In this paper we consider the compilation of quantum state permutations into quantum gates for physical quantum computers. A sequence of generic single-target gates, which realize the input permutation, are extracted using a decomposition based reversible logic synthesis algorithm. We present a compilation algorithm that translates single-target gates into a quantum circuit composed of the elementary quantum gate sets that are supported by IBM's 5-qubit and 16-qubit, and Rigetti's 8-qubit and 19-qubit superconducting transmon QPUs. Compared to generic state-of-the-art compilation techniques, our technique improves gate volume and gate depth by up to 59% and 53%, respectively.
In this paper we consider the compilation of quantum state permutations into quantum gates for physical quantum computers. A sequence of generic single-target gates, which realize the input permutation, are extracted using a decomposition based reversible logic synthesis algorithm. We present a compilation algorithm that translates single-target gates into a quantum circuit composed of the elementary quantum gate sets that are supported by IBM's 5-qubit and 16-qubit, and Rigetti's 8-qubit and 19-qubit superconducting transmon QPUs. Compared to generic state-of-the-art compilation techniques, our technique improves gate volume and gate depth by up to 59% and 53%, respectively.
Abstract As quantum processors grow in scale and reliability, the need for efficient quantum gate decomposition of circuits to a set of specific available gates, becomes ever more critical. The decomposition of a particular algorithm into a sequence of these available gates is not unique. Thus, the fidelity of an algorithm’s implementation can be increased by choosing an optimized decomposition. This is true both for noisy intermediate-scale quantum platforms as well as for implementation of quantum error correction schemes. Here we present a compilation scheme which implements a general-circuit decomposition to a sequence of Ising-type, long-range, multi-qubit (MQ) entangling gates, that are separated by layers of single qubit rotations. We use trapped ions as an example in which MQ gates naturally arise, yet any system that has connectivity beyond nearest-neighbors may gain from our approach. We evaluate our methods using the quantum volume (QV) test over N qubits. In this context, our method replaces 3 N 2 / 2 two-qubit gates with 2 N + 1 MQ gates. Furthermore, our method minimizes the magnitude of the entanglement phases, which typically enables an improved implementation fidelity, by using weaker driving fields or faster realizations. We numerically test our compilation and show that, compared to conventional realizations with sequential two-qubit gates, our compilations improves the logarithm of QV by 20% to 25%.
We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic with a non-scalable, yet exact, synthesis. Our algorithms are applicable to generic connectivity constraints, scale favorably, and achieve close-to-optimal performance in many cases. We demonstrate the utility of these algorithms by optimizing the compilation of Quantum Volume circuits, and to disprove an old conjecture on reversals being the hardest permutation on a path.
Abstract Implementing quantum algorithms on realistic devices requires translating high-level global operations into sequences of hardware-native logic gates, a process known as quantum compiling. Physical limitations, such as constraints in connectivity and gate alphabets, often result in unacceptable implementation costs. To enable successful near-term applications, it is crucial to optimize compilation by exploiting the capabilities of existing hardware. Here we implement a resource-efficient construction for a quantum version of AND logic that can reduce the compilation overhead, enabling the execution of key quantum circuits. On a high-scalability superconducting quantum processor, we demonstrate low-depth synthesis of high-fidelity generalized Toffoli gates with up to 8 qubits and Grover’s search algorithm in a search space of up to 64 entries. Our experimental demonstration illustrates a scalable and widely applicable approach to implementing quantum algorithms, bringing more meaningful quantum applications on noisy devices within reach.
Reversible computation is an emerging technology that has gained significant attention due to its critical role in quantum circuit synthesis and low-power design. This paper introduces a transformation-based method for exact synthesis of reversible circuits. The proposed approach utilizes a novel adaptation of the Quine-McCluskey algorithm to eliminate input-output discrepancies in the truth table, transforming the permutation matrix into an identity matrix. Furthermore, a novel search space reduction technique is presented which, combined with the primary method, enables the synthesis algorithm to handle high-input reversible functions. This approach combines the influence of multiple control qubits on a target qubit, evaluating their collective impact. This aggregation can decrease the control qubit count within quantum gates. Consequently, it proves beneficial for applications like surface code error correction architectures as well as current Noisy Intermediate-Scale Quantum (NISQ) hardwares. Experimental results demonstrate significant improvements over the state-of-the-art exact synthesis methods, achieving up to 99% improvements in terms of the number of levels of T-gates.
We propose a scalable, hierarchical qubit mapping and routing algorithm that harnesses the power of circuit synthesis. First, we decompose large circuits into subcircuits small enough to be directly resynthesized. For each block, we pre-synthesize them for all permutations of its input and output qubits. Following this offline step, we employ a permutation-aware, block-based generalization of the popular SABRE mapping algorithm. This mapping step stitches together blocks by choosing an input-output permutation that minimizes intrablock gate count and required inter-block communication (SWAP and bridge gates). Our approach has a twofold advantage: 1) circuit synthesis may eliminate more two-qubit gates than other optimizing compilers; 2) considering all permutations of input and output qubits eliminates communication operations transparently. In contrast, other mapping algorithms can only introduce communication operations. We show that we can produce better-quality circuits than commercial compilers: shorter by up to 68% (18% on average) fewer gates than Qiskit, up to 36% (9% on average) fewer gates than Tket. We outperform BQSkit, a permutation-unaware, synthesis-based compiler, by up to 67% (21% on average) fewer gates. We also exceed experimental optimal mappers such as OLSQ in quality (10.7% shorter circuits) and time to solution. Our scalable, heuristic approach can be seamlessly integrated into any quantum circuit compiler or optimization infrastructure, and it applies well to any qubit technology, such as superconducting and trapped ions.
Advanced simulations and calculations on quantum computers require high-fidelity implementations of quantum operations. The universal gateset approach builds complex unitaries from a small set of primitive gates, often resulting in a long gate sequence, which is typically a leading factor in the total accumulated error. Compiling a complex unitary for processors with higher-dimensional logical elements, such as qutrits, exacerbates the accumulated error per unitary, since an even longer gate sequence is required. Optimal control methods promise time- and resource-efficient compact gate sequences and, therefore, higher fidelity. These methods generate pulses that can directly implement any complex unitary on a quantum device. In this work, we demonstrate that any arbitrary qubit and qutrit gate can be realized with high fidelity, which can significantly reduce the length of a gate sequence. We generate and test pulses for a large set of randomly selected arbitrary unitaries on several quantum processing units (QPUs): the Lawrence Livermore National Laboratory Quantum Device and Integration Testbed's (QuDIT's) standard QPU and three of Rigetti's QPUs: Ankaa-2, Ankaa-9Q-1, and Aspen-M-3. On the QuDIT platform's standard QPU, the average fidelity of random qutrit gates is $97.9\ifmmode\pm\else\textpm\fi{}0.5\mathrm{%}$ measured with conventional QPT and $98.8\ifmmode\pm\else\textpm\fi{}0.6\mathrm{%}$ from QPT with gate folding. Rigetti's Ankaa-2 achieves random qubit gates with an average fidelity of $98.4\ifmmode\pm\else\textpm\fi{}0.5\mathrm{%}$ (conventional QPT) and $99.7\ifmmode\pm\else\textpm\fi{}0.1\mathrm{%}$ (QPT with gate folding). On Ankaa-9Q-1 and Aspen-M-3, the average fidelities with conventional qubit QPT measurements were higher than 99% (see Appendix). We show that optimal control gates are robust to drift for at least 3 h and that the same calibration parameters can be used for all implemented gates. Our work promises that the calibration overheads for optimal control gates can be made small enough to enable efficient quantum circuits based on this technique.