Synthesis Of Quantum Circuits Research Articles

A New Multicommodity Network Flow Model and Branch and Cut for Optimal Quantum Boolean Circuit Synthesis

This study introduces a new optimization model and a branch-and-cut approach for synthesizing optimal quantum circuits for reversible Boolean functions, which are pivotal components in quantum algorithms. Although heuristic algorithms have been extensively explored for quantum circuit synthesis, research on exact counterparts remains relatively limited. However, the need to design quantum circuits with guaranteed optimality is increasing, especially for improving computational fidelity on noisy intermediate-scale quantum devices. This study presents mathematical optimization as a viable option for optimal synthesis, with the potential to accommodate practical considerations arising in fast-evolving quantum technologies. We set a demonstrative problem to implement reversible Boolean functions using high-level gates known as multiple control Toffoli gates while minimizing a technology-based proxy called quantum cost—the number of low-level gates used to realize each high-level gate. To address this problem, we propose a discrete optimization model based on a multicommodity network and discuss potential future variations at an abstract level to incorporate technical considerations. A customized branch and cut is then developed upon different aspects of our model, including polyhedron integrality, surrogate constraints, and variable prioritization. Our experiments demonstrate the robustness of the proposed approach in finding cost-optimal circuits for all benchmark instances within a two-hour time frame. Furthermore, we present interesting intuitions from these experiments and compare our computational results with relevant studies, highlighting newly discovered circuits with the lowest quantum costs reported in this paper. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Quantum Computing. Funding: This research was supported by the Ministry of Science and Information and Communication Technology, South Korea [Grants 2017R1E1A1A0307098814 and 2020R1A4A307986411]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0562 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0562 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Synthesis of energy-conserving quantum circuits with XY interaction

Abstract We study quantum circuits constructed from $\sqrt{iSWAP}$ gates and, more
generally, from the entangling gates that can be realized with the XX+YY
interaction alone. Such gates preserve the Hamming weight of states in the
computational basis, which means they respect the global U(1) symmetry
corresponding to rotations around the z axis. Equivalently, assuming that the
intrinsic Hamiltonian of each qubit in the system is the Pauli Z operator, they
conserve the total energy of the system. We develop efficient methods for
synthesizing circuits realizing any desired energy-conserving unitary using
XX+YY interaction with or without single-qubit rotations around the z-axis.
Interestingly, implementing generic energy-conserving unitaries, such as CCZ
and Fredkin gates, with 2-local energy-conserving gates requires the use of
ancilla qubits. When single-qubit rotations around the z-axis are permitted,
our scheme requires only a single ancilla qubit, whereas with the XX+YY
interaction alone, it requires 2 ancilla qubits. In addition to exact
realizations, we also consider approximate realizations and show how a general
energy-conserving unitary can be synthesized using only a sequence of
$\sqrt{iSWAP}$ gates and 2 ancillary qubits, with arbitrarily small error,
which can be bounded via the Solovay-Kitaev theorem. Our methods are also
applicable for synthesizing energy-conserving unitaries when, rather than the
XX+YY interaction, one has access to any other energy-conserving 2-body
interaction that is not diagonal in the computational basis, such as the
Heisenberg exchange interaction. We briefly discuss the applications of these
circuits in the context of quantum computing, quantum thermodynamics, and
quantum clocks.

Quantum resource estimation for large scale quantum algorithms

Quantum algorithms are often represented in terms of quantum circuits operating on ideal (logical) qubits. However, the practical implementation of these algorithms poses significant challenges. Many quantum algorithms require a substantial number of logical qubits, and the inherent susceptibility to errors of quantum computers require quantum error correction. The integration of error correction introduces overhead in terms of both space (physical qubits required) and runtime (how long the algorithm needs to be run for). This paper addresses the complexity of comparing classical and quantum algorithms, primarily stemming from the additional quantum error correction overhead. We propose a comprehensive framework that facilitates a direct and meaningful comparison between classical and quantum algorithms. By acknowledging and addressing the challenges introduced by quantum error correction, our framework aims to provide a clearer understanding of the comparative performance of classical and quantum computing approaches. This work contributes to understanding the practical viability and potential advantages of quantum algorithms in real-world applications.We apply our framework to quantum cryptanalysis, since it is well known that quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum computers it is important to have an estimate of the resources needed to implement these quantum attacks. This analysis provides state-of-the art snap-shot estimates of the realistic costs of implementing quantum attacks on these important cryptographic algorithms, assuming quantum fault-tolerance is achieved using surface code methods, and spanning a range of potential error rates. These estimates serve as a guide for gauging the realistic impact of these algorithms and for benchmarking the impact of future advances in quantum algorithms, circuit synthesis and optimization, fault-tolerance methods and physical error rates.

From stochastic Hamiltonian to quantum simulation: exploring memory effects in exciton dynamics

The unraveling of open quantum system dynamics in terms of stochastic quantum trajectories offers a picture of open system dynamics that consistently considers memory effects stemming from the finite correlation time of environment fluctuations. These fluctuations significantly influence the coherence and energy transport properties of excitonic systems. When their correlation time is comparable to the timescale of the Hamiltonian evolution, it leads to the departure of open system dynamics from the Markovian limit. In this work, we leverage the unraveling of exciton dynamics through stochastic Hamiltonian propagators to design quantum circuits that simulate exciton transport, capturing finite memory effects. In addition to enabling the synthesis of parametrizable quantum circuits, stochastic unitary propagators provide a transparent framework for investigating non-Markovian effects on exciton transport. Our analysis reveals a nuanced relationship between environment correlation time and transport efficiency, identifying a regime of ‘memory-assisted’ quantum transport where time-correlated fluctuations allow the system to reach higher efficiency. However, this property is not universal and can only be realized in conjunction with specific features of the system Hamiltonian.

Synthesis of quantum circuits based on supervised learning and correlations

Synthesis of quantum circuits based on supervised learning and correlations

Quantum circuit synthesis with diffusion models

Quantum circuit synthesis with diffusion models

Discovering quantum circuit components with program synthesis

Despite rapid progress in the field, it is still challenging to discover new ways to leverage quantum computation: all quantum algorithms must be designed by hand, and quantum mechanics is notoriously counterintuitive. In this paper, we study how artificial intelligence, in the form of program synthesis, may help overcome some of these difficulties, by showing how a computer can incrementally learn concepts relevant to quantum circuit synthesis with experience, and reuse them in unseen tasks. In particular, we focus on the decomposition of unitary matrices into quantum circuits, and show how, starting from a set of elementary gates, we can automatically discover a library of useful new composite gates and use them to decompose increasingly complicated unitaries.

Depth-optimized quantum circuit synthesis for diagonal unitary operators with asymptotically optimal gate count

Depth-optimized quantum circuit synthesis for diagonal unitary operators with asymptotically optimal gate count

Quantum circuit synthesis on noisy intermediate-scale quantum devices

Quantum circuit synthesis on noisy intermediate-scale quantum devices

Leveraging Different Boolean Function Decompositions to Reduce T-Count in LUT-based Quantum Circuit Synthesis

Leveraging Different Boolean Function Decompositions to Reduce T-Count in LUT-based Quantum Circuit Synthesis

A dynamic programming approach to multi-objective logic synthesis of quantum circuits

A dynamic programming approach to multi-objective logic synthesis of quantum circuits

Quantum SoC and On-Chip Circuit Synthesis in the NISQ Era

In recent years, fueled by the breakthroughs in the technology in quantum computation, there has been a rising interest in the noisy intermediate-scale quantum (NISQ) era. In addition to a large number of qubits, the study of error correction and quantum algorithms has made great progress. However, as a primary goal of quantum computation, making practicable quantum computers in the NISQ era still needs further study, mainly focusing on quantum computer organization, architecture, and circuit synthesis. This paper studies the quantum circuit synthesis in a small-scale universal quantum computing device called a “quantum system-on-chip” (QSoC). We analyze the quantum compilation of the hybrid architecture for a small-scaled universal quantum computational device with a specific size (quantum chip). Two kinds of on-chip circuit synthesis algorithms are proposed and discussed.

Exploiting subspace constraints and ab initio variational methods for quantum chemistry

Variational methods offer a highly promising route to exploiting quantum computers for chemistry tasks. Here we employ methods described in a sister paper to the present report, entitled exploring ab initio machine synthesis of quantum circuits, in order to solve problems using adaptively evolving quantum circuits. Consistent with prior authors we find that this approach can outperform human-designed circuits such as the coupled-cluster or hardware-efficient ansätze, and we make comparisons for larger instances up to 14 qubits Moreover we introduce a novel approach to constraining the circuit evolution in the physically relevant subspace, finding that this greatly improves performance and compactness of the circuits. We consider both static and dynamics properties of molecular systems. The emulation environment used is QuESTlink all resources are open source and linked from this paper.

Efficient variational synthesis of quantum circuits with coherent multi-start optimization

We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that along with the discrete architecture search suffering from the combinatorial explosion of complexity, optimization over 1q gates can also be a crucial roadblock due to the omnipresence of local minimums (well known in the context of variational quantum algorithms but apparently underappreciated in the context of the variational compiling). Taking the issue seriously, we make an extensive search over the initial conditions an essential part of our approach. Another key idea we propose is to use parametrized two-qubit (2q) controlled phase gates, which can interpolate between the identity gate and the CNOT gate, and allow a continuous relaxation of the discrete architecture search, which can be executed jointly with the optimization over 1q gates. This coherent optimization of the architecture together with 1q gates appears to work surprisingly well in practice, sometimes even outperforming optimization over 1q gates alone (for fixed optimal architectures). As illustrative examples and applications we derive 8 CNOT and T depth 3 decomposition of the 3q Toffoli gate on the nearest-neighbor topology, rediscover known best decompositions of the 4q Toffoli gate on all 4q topologies including a 1 CNOT gate improvement on the star-shaped topology, and propose decomposition of the 5q Toffoli gate on the nearest-neighbor topology with 48 CNOT gates. We also benchmark the performance of our approach on a number of 5q quantum circuits from the ibm_qx_mapping database showing that it is highly competitive with the existing software. The algorithm developed in this work is available as a Python package CPFlow.

Quantum Computer-Aided Design Automation

Quantum computing is an essential issue for taking advantage of quantum properties in real-world applications. Realizing quantum computing with a corresponding quantum circuit is a critical step. This study introduces the AngelQ system, which provides quantum computing-as-a-service (QCaaS) for the cloud. The AngelQ system integrates quantum design automation (QDA) to achieve quantum and reversible circuit synthesis by a quantum-inspired optimization (QiO) technique and has visualization software interfaces to verify the QiO process and the correctness of the synthesized quantum and reversible circuits. First, the proposed novel QiO method has four significant features: Adaptive strategy, quantum-Not gate, update mechanism by Global solutions, and Entanglement Local search, named Angel QiO. which is a flexible technique to realize various circuits under different gate libraries with a few alterations. Angel QiO can construct diversified function-equivalent circuits to assess the circuit composition and boost the development of circuit synthesis. Second, researchers can observe the QiO algorithm process and inspect the intermediate result formula through AngelQ system’s visualization interface to further adjust the parameters and improve the performance. Moreover, it benefits beginners’ learning and adds convenience to education. In summary, the AngelQ system can extend and facilitate the future design and automation of quantum computing.

Optimal SAT Solver Synthesis of Quantum Circuits Representing Cryptographic Nonlinear Functions

Optimal SAT Solver Synthesis of Quantum Circuits Representing Cryptographic Nonlinear Functions

Physical constraint-aware CNOT quantum circuit synthesis and optimization

Physical constraint-aware CNOT quantum circuit synthesis and optimization

Solving the Schrödinger Equation with Genetic Algorithms: A Practical Approach

The Schrödinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 1970s, the computer began to be used to solve this equation in elementary quantum systems, and, in the most complex case, a ‘hydrogen-like’ system. Obtaining the solution means finding the wave function, which allows predicting the physical and chemical properties of the quantum system. However, when a quantum system is more complex than a ‘hydrogen-like’ system, we must be satisfied with an approximate solution of the equation. During the last decade, application of algorithms and principles of quantum computation in disciplines other than physics and chemistry, such as biology and artificial intelligence, has led to the search for alternative techniques with which to obtain approximate solutions of the Schrödinger equation. In this work, we review and illustrate the application of genetic algorithms, i.e., stochastic optimization procedures inspired by Darwinian evolution, in elementary quantum systems and in quantum models of artificial intelligence. In this last field, we illustrate with two ‘toy models’ how to solve the Schrödinger equation in an elementary model of a quantum neuron and in the synthesis of quantum circuits controlling the behavior of a Braitenberg vehicle.

Quantum reversible circuits for mathrm{GF}(2^{8}) multiplicative inverse

The synthesis of quantum circuits for multiplicative inverse over operatorname{GF}(2^{8}) are discussed in this paper. We first convert the multiplicative inverse operation in operatorname{GF}(2^{8}) to arithmetic operations in the composite field operatorname{GF}((2^{4})^{2}), and then discuss the expressions of the square calculation, the inversion calculation and the multiplication calculation separately in the finite field operatorname{GF}(2^{4}), where the expressions of multiplication calculation in operatorname{GF}(2^{4}) are given directly in operatorname{GF}(2^{4}) and given through being transformed into the composite field operatorname{GF}((2^{2})^{2}). Then the quantum circuits of these calculations are realized one by one. Finally, two quantum circuits for multiplicative inverse over operatorname{GF}(2^{8}) are synthesized. They both use 21 qubits, the first quantum circuit uses 55 Toffoli gates and 107 CNOT gates and the second one uses 37 Toffoli gates and 209 CNOT gates. As an example of the application of multiplication inverse, we apply these quantum circuits to the implementations of the S-box quantum circuit of the AES cryptographic algorithm. Two quantum circuits for implementing the S-box of the AES cryptographic algorithm are presented. The first quantum circuit uses 21 qubits, 55 Toffoli gates, 131 CNOT gates and 4 NOT gates and the second one uses 21 qubits, 37 Toffoli gates, 233 CNOT gates and 4 NOT gates. Through the evaluation of quantum cost, the two quantum circuits of the S-box of AES cryptographic algorithm use less quantum resources than the existing schemes.

Tools for Quantum Computing Based on Decision Diagrams

With quantum computers promising advantages even in the near-term NISQ era, there is a lively community that develops software and toolkits for the design of corresponding quantum circuits. Although the underlying problems are different, expertise from the design automation community, which developed sophisticated design solutions for the conventional realm in the past decades, can help here. In this respect, decision diagrams provide a promising foundation for tackling many design tasks such as simulation, synthesis, and verification of quantum circuits. However, users of the corresponding tools often do not have a proper background or an intuition about how these methods based on decision diagrams work and what their strengths and limits are. In this work, we first review the concepts of how decision diagrams can be employed, e.g., for the simulation and verification of quantum circuits. Afterwards, in an effort to make decision diagrams for quantum computing more accessible, we then present a visualization tool for quantum decision diagrams, which allows users to explore the behavior of decision diagrams in the design tasks mentioned above. Finally, we present decision diagram-based tools for simulation and verification of quantum circuits using the methods discussed above as part of the open-source Munich Quantum Toolkit (MQT)—a set of tools for quantum computing developed at the Technical University of Munich and the Johannes Kepler University Linz and released under the MIT license. More information about the corresponding tools is available at https://github.com/cda-tum/ddsim . By this, we provide an introduction of the concepts and tools for potential users who would like to work with them as well as potential developers aiming to extend them.