Optimization Of Quantum Circuits Research Articles

Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity

The Jarzynski identity can describe small-scale nonequilibrium systems through stochastic thermodynamics. The identity considers fluctuating trajectories in a phase space. The complexity geometry frames the discussions on quantum computational complexity using the method of Riemannian geometry, which builds a bridge between optimal quantum circuits and classical geodesics in the space of unitary operators. Complexity geometry enables the application of the methods of classical physics to deal with pure quantum problems. By combining the two frameworks, i.e., the Jarzynski identity and complexity geometry, we derived a complexity analog of the Jarzynski identity using the complexity geometry. We considered a set of geodesics in the space of unitary operators instead of the trajectories in a phase space. The obtained complexity version of the Jarzynski identity strengthened the evidence for the existence of a well-defined resource theory of uncomplexity and presented an extensive discussion on the second law of complexity. Furthermore, analogous to the thermodynamic fluctuation-dissipation theorem, we proposed a version of the fluctuation-dissipation theorem for the complexity. Although this study does not focus on holographic fluctuations, we found that the results are surprisingly suitable for capturing their information. The results obtained using nonequilibrium methods may contribute to understand the nature of the complexity and study the features of the holographic fluctuations.

Exact and Practical Pattern Matching for Quantum Circuit Optimization

Quantum computations are typically performed as a sequence of basic operations, called quantum gates. Different gate sequences, called quantum circuits, can implement the same overall quantum computation. Since every additional quantum gate takes time and introduces noise into the system, it is important to find the smallest possible quantum circuit that implements a given computation, especially for near-term quantum devices that can execute only a limited number of quantum gates before noise renders the computation useless. An important building block for many quantum circuit optimization techniques is pattern matching: given a large and small quantum circuit, we would like to find all maximal matches of the small circuit, called a pattern , in the large circuit, considering pairwise commutation of quantum gates. In this work, we present the first classical algorithm for pattern matching that provably finds all maximal matches and is efficient enough to be practical for circuit sizes typical for near-term devices. We demonstrate numerically 1 that combining our algorithm with known pattern-matching-based circuit optimization techniques reduces the gate count of a random quantum circuit by ∼ 30% and can further improve practically relevant quantum circuits that were already optimized with state-of-the-art techniques.

Quantum Period Finding against Symmetric Primitives in Practice

We present the first complete descriptions of quantum circuits for the offline Simon’s algorithm, and estimate their cost to attack the MAC Chaskey, the block cipher PRINCE and the NIST lightweight finalist AEAD scheme Elephant. These attacks require a reasonable amount of qubits, comparable to the number of qubits required to break RSA-2048. They are faster than other collision algorithms, and the attacks against PRINCE and Chaskey are the most efficient known to date. As Elephant has a key smaller than its state size, the algorithm is less efficient and its cost ends up very close to or above the cost of exhaustive search.We also propose an optimized quantum circuit for boolean linear algebra as well as complete reversible implementations of PRINCE, Chaskey, spongent and Keccak which are of independent interest for quantum cryptanalysis. We stress that our attacks could be applied in the future against today’s communications, and recommend caution when choosing symmetric constructions for cases where long-term security is expected.

T-count optimized quantum circuit for floating point addition and multiplication

T-count optimized quantum circuit for floating point addition and multiplication

A Quantum Circuit Optimization Framework Based on Pattern Matching

In the NISQ era, quantum computers have insufficient qubits to support quantum error correction, which can only perform shallow quantum algorithms under noisy conditions. Aiming to improve the fidelity of quantum circuits, it is necessary to reduce the circuit depth as much as possible to mitigate the coherent noise. To address the issue, we propose PaF , a Pattern matching-based quantum circuit rewriting algorithm Framework to optimize quantum circuits. The algorithm framework finds all sub-circuits satisfied in the input quantum circuit according to the given external pattern description, then replaces them with better circuit implementations. To extend the capabilities of PaF , a general pattern description format is proposed to make rewriting patterns in existing work become machine-readable. In order to evaluate the effectiveness of PaF , we employ the BIGD benchmarks in QUEKO benchmark suite to test the performance and the result shows that PaF provides a maximal speedup of [Formula: see text] by using few patterns.

Natural evolutionary strategies for variational quantum computation

Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly initialized parameterized quantum circuits (PQCs) in the region of vanishing gradients. We show that using the NES gradient estimator the exponential decrease in variance can be alleviated. We implement two specific approaches, the exponential and separable NES, for parameter optimization of PQCs and compare them against standard gradient descent. We apply them to two different problems of ground state energy estimation using variational quantum eigensolver and state preparation with circuits of varying depth and length. We also introduce batch optimization for circuits with larger depth to extend the use of ES to a larger number of parameters. We achieve accuracy comparable to state-of-the-art optimization techniques in all the above cases with a lower number of circuit evaluations. Our empirical results indicate that one can use NES as a hybrid tool in tandem with other gradient-based methods for optimization of deep quantum circuits in regions with vanishing gradients.

Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

As quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

Efficient Implementation of PRESENT and GIFT on Quantum Computers

Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.

Quantum Circuit Synthesis Using Projective Simulation

Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance routines have been huge barriers for quantum algorithms efficient use.These restrictions lead us to search for ways to minimize algorithms costs, i.e the number of quantum logical gates and the depth of the circuit. For this, quantum circuit synthesis and quantum circuit optimization techniques are explored.We studied the viability of using Projective Simulation, a reinforcement learning technique, to tackle the problem of quantum circuit synthesis. The agent had the task of creating quantum circuits up to 5 qubits. Our simulations demonstrated that the agent had a good performance but its capacity for learning new circuits decreased as the number of qubits increased.

Spacetime as a quantum circuit

We propose that finite cutoff regions of holographic spacetimes represent quantum circuits that map between boundary states at different times and Wilsonian cutoffs, and that the complexity of those quantum circuits is given by the gravitational action. The optimal circuit minimizes the gravitational action. This is a generalization of both the “complexity equals volume” conjecture to unoptimized circuits, and path integral optimization to finite cutoffs. Using tools from holographic Toverline{T} , we find that surfaces of constant scalar curvature play a special role in optimizing quantum circuits. We also find an interesting connection of our proposal to kinematic space, and discuss possible circuit representations and gate counting interpretations of the gravitational action.

T-Count Optimized Quantum Circuit Designs for Single-Precision Floating-Point Division

The implementation of quantum computing processors for scientific applications includes quantum floating points circuits for arithmetic operations. This work adopts the standard division algorithms for floating-point numbers with restoring, non-restoring, and Goldschmidt division algorithms for single-precision inputs. The design proposals are carried out while using the quantum Clifford+T gates set, and resource estimates in terms of numbers of qubits, T-count, and T-depth are provided for the proposed circuits. By improving the leading zero detector (LZD) unit structure, the proposed division circuits show a significant reduction in the T-count when compared to the existing works on floating-point division.

Adaptive pruning-based optimization of parameterized quantum circuits

Variational hybrid quantum–classical algorithms are powerful tools to maximize the use of noisy intermediate-scale quantum devices. While past studies have developed powerful and expressive ansatze, their near-term applications have been limited by the difficulty of optimizing in the vast parameter space. In this work, we propose a heuristic optimization strategy for such ansatze used in variational quantum algorithms, which we call ‘parameter-efficient circuit training (PECT)’. Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms, in which each iteration of the algorithm activates and optimizes a subset of the total parameter set. To update the parameter subset between iterations, we adapt the Dynamic Sparse Reparameterization scheme which was originally proposed for training deep convolutional neural networks. We demonstrate PECT for the Variational Quantum Eigensolver, in which we benchmark unitary coupled-cluster ansatze including UCCSD and k-UpCCGSD, as well as the Low-Depth Circuit Ansatz (LDCA), to estimate ground state energies of molecular systems. We additionally use a layerwise variant of PECT to optimize a hardware-efficient circuit for the Sycamore processor to estimate the ground state energy densities of the one-dimensional Fermi-Hubbard model. From our numerical data, we find that PECT can enable optimizations of certain ansatze that were previously difficult to converge and more generally can improve the performance of variational algorithms by reducing the optimization runtime and/or the depth of circuits that encode the solution candidate(s).

Large gradients via correlation in random parameterized quantum circuits

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover’s algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward , the optimal oracle complexity of quantum unstructured search.

A Multiobjective Approach for Nearest Neighbor Optimization of N-Dimensional Quantum Circuits

A Multiobjective Approach for Nearest Neighbor Optimization of N-Dimensional Quantum Circuits

Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications

There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of quantum devices produced over a next decade. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and effcient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.

Optimized Quantum Circuit Partitioning

The main objective of this paper is to improve the communication costs in distributed quantum circuits. To this end, we present a method for generating distributed quantum circuits from monolithic quantum circuits in such a way that communication between partitions of a distributed quantum circuit is minimized. Thus, the communication between distributed components is performed at a lower cost. Compared to existing works, our approach can effectively map a quantum circuit into an appropriate number of distributed components. Since teleportation is usually the protocol used to connect components in a distributed quantum circuit, our approach ultimately reduces the number of teleportations. The results of applying our approach to the benchmark quantum circuits determine its effectiveness and show that partitioning is a necessary step in constructing distributed quantum circuit.

Quantum circuit optimization using quantum Karnaugh map

Every quantum algorithm is represented by set of quantum circuits. Any optimization scheme for a quantum algorithm and quantum computation is very important especially in the arena of quantum computation with limited number of qubit resources. Major obstacle to this goal is the large number of elemental quantum gates to build even small quantum circuits. Here, we propose and demonstrate a general technique that significantly reduces the number of elemental gates to build quantum circuits. This is impactful for the design of quantum circuits, and we show below this could reduce the number of gates by 60% and 46% for the four- and five-qubit Toffoli gates, two key quantum circuits, respectively, as compared with simplest known decomposition. Reduced circuit complexity often goes hand-in-hand with higher efficiency and bandwidth. The quantum circuit optimization technique proposed in this work would provide a significant step forward in the optimization of quantum circuits and quantum algorithms, and has the potential for wider application in quantum computation.

Grover on Korean Block Ciphers

The Grover search algorithm reduces the security level of symmetric key cryptography with n-bit security level to O(2n/2). In order to evaluate the Grover search algorithm, the target block cipher should be efficiently implemented in quantum circuits. Recently, many research works evaluated required quantum resources of AES block ciphers by optimizing the expensive substitute layer. However, few works were devoted to the lightweight block ciphers, even though it is an active research area, nowadays. In this paper, we present optimized implementations of every Korean made lightweight block ciphers for quantum computers, which include HIGHT, CHAM, and LEA, and NSA made lightweight block ciphers, namely SPECK. Primitive operations for block ciphers, including addition, rotation, and exclusive-or, are finely optimized to achieve the optimal quantum circuit, in terms of qubits, Toffoli gate, CNOT gate, and X gate. To the best of our knowledge, this is the first implementation of ARX-based Korean lightweight block ciphers in quantum circuits.

An optimized quantum circuit for converting from sign–magnitude to two’s complement

Nowadays, one of the critical issues to implement quantum algorithms is the required number of elementary gates, qubits and delay. Current quantum computers and simulators are mainly prototypes, and there is a lack of computational resources. Therefore, it is necessary to optimize the quantum operations to reduce the necessary number of gates and qubits. This work presents a novel reversible circuit which is able to convert signed binary numbers to two’s complement of N digits in a quantum environment. The depth of the circuit is O(log N). It is based on the fastest out-of-place carry look-ahead addition quantum circuit currently available. This addition circuit has been adapted to make the conversion using the minimum number of gates and qubits, being faster than other adder circuits. A robust metric has been used to measure the quantum cost, delay, ancilla inputs and garbage outputs of the proposed converter. Moreover, it has been compared with others described in the literature.

Efficient Design of Quantum Circuits Using Nearest Neighbor Constraint in 3D Architecture

Synthesis and optimization of quantum circuits have received significant attention from researchers in recent years. Developments in the physical realization of qubits in quantum computing have led to new physical constraints to be addressed. One of the most important constraints that is considered by many researchers is the nearest neighbor constraint which limits the interaction distance between qubits for quantum gate operations. Various works have been reported in the literature that deal with nearest neighbor compliance in multi-dimensional (mostly 1D and 2D) qubit arrangements. This is normally achieved by inserting SWAP gates in the gate netlist to bring the interacting qubits closer together. The main objective function to minimize here is the number of SWAP gates. The present paper proposes an efficient qubit placement strategy in a three-dimensional (3D) grid that considers not only qubit interactions but also the relative positions of the gates in the circuit. Experimental evaluation on a number of benchmark circuits show that the proposed method reduces the number of SWAP gates by 16.2% to 47.0% on the average as compared to recently published works.