We consider the long-time limit of out-of-time-order correlators (OTOCs) in two classes of quantum lattice models with time evolution governed by local unitary quantum circuits and maximal butterfly velocity $v_{B} = 1$. Using a transfer matrix approach, we present analytic results for the long-time value of the OTOC on and inside the light cone. First, we consider `dual-unitary' circuits with various levels of ergodicity, including the integrable and non-integrable kicked Ising model, where we show exponential decay away from the light cone and relate both the decay rate and the long-time value to those of the correlation functions. Second, we consider a class of kicked XY models similar to the integrable kicked Ising model, again satisfying $v_{B}=1$, highlighting that maximal butterfly velocity is not exclusive to dual-unitary circuits.
We examine Ralph's equivalent circuit model of D-CTCs, which was proposed to derive Deutsch's maximum entropy rule of D-CTCs. By constructing counterexamples we show that the equivalent circuit model does not always reproduce the unique fixed state with the maximal von Neumann entropy. We speculate that the equivalent circuit model remains the correct description of D-CTCs and it can reproduce a revised maximum entropy rule of D-CTCs. We also suggest that the revised maximum entropy rule may eliminate the discontinuous quantum evolutions of D-CTCs.
Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of circuit errors are also analyzed; these generate a family of related asymmetric LDPC codes of varying degeneracy. More generally, such a family is associated with any quantum code. Implications for decoding highly-degenerate qua…
The butterfly velocity $v_B$ has been proposed as a characteristic velocity for information propagation in local systems. It can be measured by the ballistic spreading of local operators in time (or, equivalently, by out-of-time-ordered commutators). In general, this velocity can depend on the direction of spreading and, indeed, the asymmetry between different directions can be made arbitrarily large using arbitrarily deep quantum circuits. Nevertheless, in almost all examples of local time-independent Hamiltonians that have been examined thus far, this velocity is independent of the direction…
Finding a maximum or minimum is a fundamental building block in many mathematical models. Compared with classical algorithms, Durr, Hoyer's quantum algorithm (DHA) achieves quadratic speed. However, its key step, the quantum exponential searching algorithm (QESA), which is based on Grover algorithm, is not a sure-success algorithm. Meanwhile, quantum circuits encounter the gate decomposition problem due to variation of the scale of data. In this paper, we propose an optimized quantum algorithm for searching maximum and minimum, based on DHA and the optimal quantum exact search algorithm. Furth…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently know about the capabilities of QAOA, or of the difficulty of the requisite parameters optimization. Here, we study the performance of QAOA on the MaxCut combinatorial optimization problem, optimizing the quantum circuits on a classical computer using automatic differentiation and stochastic gradient descent, using QuantumFlow, a quantum circuit simulator implem…
We present an electronic circuit which simulates wave propagation in dispersive media. The circuit is an array of phase shifter composed of operational amplifiers and can be described with a discretized version of one-dimensional wave equation for envelopes. The group velocity can be changed both spatially and temporarily. It is used to emulate slow light or stopped light, which has been realized in a medium with electromagnetically induced transparency (EIT). The group-velocity control of optical pulses is expected to be a useful tool in the field of quantum information and communication.
Scalability from single qubit operations to multi-qubit circuits for quantum information processing requires architecture-specific implementations. Semiconductor hybrid qubit architecture is a suitable candidate to realize large scale quantum information processing, as it combines a universal set of logic gates with fast and all-electrical manipulation of qubits. We propose an implementation of hybrid qubits, based on Si Metal-Oxide-Semiconductor (MOS) quantum dots, compatible with the CMOS industrial technologic standards. We discuss the realization of multi-qubit circuits capable of fault-to…
Whether noisy quantum devices without error correction can provide quantum advantage over classical computers is a critical issue of current quantum computation. In this work, the random quantum circuits, which are used as the paradigm model to demonstrate quantum advantage, are simulated with depolarizing noise on experiment relevant two-dimensional architecture. With comprehensive numerical simulation and theoretical analysis, we find that the maximum achievable operator entanglement entropy, which indicates maximal simulation cost, has area law scaling with the system size for constant nois…
We observe how an active (i.e., requring $2^n$ parallel control operations) QRAM-like effect $$\sum_{y=0}^{N-1} |y\rangle\langle y| \otimes U^y_{\text{result},\text{memory}_y}$$ can be realized, as a quantum circuit of depth $O(n+\sqrt m)$ (where $m$ is the size of the result register) plus the maximum over all~$z$ of the circuit depths of controlled-$U^z$ operations.
We discover the quantum analog of the well-known classical maximum power transfer theorem. Our theoretical framework considers the continuous steady-state problem of coherent energy transfer through an N-node bosonic network coupled to an external dissipative load. We present an exact solution for optimal power transfer in the form of the maximum power transfer theorem known in the design of electrical circuits. We provide analytical expressions for both the maximum power delivered to the load as well as the energy transfer efficiency which are exact analogs to their classical counterparts. Ou…
We derive a dynamical bound on the propagation of correlations in local random quantum circuits - lattice spin systems where piecewise quantum operations - in space and time - occur with classical probabilities. Correlations are quantified by the Frobenius norm of the commutator of two positive operators acting on space-like separated local Hilbert spaces. For times $t=O(L)$ correlations spread to distances $\mathcal{D}=t$ growing, at best, diffusively for any distance within that radius with extensively suppressed distance dependent corrections whereas for $t=o(L^2)$ all parts of the system g…
A global quantum quench can be modeled by a quantum circuit with local unitary gates. In general, entanglement grows linearly at a rate given by entanglement velocity, which is upper bounded by the growth of the light cone. We show that the unitary interactions achieving the maximal rate must remain unitary if we exchange the space and time directions -- a property known as dual unitarity. Our results are robust: approximate maximal entanglement velocity also implies approximate dual unitarity. We further show that maximal entanglement velocity is always accompanied by a specific dynamical pat…
We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely related algorithms in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This make it possible to implement the last two algorithms by Hamiltonian evolution on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm.
Generative learning of time series with holographic quantum circuit sampling
University of Southern California（南加州大学）；Applied Quantum Software（应用量子软件）；Triaxiom Capital, LLC（Triaxiom资本有限责任公司）；Department of Physics and Astronomy, University of Southern California（南加州大学物理与天文学系）
We explore quantum dynamics in Floquet many-body systems with local conservation laws in one spatial dimension, focusing on sectors of the Hilbert space which are highly polarized. We numerically compare the predicted charge diffusion constants and quantum butterfly velocity of operator growth between models of chaotic Floquet dynamics (with discrete spacetime translation invariance) and random unitary circuits which vary both in space and time. We find that for small but finite polarization per length (in the thermodynamic limit), the random unitary circuit correctly predicts the scaling of t…
The use of quantum computation for wireless network applications is emerging as a promising paradigm to bridge the performance gap between in-practice and optimal wireless algorithms. While today's quantum technology offers limited number of qubits and low fidelity gates, application-based quantum solutions help us to understand and improve the performance of such technology even further. This paper introduces QGateD-Polar, a novel Quantum Gate-based Maximum-Likelihood Decoder design for Polar error correction codes, which are becoming widespread in today's 5G and tomorrow's NextG wireless net…
This is an investigation of the limits of quantum circuit simulation with Schrodinger's formulation and low precision arithmetic. The goal is to estimate how much memory can be saved in simulations that involve random, maximally entangled quantum states. An arithmetic polar representation of $B$ bits is defined for each quantum amplitude and a normalization procedure is developed to minimize rounding errors. Then a model is developed to quantify the cumulative errors on a circuit of $Q$ qubits and $G$ gates. Depending on which regime the circuit operates, the model yields explicit expressions …
The hallmark of superfluidity is the appearance of "vortex states" carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will randomize the velocity, as in the Drude model, and eventually the ergodic steady state will be characterized by a vanishingly small fluctuating current. However, Landau and followers have shown that this is not always the case. If elementary excitations (e.g. phonons) have higher velocity than that of the flow, simple kinematic considerations imply metastability of…
The polarization emerging in the subsequent scattering processes can never exceed $1$ which corresponds to the fully polarized pure state. This property is shown to be provided by the addition rule similar to that for relativistic velocities never exceeding the speed of light. The cases of spin $1/2$ and $1$ are considered. The photon linear polarization in Thomson scattering is monotonically increasing. This directness is shown to be a consequence of spin measurement procedure and may be the particular example of ithe anticipated relation between quantum measurement and time irreversibility. …
We consider a method to reduce the kinetic energy in a low-order mode of a miniature cantilever. If the cantilever contributes to the capacitance of a driven RF circuit, a force on the cantilever exists due to the electric field energy stored in the capacitance. If this force acts with an appropriate phase shift relative to the motion of the cantilever, it can oppose the velocity of the cantilever, leading to cooling. Such cooling may enable reaching the quantum regime of cantilever motion.
We consider the feedback stabilization of Rabi oscillations in a superconducting qubit which is coupled to a microwave readout cavity. The signal is readout by homodyne detection of the in-phase quadrature amplitude of the weak measurement output. By multiplying the time-delayed Rabi reference, one can extract the signal, with maximum signal-to-noise ratio, from the noise. We further track and stabilize the Rabi oscillations by using Lyapunov feedback control to properly adjust the input Rabi drives. Theoretical and simulation results illustrate the effectiveness of the proposed control law.
Diners dilemma is one of the most interesting problems in both economic and game theories. Here, we solve this problem for n (number of players) =4 with quantum rules and we are able to remove the dilemma of diners between the Pareto optimal and Nash equilibrium points of the game. We find the quantum strategy that gives maximum payoff for each diner without affecting the payoff and strategy of others. We use the quantum principles of superposition and entanglement that gives supremacy over any classical strategies. We present the circuit implementation for the game, design it on the IBM quant…
On-chip integrated photonic circuits are crucial to further progress towards quantum technologies and in the science of quantum optics. Here we report precise control of single photon states and multi-photon entanglement directly on-chip. We manipulate the state of path-encoded qubits using integrated optical phase control based on resistive elements, observing an interference contrast of 98.2+/-0.3%. We demonstrate integrated quantum metrology by observing interference fringes with 2- and 4-photon entangled states generated in a waveguide circuit, with respective interference contrasts of 97.…
In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer coefficients. Next, as an application example, we formulate multiple-input multiple-output maximum likelihood detection as a HUBO problem with real-valued coefficients, where we use the Gray-coded bit-to-symbol mapping specified in the 5G standard. The proposed approach allows us to construct an efficient quantum circuit for the detection problem and to analyze s…
Quantum MeanFlow: single-shot generative sampling on NISQ hardware
Keio University（庆应义塾大学）；Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q)（人类生物学-微生物组-量子研究中心（WPI-Bio2Q））；Keio University Sustainable Quantum Artificial Intelligence Center (KSQAIC)（庆应义塾大学可持续量子人工智能中心（KSQAIC））；University of California, Berkeley（加州大学伯克利分校）
Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in 1D with Matrix Product Density Operators (MPDO), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on Matrix Product States (MPS) fails to approximate the noisy output quantum states for any of the noise models considered, while the MP…
We observe the quantum Zeno effect -- where the act of measurement slows the rate of quantum state transitions -- in a superconducting qubit using linear circuit quantum electrodynamics readout and a near-quantum-limited following amplifier. Under simultaneous strong measurement and qubit drive, the qubit undergoes a series of quantum jumps between states. These jumps are visible in the experimental measurement record and are analyzed using maximum likelihood estimation to determine qubit transition rates. The observed rates agree with both analytical predictions and numerical simulations. The…
We introduce a novel class of quantum circuits that are unitary along three distinct "arrows of time". These dynamics share some of the analytical tractability of "dual-unitary" circuits, while exhibiting distinctive and richer phenomenology. We find that two-point correlations in these dynamics are strictly confined to three directions in $(1+1)$-dimensional spacetime -- the two light cone edges, $δx=\pm vδt$, and the static worldline $δx=0$. Along these directions, correlation functions are obtained exactly in terms of quantum channels built from the individual gates that make up the circuit…
Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not least due to a polynomial-time decoding algorithm which admits one of the highest predicted error thresholds. We consider the dependence of this threshold on underlying assumptions including different noise models, and analyze the performance of a minimum weight perfect matching (MWPM) decoding compared to a mathematically optimal maximum likelihood (ML) dec…
Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory and holography. We tackle this problem in 1D spin-chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs), and entanglement growth in this setting. These results follow from the observation that the spreading of operators in random circuits is described by a `hydrodynamical' equation of motion, despite the fact that …
We consider quantum circuits with time travel designed for distinguishing specific nonorthogonal quantum states in two most popular models: Deutschs and postselected. We modify them by a presence of weakly coupled thermal environment. Using the Davies approximation we study how the thermal noise affects an ability of the circuits to distinguish nonorthogonal quantum states. We show that for purely dephasing environment a paradoxial power of such circuits remains preserved. We also present a physics based argument for conditions of validity of the maximum entropy rule introduced by David Deutsc…
The emerging quantum technological applications call for fast and accurate initialization of the corresponding devices to low-entropy quantum states. To this end, we theoretically study a recently demonstrated quantum-circuit refrigerator in the case of non-linear quantum electric circuits such as superconducting qubits. The maximum refrigeration rate of transmon and flux qubits is observed to be roughly an order of magnitude higher than that of usual linear resonators, increasing flexibility in the design. We find that for typical experimental parameters, the refrigerator is suitable for rese…
We study the propagation and amplification of a microwave field in a four-level cascade quantum system which is realized in a superconducting phase quantum circuit. It is shown that by increasing the microwave pump tones feeding the system, the normal dispersion switches to the anomalous and the gain-assisted superluminal microwave propagation is obtained in this system. Moreover, it is demonstrated that the stimulated microwave field is generated via four-wave mixing without any inversion population in the energy levels of the system (amplification without inversion) and the group velocity of…
We report on a robust method to achieve strong coupling between a superconducting flux qubit and a high-quality quarter-wavelength coplanar waveguide resonator. We demonstrate the progression from the strong to ultrastrong coupling regime by varying the length of a shared inductive coupling element, ultimately achieving a qubit-resonator coupling strength of 655 MHz, $10\%$ of the resonator frequency. We derive an analytical expression for the coupling strength in terms of circuit parameters and also discuss the maximum achievable coupling within this framework. We experimentally characterize …
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences（中国科学院大学拓扑量子计算卓越创新中心）
Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum circuits exhibit stronger expressibility compared to classical neural networks. One can efficiently draw samples from the quantum circuits via projective measurements on qubits. However, similar to the leading implicit generative models in deep learning, such as the generative adversarial networks, the quantum circuits cannot provide the likelihood of the gen…
