optimization techniques based on the ZX-calculus, where we add a greedy strategy that selectively replaces ZX-diagrams with small phase angles with stochastic mixtures of the identity and carefully chosen over-rotations, which are designed to reduce the overall gate count in expectation while staying within a strict error budget. This approach yields modest two-qubit gate count reduction in random quantum circuits, and achieves a substantial reduction in structured circuits such as the quantum Fourier transform. Fundamentally, our protocol converts experimental noise due to gate applications into deliberately engineered random noise, outperforming many other approximation methods on average. These results highlight the potential of mixed-channel approximations to enhance future quantum circuit performance, suggesting new directions for resource-aware automated quantum compilation beyond pure unitary channels.
As in classical computing, compilers play an important role in quantum computing. Quantum processors typically support a limited set of primitive operations or quantum gates and have certain hardware-related limitations. A quantum compiler is responsible for adapting a quantum program to these constraint environments and decomposing quantum gates into a sequence of the primitive ones. During the compilation process, it is also critical for the compiler to optimize the quantum circuits in order to reduce the noise in the computation results. Since the noise is introduced by operations and decoherence, reducing the gate count is the key for improving performance. In this paper, we propose a novel quantum compiler optimization, named relaxed peephole optimization (RPO) for quantum computers. RPO leverages the single-qubit state information that can be determined statically by the compiler. We define that a qubit is in a basis state when, at a given point in time, its state is either in the X-, Y-, or Z-basis (|+) / |-〉, |L〉 / R〉 and 10〉 / |1〉). When basis qubits are used as inputs to quantum gates, there exist opportunities for strength reduction, which replaces quantum operations with equivalent but less expensive ones. Compared to the existing peephole optimization for quantum programs, the difference is that our proposed optimization does not require an identical unitary matrix, thereby named `relaxed' peephole optimization. We also extend our approach to optimize the quantum gates when some input qubits are in known pure states. Both optimizations, namely the Quantum Basis-state Optimization (QBO) and the Quantum Pure-state Optimization (QPO), are implemented in the IBM's Qiskit transpiler. Our experimental results show that our proposed optimization pass is fast and effective. The circuits optimized with our compiler optimizations obtain up to 18.0% (11.7% on average) fewer CNOT gates and up to 8.2% (7.1% on average) lower transpilation time than that of the most aggressive optimization level in the Qiskit compiler. When running on real quantum computers, the success rates of 3-qubit quantum phase estimation algorithm improve by 2.30X due to the reduced gate counts.
Abstract While the capabilities of quantum hardware have significantly advanced in recent years, executing quantum algorithms as quantum circuits at the lowest possible cost remains crucial, regardless of the hardware progress. We are developing a quantum-state-dependent circuit optimizer called Aqcel . Our guiding principle, implemented as the Aqcel optimization protocol, is to optimize quantum circuits by measuring the states of the control qubits to identify and eliminate unnecessary control operations. In this paper, we introduce two key improvements: the state label manager that reduces unnecessary state measurements and the C X -pair removal process that eliminates redundant gate pairs. These enhancements significantly reduce the number of two-qubit gates, improving the fidelity of quantum circuits executed on quantum hardware. To demonstrate the effectiveness of our method, we apply Aqcel to quantum circuits for the quantum parton shower algorithm. Experimental results using the IBM quantum computer show a substantial reduction in gate counts and an improvement in fidelity compared to the conventional optimization technique as well as the original Aqcel protocol. These results demonstrate that fixed-initial-state information can enable state-dependent optimizations that are complementary to general-purpose, unitary-equivalence-preserving circuit optimizers.
Near-term quantum computers have significant error rates and short coherence times, so compilation of circuits to be as short as possible is essential. Two types of compilation problems are typically considered: circuits to prepare a given state from a fixed input state, called “state preparation”; and circuits to implement a given unitary operation, for example by “unitary synthesis”. In this paper we solve a more general problem: the transformation of a set of m states to another set ofmstates, which we call “multi-state preparation”. State preparation and unitary synthesis are special cases; for state preparation, m=1, while for unitary synthesis, m is the dimension of the full Hilbert space. We generate and optimize circuits for multi-state preparation numerically. In cases where a top-down approach based on matrix decompositions is also possible, our method finds circuits with substantially (up to 40 %) fewer two-qubit gates. We discuss possible applications, including efficient preparation of macroscopic superposition (“cat”) states and synthesis of quantum channels.
Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more efficient and accurate quantum computations. However, the attainment of optimal solutions is hindered by the complexity of modeling superposition and entanglement. In this paper, we propose an effective state preparation algorithm using an exact CNOT synthesis formulation. Our method represents a milestone as the first design automation algorithm to surpass manual design, reducing the best CNOT count to prepare a Dicke state by 2x. For general states with up to 20 qubits, our method reduces the CNOT count by 9% and 32% for dense and sparse states, respectively, on average, compared to the latest algorithms.
We perform optimal-control-theory calculations to determine the minimum number of two-qubit controlled-not (cnot) gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we determine the maximum achievable fidelity as a function of quantum circuit size. This information allows us to identify the minimum circuit size needed for a specific target operation and enumerate the different gate configurations that allow a perfect implementation of the operation. We find that there are a large number of configurations that all produce the desired result, even at the minimum number of gates. We also show that the number of entangling gates can be reduced if we use multiqubit entangling gates instead of two-qubit cnot gates, as one might expect based on parameter counting calculations. In addition to treating the general case of arbitrary target states or unitary operators, we apply the numerical approach to the special case of synthesizing the multiqubit Toffoli gate. This approach can be used to investigate any other specific few-qubit task and provides insight into the tightness of different bounds in the literature.