Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid quantum-classical algorithm for time evolving a one-dimensional uniform system in the thermodynamic limit. This algorithm uses a layered uniform sequential quantum circuit as a variational ansatz to represent infinite translation-invariant quantum states. We show numerically that this ansatz requires a number of parameters polynomial in the simulation time for a given accuracy. Furthermore, this favourable scaling of the ansatz is maintained during our variational evolution algorithm. All steps of the hybrid optimization are designed with near-term digital quantum computers in mind. After benchmarking the evolution algorithm on a classical computer, we demonstrate the measurement of observables of this uniform state using a finite number of qubits on a cloud-based quantum processing unit. With more efficient tensor contraction schemes, this algorithm may also offer improvements as a classical numerical algorithm.
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）
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）
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…
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）
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）
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…
In order to establish the computational equivalence between quantum Turing machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit simulation of QTMs, we previously introduced the class of uniform QCFs based on an infinite set of elementary gates, which has been shown to be computationally equivalent to the polynomial-time QTMs (with appropriate restriction of amplitudes) up to bounded error simulation. This result implies that the complexity class BQP introduced by Bernstein and Vazirani for QTMs equals its counterpart for uniform QCFs. However, the complexity classes …
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 study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the "useless" uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we…
We develop a quantum circuit model describing unitary interactions between quantum fields and a uniformly accelerated object, and apply it to a semi-transparent mirror which uniformly accelerates in the Minkowski vacuum. The reflection coefficient $R_ω$ of the mirror varies between 0 and 1, representing a generalization of the perfect mirror ($R_ω=1$) discussed extensively in the literature. Our method is non-perturbative, not requiring $R_ω \sim 0$. We use the circuit model to calculate the radiation from an eternally accelerated mirror and obtain a finite particle flux along the past horizon…
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.
Yao (1993) proved that quantum Turing machines and uniformly generated quantum circuits are polynomially equivalent computational models: $t \geq n$ steps of a quantum Turing machine running on an input of length $n$ can be simulated by a uniformly generated family of quantum circuits with size quadratic in $t$, and a polynomial-time uniformly generated family of quantum circuits can be simulated by a quantum Turing machine running in polynomial time. We revisit the simulation of quantum Turing machines with uniformly generated quantum circuits, which is the more challenging of the two simulat…
Variational Approach for Uniform Quantum Permutation Generators
University of Ottawa（渥太华大学）；IMDEA Networks Institute（IMDEA网络研究所）；ETH, Zurich（苏黎世联邦理工学院）；IMDEA Software Institute（IMDEA软件研究所）；Dipartimento di Ingegneria, Università degli Studi di Palermo（巴勒莫大学工程学院）
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. …
A long standing obstacle to realizing highly sought on-chip monolithic solid state quantum optical circuits has been the lack of a starting platform comprising buried (protected) scalable spatially ordered and spectrally uniform arrays of on-demand single photon sources (SPSs). In this paper we report the first realization of such SPS arrays based upon a class of single quantum dots (SQDs) with single photon emission purity > 99.5% and uniformity < 2nm. Such SQD synthesis approach offers rich flexibility in material combinations and thus can cover the emission wavelength regime from long- to m…
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…
A quantum circuit to construct all maximal cliques using Grover search algorithm is presented. This oracle circuit takes as input an n-qubit state |x> and the adjacency matrix data A of an n-node network, and outputs the state (-1)^f(x) |x> where f(x)=1 if |x> is a maximal clique, and f(x)=0, otherwise. The oracle workspace requires 2n^2 qubits. Each oracle call makes about 10n^2 calls to the Toffoli gates. The overall Grover search algorithm takes as input a uniform superposition n-qubit state and the adjacency matrix data, and outputs a uniform superposition of all maximal clique states.
Absence of poor local minima in matrix product states
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Department of Physics, Princeton University（普林斯顿大学物理系）
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…
Deutsch proposed two sorts of models of quantum computers, quantum Turing machines (QTMs) and quantum circuit families (QCFs). In this paper we explore the computational powers of these models and re-examine the claim of the computational equivalence of these models often made in the literature without detailed investigations. For this purpose, we formulate the notion of the codes of QCFs and the uniformity of QCFs by the computability of the codes. Various complexity classes are introduced for QTMs and QCFs according to constraints on the error probability of algorithms or transition amplitud…
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…
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…
An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in accuracy by utilizing the high dimensionality of the Hilbert space as feature space. But is the ability of a quantum circuit to uniformly address the Hilbert space a good indicator of classification accuracy? In our work, we use methods and quantifications from prior art to perform a numerical study in order to evaluate the level of correlation. We find a stron…
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…
We consider a unitary transformation which maps any given state of an $n$-qubit quantum register into another one. This transformation has applications in the initialization of a quantum computer, and also in some quantum algorithms. Employing uniformly controlled rotations, we present a quantum circuit of $2^{n+2}-4n-4$ CNOT gates and $2^{n+2}-5$ one-qubit elementary rotations that effects the state transformation. The complexity of the circuit is noticeably lower than the previously published results. Moreover, we present an analytic expression for the rotation angles needed for the transfor…
