EQISA: Energy-efficient Quantum Instruction Set Architecture using Sparse Dictionary Learning

Abstract

The scalability of quantum computing in supporting sophisticated algorithms critically depends not only on qubit quality and error handling, but also on the efficiency of classical control, constrained by the cryogenic control bandwidth and energy budget. In this work, we address this challenge by investigating the algorithmic complexity of quantum circuits at the instruction set architecture (ISA) level. We introduce an energy-efficient quantum instruction set architecture (EQISA) that synthesizes quantum circuits in a discrete Solovay-Kitaev basis of fixed depth and encodes instruction streams using a sparse dictionary learned from decomposing a set of Haar-random unitaries, followed by entropy-optimal Huffman coding and an additional lossless bzip2 compression stage. This approach is evaluated on benchmark quantum circuits demonstrating over 60% compression of quantum instruction streams across system sizes, enabling proportional reductions in classical control energy and communication overhead without loss of computational fidelity. Beyond compression, EQISA facilitates the discovery of higher-level composable abstractions in quantum circuits and provides estimates of quantum algorithmic complexity. These findings position EQISA as an impactful direction for improving the energy efficiency and scalability of quantum control architectures.

Figures (19)

• Figure 1: Overview of the proposed EQISA. The workflow is as follows: (i) A universal gate set (say, [$H$, $T$, $T^\dagger$], depicted in red, green, blue) is used to generate the Solovay-Kitaev basis of composite gates up to a specific depth (say, 3) based on required decomposition accuracy. (ii) Equivalent elements and identities are pruned (denoted by $\times$). (iii) The usage frequency for the remaining elements are determined by decomposing a set of Haar-random unitaries. (iv) High-frequency elements are used to construct a Huffman code. The original gate set is always included to decompose elements not included. (v) The EQISA thus constructed is deployed in the quantum compilation and control pipeline. The unitary of a quantum algorithm is decomposed into the basis elements. Elements not in the sparse dictionary are encoded in the original gate set. The bit sequence encodes the unitary and can be further compressed using bzip2. (vi) This stream is sent to the cryo-FPGA that decompresses and decodes the EQISA and dispatches the corresponding control signals for the quantum processor.
• Figure 2: Comparison of classical and quantum computation across (1) computability, (2) resource efficiency, and (3) pragmatic deployment. Quantum resource advantages are the differentiating factor in achieving provable quantum advantage, driving quantum accelerator research and development.
• Figure 3: Definitions of metrics that involve trade-offs between multiple resources - time, space, fidelity, program size, and energy.
• Figure 4: Overview of the system design of a quantum accelerator with classical control and various software modules required for research and development is shown on the left. The different abstraction layers for full-stack quantum computing are shown on the right. This research pertains to the quantum instruction set (indicated in a dotted outline).
• Figure 5: Flowchart of the Solovay-Kitaev decomposition algorithm for 1-qubit unitary quantum operator $U$ and recursion depth $n$. It returns the $\epsilon_n$ approximation to the target unitary $U$ computed through the function call at the $n-1$ degree of recursion, and returns the $\epsilon_0$ approximation in the base case.