Optimization Of Quantum Circuits Research Articles

Quarl: A Learning-Based Quantum Circuit Optimizer

Optimizing quantum circuits is challenging due to the very large search space of functionally equivalent circuits and the necessity of applying transformations that temporarily decrease performance to achieve a final performance improvement. This paper presents Quarl, a learning-based quantum circuit optimizer. Applying reinforcement learning (RL) to quantum circuit optimization raises two main challenges: the large and varying action space and the non-uniform state representation. Quarl addresses these issues with a novel neural architecture and RL-training procedure. Our neural architecture decomposes the action space into two parts and leverages graph neural networks in its state representation, both of which are guided by the intuition that optimization decisions can be mostly guided by local reasoning while allowing global circuit-wide reasoning. Our evaluation shows that Quarl significantly outperforms existing circuit optimizers on almost all benchmark circuits. Surprisingly, Quarl can learn to perform rotation merging—a complex, non-local circuit optimization implemented as a separate pass in existing optimizers.

New SAT-based Model for Quantum Circuit Decision Problem: Searching for Low-Cost Quantum Implementation

In recent years, quantum technology has been rapidly developed. As security analyses for symmetric ciphers continue to emerge, many require an evaluation of the resources needed for the quantum circuit implementation of the encryption algorithm. In this regard, we propose the quantum circuit decision problem, which requires us to determine whether there exists a quantum circuit for a given permutation f using M ancilla qubits and no more than K quantum gates within the circuit depth D. Firstly, we investigate heuristic algorithms and classical SAT-based models in previous works, revealing their limitations in solving the problem. Hence, we innovatively propose an improved SAT-based model incorporating three metrics of quantum circuits. The model enables us to find the optimal quantum circuit of an arbitrary 3 or 4-bit S-box under a given optimization goal based on SAT solvers, which has proved the optimality of circuits constructed by the tool, LIGHTER-R. Then, by combining different criteria in the model, we find more compact quantum circuit implementations of S-boxes such as RECTANGLE and GIFT. For GIFT S-box, our model provides the optimal quantum circuit that only requires 8 gates with a depth of 31. Furthermore, our model can be generalized to linear layers and improve the previous SAT-based model proposed by Huang et al. in ASIACRYPT 2022 by adding the criteria on the number of qubits and the circuit depth.

Optimized quantum circuit implementation of SATURNIN for Grover’s algorithm

Optimized quantum circuit implementation of SATURNIN for Grover’s algorithm

Riemannian quantum circuit optimization for Hamiltonian simulation

Hamiltonian simulation, i.e. simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful approximation can lead to relatively deep circuits. Here we start from the insight that for translation invariant systems, the gates in such circuit topologies can be further optimized on classical computers to decrease the circuit depth and/or increase the accuracy. We employ tensor network techniques and devise a method based on the Riemannian trust-region algorithm on the unitary matrix manifold for this purpose. For the Ising and Heisenberg models on a one-dimensional lattice, we achieve orders of magnitude accuracy improvements compared to fourth-order splitting methods. The optimized circuits could also be of practical use for the time-evolving block decimation algorithm.

On the optimality of quantum circuit initial mapping using reinforcement learning

Quantum circuit optimization is an inevitable task with the current noisy quantum backends. This task is considered non-trivial due to the varying circuits’ complexities in addition to hardware-specific noise, topology, and limited connectivity. The currently available methods either rely on heuristics for circuit optimization tasks or reinforcement learning with complex unscalable neural networks such as transformers. In this paper, we are concerned with optimizing the initial logical-to-physical mapping selection. Specifically, we investigate whether a reinforcement learning agent with simple scalable neural network is capable of finding a near-optimal logical-to-physical mapping, that would decrease as much as possible additional CNOT gates, only from a fixed-length feature vector. To answer this question, we train a Maskable Proximal Policy Optimization agent to progressively take steps towards a near-optimal logical-to-physical mapping on a 20-qubit hardware architecture. Our results show that our agent coupled with a simple routing evaluation is capable of outperforming other available reinforcement learning and heuristics approaches on 12 out of 19 test benchmarks, achieving geometric mean improvements of 2.2% and 15% over the best available related work and two heuristics approaches, respectively. Additionally, our neural network model scales linearly as the number of qubits increases.

Quantum Circuit Optimization of Arithmetic Circuits using ZX Calculus

Quantum computing is an emerging technology in which quantum mechanical properties are suitably utilized to perform certain compute-intensive operations faster than classical computers. Quantum algorithms are designed as a combination of quantum circuits that each require a large number of quantum gates, which is a challenge considering the limited number of qubit resources available in quantum computing systems. Our work proposes a technique to optimize quantum arithmetic algorithms by reducing the hardware resources and the number of qubits based on ZX calculus. We have utilized ZX calculus rewrite rules for the optimization of fault-tolerant quantum multiplier circuits where we are able to achieve a significant reduction in the number of ancilla bits and T-gates as compared to the originally required numbers to achieve fault-tolerance. Our work is the first step in the series of arithmetic circuit optimization using graphicalrewrite tools and it pavesthe way for advancing the optimization of various complex quantum circuits and establishing the potential for new applications of the same.

Quantum image encryption algorithm via optimized quantum circuit and parity bit-plane permutation

Quantum image encryption technology employs the unique features of superposition, entanglement, and quantum state instability, offering advantages like high efficiency, parallelism, and robust resistance to decryption attempts. In this work, we propose a quantum image encryption algorithm via an optimized quantum circuit and parity bit-plane permutation named OCPBP. Our research commences with applying an optimization algorithm to BRQI image preparation. This optimization significantly reduces the number of auxiliary qubits from n+3 to 2 in the preparation of (n+5)-CNOT gate preparation. This reduction makes a significant simplification of the complexity and memory space required for BRQI image preparation. Moreover, we introduce an innovative operation based on parity pixel bit-planes for permutation, which provides a fresh perspective on quantum image encryption based on the BRQI model. Furthermore, we generate quantum key images for XOR operations using the improved logistic map, effectively tackling the challenge of non-random keys that can be a concern in conventional BRQI encryption techniques. We also perform a row-column-based permutation operation to enhance the algorithm’s resilience against potential attacks. Through extensive theoretical analysis and comparative experiments, we confirm the heightened security and reduced complexity of the proposed OCPBP algorithm compared to BRQI-based and chaotic image encryption methods. It holds significant promise for improving quantum image communication and application.

Optimization of Quantum Circuits for Stabilizer Codes

Optimization of Quantum Circuits for Stabilizer Codes

Monte Carlo graph search for quantum circuit optimization

Monte Carlo graph search for quantum circuit optimization

Reducing 2-QuBit Gate Count for ZX-Calculus based Quantum Circuit Optimization

Reducing 2-QuBit Gate Count for ZX-Calculus based Quantum Circuit Optimization

Optimized Quantum Circuit for Quantum Security Strength Analysis of Argon2

This paper explores the optimization of quantum circuits for Argon2, a memory-hard function used in password hashing applications. With the rise of quantum computers, the security of classical cryptographic systems is at risk. This paper emphasizes the need to accurately measure the quantum security strength of cryptographic schemes through highly optimized quantum circuits for the target cryptography algorithm. The proposed method focuses on two perspectives: qubit reduction (qubit-optimized quantum circuit) and depth reduction (depth-optimized quantum circuit). The qubit-optimized quantum circuit was designed to find a point where an appropriate inverse is possible and reuses the qubit through the inverse to minimize the number of qubits. The start and end points of the inverse are determined by identifying a point where qubits can be reused with minimal computation. The depth-optimized quantum circuit reduces the depth of the quantum circuit by using the minimum number of qubits necessary without performing an inverse operation. The trade-off between qubit and depth is confirmed by modifying the internal structure of the circuits and the quantum adders. The qubit optimization achieved up to a 12,229 qubit reduction, while the depth optimization resulted in an approximately 196,741 (approximately 69.02%) depth reduction. In conclusion, this research demonstrates the importance of implementing and analyzing quantum circuits from multiple optimization perspectives. The results contribute to the post-quantum strength analysis of Argon2 and provide valuable insights for future research on optimized quantum circuit design, considering the appropriate trade-offs of quantum resources in response to advancements in quantum computing technology.

Design Method of Meta Operators Based on Equivalence Class Distribution

Currently, there are many physical systems for quantum computing and to adapt to the physical characteristics of different systems, engineers have designed different basic gate groups for gate circuit calculation models. The quantum algorithm realizes the evolution of the quantum state by applying unitary operators to the quantum states, and the results are obtained by measuring the outputs. These operators will be done in the corresponding physical system by compiling and decomposing into hardware supported basic gates. Universal fundamental gates can construct all quantum algorithms, but their computational efficiency is limited. Drawing on the idea of meta operators in classical machine learning, by constructing a deep learning framework for deep learning models, the common computational logic of operators in different deep learning frameworks is abstracted as ‘meta operators’ [1, 2]. This article aims to study and propose the common computational logic of quantum computing with geometric equivalence class distribution methods, using the volume size of the equivalence class space as a performance indicator for meta operators and identifying the optimal meta operators to optimize the depth of the circuits in the experiments. Which proves the effectiveness of the design method proposed and provides solutions for quantum circuit optimization and dedicated gate design.

Hardware-Conscious Optimization of the Quantum Toffoli Gate

While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an 18% reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a 25% reduction from the canonical eight multi-qubit implementations for linearly connected qubits.

LIMDD: A Decision Diagram for Simulation of Quantum Computing Including Stabilizer States

Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable of capturing relevant aspects of quantum systems, but their limits are not well understood. In this work, we investigate and bridge the gap between existing DD-based structures and the stabilizer formalism, an important tool for simulating quantum circuits in the tractable regime. We first show that although DDs were suggested to succinctly represent important quantum states, they actually require exponential space for certain stabilizer states. To remedy this, we introduce a more powerful decision diagram variant, called Local Invertible Map-DD (LIMDD). We prove that the set of quantum states represented by poly-sized LIMDDs strictly contains the union of stabilizer states and other decision diagram variants. Finally, there exist circuits which LIMDDs can efficiently simulate, while their output states cannot be succinctly represented by two state-of-the-art simulation paradigms: the stabilizer decomposition techniques for Clifford + T circuits and Matrix-Product States. By uniting two successful approaches, LIMDDs thus pave the way for fundamentally more powerful solutions for simulation and analysis of quantum computing.

Error mitigation enables PET radiomic cancer characterization on quantum computers

BackgroundCancer is a leading cause of death worldwide. While routine diagnosis of cancer is performed mainly with biopsy sampling, it is suboptimal to accurately characterize tumor heterogeneity. Positron emission tomography (PET)-driven radiomic research has demonstrated promising results when predicting clinical endpoints. This study aimed to investigate the added value of quantum machine learning both in simulator and in real quantum computers utilizing error mitigation techniques to predict clinical endpoints in various PET cancer patients.MethodsPreviously published PET radiomics datasets including 11C-MET PET glioma, 68GA-PSMA-11 PET prostate and lung 18F-FDG PET with 3-year survival, low-vs-high Gleason risk and 2-year survival as clinical endpoints respectively were utilized in this study. Redundancy reduction with 0.7, 0.8, and 0.9 Spearman rank thresholds (SRT), followed by selecting 8 and 16 features from all cohorts, was performed, resulting in 18 dataset variants. Quantum advantage was estimated by Geometric Difference (GDQ) score in each dataset variant. Five classic machine learning (CML) and their quantum versions (QML) were trained and tested in simulator environments across the dataset variants. Quantum circuit optimization and error mitigation were performed, followed by training and testing selected QML methods on the 21-qubit IonQ Aria quantum computer. Predictive performances were estimated by test balanced accuracy (BACC) values.ResultsOn average, QML outperformed CML in simulator environments with 16-features (BACC 70% and 69%, respectively), while with 8-features, CML outperformed QML with + 1%. The highest average QML advantage was + 4%. The GDQ scores were ≤ 1.0 in all the 8-feature cases, while they were > 1.0 when QML outperformed CML in 9 out of 11 cases. The test BACC of selected QML methods and datasets in the IonQ device without error mitigation (EM) were 69.94% BACC, while EM increased test BACC to 75.66% (76.77% in noiseless simulators).ConclusionsWe demonstrated that with error mitigation, quantum advantage can be achieved in real existing quantum computers when predicting clinical endpoints in clinically relevant PET cancer cohorts. Quantum advantage can already be achieved in simulator environments in these cohorts when relying on QML.

Optimal Universal Quantum Circuits for Unitary Complex Conjugation

Let $U_d$ be a unitary operator representing an arbitrary $d$-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number $k$ of calls of $U_d$ into its complex conjugate $\bar{U_d}$. Our circuits admit a parallel implementation and are proven to be optimal for any $k$ and $d$ with an average fidelity of $\left\langle{F}\right\rangle =\frac{k+1}{d(d-k)}$. Optimality is shown for average fidelity, robustness to noise, and other standard figures of merit. This extends previous works which considered the scenario of a single call ($k=1$) of the operation $U_d$, and the special case of $k=d-1$ calls. We then show that our results encompass optimal transformations from $k$ calls of $U_d$ to $f(U_d)$ for any arbitrary homomorphism $f$ from the group of $d$-dimensional unitary operators to itself, since complex conjugation is the only non-trivial automorphisms on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.

Optimized Implementation and Analysis of CHAM in Quantum Computing

A quantum computer capable of running the Grover search algorithm, which reduces the complexity of brute-force attacks by a square root, has the potential to undermine the security strength of symmetric-key cryptography and hash functions. Recently, studies on quantum approaches have proposed analyzing potential quantum attacks using the Grover search algorithm in conjunction with optimized quantum circuit implementations for symmetric-key cryptography and hash functions. Analyzing quantum attacks on a cipher (i.e., quantum cryptanalysis) and estimating the necessary quantum resources are related to evaluating post-quantum security for the target cryptography algorithms. In this paper, we revisit quantum implementations of CHAM block cipher, an ultra lightweight cipher, with a focus on optimizing the linear operations in its key schedule. We optimized the linear equations of CHAM as matrices by applying novel optimized decomposition techniques. Using the improved CHAM quantum circuits, we estimate the cost of Grover’s key search and evaluate the post-quantum security strength with further reduced costs.

Barren plateaus in quantum tensor network optimization

We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer.

Compositional optimization of quantum circuits for quantum kernels of support vector machines

While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a Bayesian algorithm for constructing quantum kernels for support vector machines that adapts quantum gate sequences to data. The algorithm increases the complexity of quantum circuits incrementally by appending quantum gates selected with Bayesian information criterion as circuit selection metric and Bayesian optimization of the parameters of the locally optimal quantum circuits identified. The performance of the resulting quantum models for the classification problems considered here significantly exceeds that of optimized classical models with conventional kernels.

Suppressing Quantum Circuit Errors Due to System Variability

We present a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present day noisy quantum computing platforms. This method can be run post qubit routing or post-compilation, and consists of computing isomorphic subgraphs to input circuits and scoring each using heuristic cost functions derived from system calibration data. Using an independent standard algorithmic test suite we show that it is possible to recover on average nearly 40% of missing fidelity using better qubit selection via efficient to compute cost functions. We demonstrate additional performance gains by considering qubit placement over multiple quantum processors. The overhead from these tools is minimal with respect to other compilation steps, such as qubit routing, as the number of qubits increases. As such, our method can be used to find qubit mappings for problems at the scale of quantum advantage and beyond.