This work introduces and characterizes quantum sequential circuits (QSCs) as a hardware-oriented paradigm for quantum computing, built upon a novel foundational element termed the quantum transistor. Unlike conventional qubit-based architectures, QSCs employ symmetry-protected topological junctions where quantum gates are encoded as Choi states via channel-state duality and activated through bulk measurements, utilizing ebits to realize the functional analog of feedback loops in classical sequential circuits. This framework establishes a universal model for quantum computation that inherently incorporates memory and temporal sequencing, complementing existing combinational quantum circuit model. Our work advances the conceptual bridge towards a quantum von Neumann architecture, underscoring the potential of hybrid and modular design principles for the development of large-scale, integrated quantum information processors.
State preparation with parallel-sequential circuits
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与工程中心）；Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（联合量子研究所与联合量子信息与计算机科学中心，美国国家标准与技术研究院/马里兰大学）；University of Basel（巴塞尔大学）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
A clear protocol for synthesis of sequential reversible circuits from any particular gate library has been provided. Using that protocol, reversible circuits for SR latch, D latch, JK latch and T latch are designed from NCT gate library. All the circuits have been optimized with the help of existing local optimization algorithms (e.g. template matching, moving rule and deletion rule). It has been shown that the present proposals have lower gate complexities, lower number of garbage bits, lower quantum cost and lower number of feedback loops compared to the earlier proposals. For a fair compari…
We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalisation of Mealy machines. A major difficulty in checking quantum circuits (but not present in checking classical circuits) is that the state spaces of quantum circuits are continuums. This difficulty is resolved by our main theorem showing that equivalence checking of two quantum Mealy machines can be done with input sequences that are taken from some chosen basis (which are finite) and have a length quadratic in the dimensions …
Reversible circuits for SR flip flop, JK flip flop, D flip flop, T flip flop, Master Slave D flip flop and Master Slave JK flip flop have been provided with three different logical approaches. All the circuits have been optimized with the help of existing local optimization algorithms (e.g. template matching, moving rule and deletion rule) and the optimized sequential circuits have been compared with the earlier proposals for the same. It has been shown that the present proposals have lower gate complexities and lower number of garbage bits compared to the earlier proposals. It has also been s…
QSeqSim: A Symbolic Simulator for Qiskit While Loops Using Sequential Quantum Circuits
Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所系统软件重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息研究中心）
Sequential Circuits as Generalized Symmetry on the Lattice
Walter Burke Institute for Theoretical Physics（沃尔特·伯克理论物理研究所）；Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院物理系与量子信息与物质研究所）；C. N. Yang Institute for Theoretical Physics, Stony Brook University（石溪大学陈省身理论物理研究所）
Invariants of Sequential Circuits and Generalized Non-Abelian Statistics
The University of Tokyo（东京大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论与数学科学中心（iTHEMS））；Department of Applied Physics, The University of Tokyo（东京大学应用物理系）
Noise-resilient sequential circuits for generating quantum order
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与工程中心）；University of British Columbia（不列颠哥伦比亚大学）
Scalable Preparation of Matrix Product States with Sequential and Brick Wall Quantum Circuits
Zentrum für Optische Quantentechnologien, Universität Hamburg（汉堡大学光学量子技术中心）；Department of Physics and Astronomy, University of Tennessee, Chattanooga（田纳西大学查塔努加分校物理与天文系）；UTC Quantum Center, University of Tennessee, Chattanooga（田纳西大学查塔努加分校UTC量子中心）；The Hamburg Centre for Ultrafast Imaging, Universität Hamburg（汉堡大学超快成像中心）
Sequential minimum optimization is a machine-learning global search training algorithm. It is applicable when the functional dependence of the cost function on a tunable parameter given the other parameters can be cheaply determined. This assumption is satisfied by quantum circuits built of known gates. We apply it to photonics circuits where the additional challenge appears: low frequency of coincidence events lowers the speed of the algorithm. We propose to modify the algorithm such that small sample size estimators are enough to successfully run the machine learning task. We demonstrate the…
We show that, on the abstraction level of quantum circuit diagrams, quantum circuit algorithms belong to the species of interactive sequential algorithms that we studied in earlier work. This observation leads to a natural specification language for quantum circuit algorithms.
We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.
In all the various proposals for quantum computers, a common feature is that the quantum circuits are expected to be made of cascades of unitary transformations acting on the quantum states. A framework is proposed to express these elementary quantum gates directly in terms of the control inputs entering into the continuous time forced Schrodinger equation.
SPLIT-Q: A Scalable Sequential Quantum Computing Framework for Coherent Controlled Islanding
The Pennsylvania State University（宾夕法尼亚州立大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Kent State University（肯特州立大学）；Clemson University（克莱姆森大学）；University of Pretoria（比勒陀利亚大学）
Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in quantum logic operations is at odds with realistic environments where error-sources may exhibit strong temporal correlations. We present experiments enabling the identification of error correlations between operations in quantum circuits, using only projective measurements at the end of the circuit. Using a single trapped ion qubit and engineered noise with tunab…
This work analyses the performance of quantum circuits and general processes to transform $k$ uses of an arbitrary unitary operation $U$ into another unitary operation $f(U)$. When the desired function $f$ a homomorphism, i.e., $f(UV)=f(U)f(V)$, it is known that optimal average fidelity is attainable by parallel circuits and indefinite causality does not provide any advantage. Here we show that the situation changes dramatically when considering anti-homomorphisms, i.e., $f(UV)=f(V)f(U)$. In particular, we prove that when $f$ is an anti-homomorphism, sequential circuits could exponentially out…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the existing techniques and tools for verification of classical logic circuits in reasoning about quantum circuits.
Quantum circuits for basic image processing functions such as bilinear interpolation are required to implement image processing algorithms on quantum computers. In this work, we propose quantum circuits for the bilinear interpolation of NEQR encoded images based on Clifford+T gates. Quantum circuits for the scale up operation and scale down operation are illustrated. The proposed quantum circuits are based on quantum Clifford+T gates and are optimized for T-count. Quantum circuits based on Clifford+T gates can be made fault tolerant but the T gate is very costly to implement. As a result, redu…
Existing quantum systems provide very limited physical qubit counts, trying to execute a quantum algorithm/circuit on them that have a higher number of logical qubits than physically available lead to a compile-time error. Given that it is unrealistic to expect existing quantum systems to provide, in near future, sufficient number of qubits that can accommodate large circuit, there is a pressing need to explore strategies that can somehow execute large circuits on small systems. In this paper, first, we perform an analysis to identify the qubits that are most suitable for circuit resizing. Our…
In this work, we report on a novel quantum gate approximation algorithm based on the application of parametric two-qubit gates in the synthesis process. The utilization of these parametric two-qubit gates in the circuit design allows us to transform the discrete combinatorial problem of circuit synthesis into an optimization problem over continuous variables. The circuit is then compressed by a sequential removal of two-qubit gates from the design, while the remaining building blocks are continuously adapted to the reduced gate structure by iterated learning cycles. We implemented the develope…
A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are defined. In addition, a notion of equivalence between two games is defined. Finally, the following three theorems are shown: (1) For any quantum simultaneous game G, there exists a quantum sequential game equivalent to G. (2) For any finite quantum simultaneous game G, there exists a finite quantum sequential game equivalent to G. (3) For any finite quantum se…
In this paper, we introduce VeriQBench -- an open source benchmark for quantum circuits. It offers high-level quantum circuit abstractions of various circuit types, including 1) combinational, 2) dynamic, 3) sequential, and 4) variational quantum circuits, which cover almost all existing types of quantum circuits in the literature. Meanwhile, VeriQBench is a versatile benchmark which can be used in verifying quantum software for different applications, as is evidenced by the existing works including quantum circuit verification (e.g., equivalence checking [Hon+21a; WLY21] and model checking [Y…
In this paper, we present a general quantum computation compiler, which maps any given quantum algorithm to a quantum circuit consisting a sequential set of elementary quantum logic gates based on recursive cosine-sine decomposition. The resulting quantum circuit diagram is provided by directly linking the package output written in LaTex to Qcircuit.tex $<$http://www.cquic.org/Qcircuit$>$. We illustrate the use of the Qcompiler package through various examples with full details of the derived quantum circuits. Besides its generality and simplicity, Qcompiler produces quantum circuits which ref…
Bias Analysis and Regularization of Sequential Minimal Optimization in Variational Quantum Eigensolvers
Berlin Institute for the Foundations of Learning and Data BIFOLD（柏林学习与数据基础研究所）；Technische Universität Berlin（柏林工业大学）；Padova University（帕多瓦大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器中心）；Computation-Based Science and Technology Research Center, The Cyprus Institute（塞浦路斯研究所计算科学与技术研究中心）；RIKEN AIP（理化学研究所先进智能计算中心）
We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the parameterized quantum circuits is divided into solvable subproblems by considering only a subset of the parameters. In fact, if we choose a single parameter, the cost function becomes a simple sine curve with period $2π$, and hence we can exactly minimize with respect to the chosen parameter. Furthermore, even in general cases, the cost function is given by a simple sum…
In this paper, we present Clifford+T gates based quantum circuit design of integer division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring division algorithm. The proposed quantum circuit of integer division consists of (i) quantum circuitry of conditional addition operation, (ii) quantum circuitry of integer subtraction. To design ancillary and T-count optimized design of quantum integer division, the optimized quantum circuit design of integer conditional addition operation and integer subtraction are presented. The proposed quantum integer division circuitry…
We show that low-depth random quantum circuits can be efficiently simulated by a quantum teleportation-inspired algorithm. By using logical qubits to redirect and teleport the quantum information in quantum circuits, the original circuits can be renormalized to new circuits with a smaller number of logical qubits. We demonstrate the algorithm to simulate several random quantum circuits, including 1D-chain 1000-qubit 42-depth, 2D-grid 125*8-qubit 42-depth and 2D-Bristlecone 72-qubit 32-depth circuits. Our results present a memory-efficient method with a clear physical picture to simulate low-de…
Some multipartite quantum states can be generated in a sequential manner which may be implemented by various physical setups like microwave and optical cavity QED, trapped ions, and quantum dots etc. We analyze the general N to M qubits Universal Quantum Cloning Machine (UQCM) within a sequential generation scheme. We show that the N to M sequential UQCM is available. The case of d-level quantum states sequential cloning is also presented.
Existing quantum compilers focus on mapping a logical quantum circuit to a quantum device and its native quantum gates. Only simple circuit identities are used to optimize the quantum circuit during the compilation process. This approach misses more complex circuit identities, which could be used to optimize the quantum circuit further. We propose Quanto, the first quantum optimizer that automatically generates circuit identities. Quanto takes as input a gate set and generates provably correct circuit identities for the gate set. Quanto's automatic generation of circuit identities includes sin…
Sequences of commuting quantum operators can be parallelized using entanglement. This transformation is behind some optimal quantum metrology protocols and recent results on quantum circuit complexity. We show that dephasing quantum maps in arbitrary dimension can also be parallelized. This implies that for general dephasing noise the protocol with entanglement is not more fragile than the corresponding sequential protocol and, conversely, the sequential protocol is not less effective than the entangled one. We derive this result using tensor networks. Furthermore, we only use transformations …
Noise in quantum systems is a major obstacle to implementing many quantum algorithms on large quantum circuits. In this work, we study the effects of noise on the Rademacher complexity of quantum circuits, which is a measure of statistical complexity that quantifies the richness of classes of functions generated by these circuits. We consider noise models that are represented by convex combinations of unitary channels and provide both upper and lower bounds for the Rademacher complexities of quantum circuits characterized by these noise models. In particular, we find a lower bound for the Rade…
We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on it. The iterative optimization of the parameters allows us to circumvent the high-depth circuit. Theoretical investigation shows that a quantum circuit can approximate nonlinear functions, which is further confirmed by numerical simulations. Hybridizing a low-depth quantum circuit and a classical computer for machine learning, the proposed framework paves th…
Although many of works have been done in multivalued quantum logic synthesis, the question whether multivalued quantum circuits are more efficient than the conventional binary quantum circuits is still open. In this article we devote to the optimization of generic multivalued quantum circuits. The multivalued quantum Shannon decompositions (QSD) are improved so that the circuits obtained are asymptotically optimal for all dimensionality d. The syntheses of uniformly multifold controlled $R_y$ rotations are also optimized to make the circuits further simplified. Moreover, the theoretical lower …
We propose a quantum communication protocol that can be used to transmit any quantum state, one party to another via several intermediate nodes, securely on quantum communication network. The scheme makes use of the sequentially chained and approximate version of private quantum channels satisfying certain commutation relation of $n$-qubit Pauli operations. In this paper, we study the sequential structure, security analysis, and efficiency of the quantum sequential transmission (QST) protocol in depth.
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix, which can be non-unitary, in an efficient way. We also give both classical and quantum complexity analysis for these circuits and show…
Quantum algorithms and protocols are often presented as quantum circuits for a better understanding. We give a list of equivalence rules which can help in the analysis and design of quantum circuits. As example applications we study quantum teleportation and dense coding protocols in terms of a simple XOR swapping circuit and give an intuitive picture of a basic gate teleportation circuit.
We describe the implementation of weak quantum measurements in superconducting qubits, focusing specifically on transmon type devices in the circuit quantum electrodynamics architecture. To access this regime, the readout cavity is probed with on average a single microwave photon. Such low-level signals are detected using near quantum-noise-limited superconducting parametric amplifiers. Weak measurements yield partial information about the quantum state, and correspondingly do not completely project the qubit into an eigenstate. As such, we use the measurement record to either sequentially rec…
