R. Schack, C. M. Caves
We present two complementary ways in which Saraceno's symmetric version of the quantum baker's map can be written as a shift map on a string of quantum bits. One of these representations leads naturally to a family of quantizations of the baker's map.
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We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure for application of various entanglement measures. We find that, in general, the quantum baker's maps are good at generating entanglement, producing multipartite entanglement amongst the qubits close to that expected in random states. We investigate the evolution of several entanglement measures: the subsystem linear entropy, the concurrence to characterize entanglement between pairs of qubits, and two proposal…
By numerically simulating an implementation of the quantum baker's map on a 3-qubit NMR quantum computer based on the molecule trichloroethylene, we demonstrate the feasibility of quantum chaos experiments on present-day quantum computers. We give detailed descriptions of proposed experiments that investigate (a) the rate of entropy increase due to decoherence and (b) the phenomenon of hypersensitivity to perturbation.
We show that the coarse-grained quantum baker's map exhibits a linear entropy increase at an asymptotic rate given by the Kolmogorov-Sinai entropy of the classical chaotic baker's map. The starting point of our analysis is a symbolic representation of the map on a string of $N$ qubits, i.e., an $N$-bit register of a quantum computer. To coarse-grain the quantum evolution, we make use of the decoherent histories formalism. As a byproduct, we show that the condition of medium decoherence holds asymptotically for the coarse-grained quantum baker's map.
The quantum baker map possesses two symmetries: a canonical "spatial" symmetry, and a time-reversal symmetry. We show that, even when these features are taken into account, the asymptotic entangling power of the baker's map does not always agree with the predictions of random matrix theory. We have verified that the dimension of the Hilbert space is the crucial parameter which determines whether the entangling properties of the baker are universal or not. For power-of-two dimensions, i.e., qubit systems, an anomalous entangling power is observed; otherwise the behavior of the baker is consiste…
The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting generalized baker map arises if the stacking orders for the factor maps are allowed to interact. These maps are readily quantized, in such a way that the stacking interaction is entirely attributed to primary qubits in each map, if each subsystem has power-of-two Hilbert space dimension. We here study the particular example of two baker maps that interact via a con…
Because of a formal equivalence with the partition function of an Ising chain, the semiclassical traces of the quantum baker map can be calculated using the transfer-matrix method. We analyze the transfer matrices associated with the baker map and the symmetry-reflected baker map (the latter happens to be unitary but the former is not). In both cases simple quantum-circuit representations are obtained, which exhibit the typical structure of qubit quantum bakers. In the case of the baker map it is shown that nonunitarity is restricted to a one-qubit operator (close to a Hadamard gate for some p…
This paper reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance (NMR) quantum information processor. The experiments tested the sensitivity of the quantum chaotic map to perturbations. In the first experiment, the map was iterated forward and then backwards to provide benchmarks for intrinsic errors and decoherence. In the second set of experiments, the least significant qubit was perturbed in between the iterations to test the sensitivity of the quantum chaotic map to applied perturbations. These experiments are used to investigate p…
We present a broad family of quantum baker maps that generalize the proposal of Schack and Caves to any even Hilbert space with arbitrary boundary conditions. We identify a structure, common to all maps consisting of a simple kernel perturbed by diffraction effects. This "essential" baker's map has a different semiclassical limit and can be diagonalized analytically for Hilbert spaces spanned by qubits. In all cases this kernel provides an accurate approximation to the spectral properties - eigenvalues and eigenfunctions - of all the different quantizations.
Application of current and near-term quantum hardware to the electronic structure problem is highly limited by qubit counts, coherence times, and gate fidelities. To address these restrictions within the variational quantum eigensolver (VQE) framework, many recent contributions have suggested dressing the electronic Hamiltonian to include a part of electron correlation, leaving the rest to be accounted by VQE state preparation. We present a new dressing scheme that combines preservation of the Hamiltonian hermiticity and an exact quadratic truncation of the Baker-Campbell-Hausdorff expansion. …
The modular multiplication operator, a central subroutine in Shor's factoring algorithm, is shown to be a coherent superposition of two quantum bakers maps when the multiplier is 2. The classical limit of the maps being completely chaotic, it is shown that there exist perturbations that push the modular multiplication operator into regimes of generic quantum chaos with spectral fluctuations that are those of random matrices. For the initial state of relevance to Shor's algorithm we study fidelity decay due to phase and bit-flip errors in a single qubit and show exponential decay with shoulders…
We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.
Several kinds of qubit-string-based(QS-based) bit commitment protocols are presented, and a definition of information-theoretic concealing is given. All the protocols presented here are proved to be secure under this definition. We suggest an attack algorithm to obtain the local unitary transformation introduced in no-go theorem, which is used to attack the binding condition, then study the security of our QS-based bit commitment protocols under this attack via introducing a new concept "physical security of protocol". At last we present a practical QS-based bit commitment scheme against chann…
We investigate the problem of enhancement of mutual information by encoding classical data into entangled input states of arbitrary length and show that while there is a threshold memory or correlation parameter beyond which entangled states outperform the separable states, resulting in a higher mutual information, this memory threshold increases toward unity as the length of the string increases. These observations imply that encoding classical data into entangled states may not enhance the classical capacity of quantum channels.
In this paper fields of quantum reference frames based on gauge transformations of rational string states are described in a way that, hopefully, makes them more understandable than their description in an earlier paper. The approach taken here is based on three main points: (1) There are a large number of different quantum theory representations of natural numbers, integers, and rational numbers as states of qubit strings. (2) For each representation, Cauchy sequences of rational string states give a representation of the real (and complex) numbers. A reference frame is associated to each rep…
In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by 't Hooft. Our result illustrates a new Baker-Campbell-Hausdorff formula with terminating series expansion.
High-Precision Observable Estimation with Single Qubit Quantum Memory
针对多量子比特可观测量估计中散粒噪声累积问题，提出利用单量子比特量子存储器累积测量数据，以更少交互次数实现高精度估计，所需测量次数随泡利字符串数按N^(2/3)规模减少。
Scalable quantum circuits for exponential of Pauli strings and Hamiltonian simulations
本研究设计了可在低连接度硬件实现的泡利字符串指数量子电路，验证其可扩展性，将其用于多类哈密顿量演化模拟，18量子比特下精度接近数值Trotter误差，且在NISQ量级噪声下表现稳定。
We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.
Trapped-ion quantum computers have demonstrated high-performance gate operations in registers of about ten qubits. However, scaling up and parallelizing quantum computations with long one-dimensional (1D) ion strings is an outstanding challenge due to the global nature of the motional modes of the ions which mediate qubit-qubit couplings. Here, we devise methods to implement scalable and parallel entangling gates by using engineered localized phonon modes. We propose to tailor such localized modes by tuning the local potential of individual ions with programmable optical tweezers. Localized mo…
Necessary and Sufficient Conditions for Universal Gates with Pauli Strings and Beyond
研究由 Pauli 字符串或一般哈密顿量生成的量子门通用性，给出了生成 su(2^n) 的必要充分条件，并证明了 XYZ 海森堡哈密顿量在局部控制下的通用性。
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained in the string. We define the quantum Kolmogorov complexity of a qubit string as the length of the shortest quantum input to a universal quantum Turing machine that produces the initial qubit string with high fidelity. The definition of Vitanyi (Proceedings of the 15th IEEE Annual Conference on Computation…
Enhancement of Harvesting Vacuum Entanglement in Cosmic String Spacetime
研究宇宙弦时空中量子比特对通过Unruh-DeWitt探测器提取真空纠缠，引入海森堡XY相互作用增强纠缠，发现靠近宇宙弦及共振点可提升纠缠提取。
A photon-interfaced ten qubit quantum network node
本文展示一个十量子比特光子接口量子网络节点，利用可切换囚禁势和光学腔使十个离子逐个与光子纠缠，获得92(1)%的平均Bell态保真度。
One of the key compilation steps in Quantum Computing (QC) is to determine an initial logical to physical mapping of the qubits used in a quantum circuit. The impact of the starting qubit layout can vastly affect later scheduling and placement decisions of QASM operations, yielding higher values on critical performance metrics (gate count and circuit depth) as a result of quantum compilers introducing SWAP operations to meet the underlying physical neighboring and connectivity constraints of the quantum device. In this paper we introduce a novel qubit mapping approach, string-based qubit mappi…
We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on at least R^2 qubits. Composite particles that consist of two monopoles (dipoles) and f…
The thesis is divided into three parts. In the first part a new theoretical analysis of interferometric experiments by Alley-Shih, Ou-Mandel and the entanglement swapping experiment is performed. It is shown that the double- and single-photon distinguishability is not necessary for the experiments to be genuine tests against local realism. In the second part, basing on simple geometrical properties of Hilbert space, new, stronger Bell inequalities for M qubits in a maximally entangled state are derived. Application of the same method to two maximally entangled qubits yields an inequality for a…
We present a scheme for multi-bit quantum random number generation using a single qubit discrete-time quantum walk in one-dimensional space. Irrespective of the initial state of the qubit, quantum interference and entanglement of particle with the position space in the walk dynamics certifies high randomness in the system. Quantum walk in a position space of dimension $2^l+1$ ensures string of $(l+ 2)$-bits of random numbers from a single measurement. Bit commitment with the position space and control over the spread of the probability distribution in position space enable us with options to e…
Quantum expectation value estimation by doubling the number of qubits
本研究评估了一种通过将量子比特数量加倍并在 Bell basis 中相干测量两份量子态，以同时估计所有 Pauli strings 期望值绝对值的方法，数值实验表明在中等精度下可显著减少测量次数。
We show that any sequence of measurements on a permutationally-symmetric (pure or mixed) multi-qubit string leaves the unmeasured qubit substring also permutationally-symmetric. In addition, we show that the measurement probabilities for an arbitrary sequence of single-qubit measurements are independent of how many unmeasured qubits have been lost prior to the measurement. Our results are valuable for quantum information processing of indistinguishable particles by post-selection, e.g. in cases where the results of an experiment are discarded conditioned upon the occurrence of a given event su…
On The Study Of Partial Qubit Hamiltonian For Efficient Molecular Simulation Using Variational Quantum Eigensolvers
本文提出部分量子比特哈密顿量方法（PHA），通过逐项筛选泡利字符串构建截断哈密顿量，以更低计算成本实现高效VQE分子模拟，并可用于复杂系统初始化和抑制量子电路噪声误差。
Recently it has been observed that the group $E_7$ can be used to describe a special type of quantum entanglement of seven qubits partitioned into seven tripartite systems. Here we show that this curious type of entanglement is entirely encoded into the discrete geometry of the Fano plane. We explicitly work out the details concerning a qubit interpretation of the $E_7$ generators as representatives of tripartite protocols acting on the 56 dimensional representation space. Using these results we extend further the recently studied analogy between quantum information theory and supersymmetric b…
In secure quantum communication protocols, a set of single qubits prepared using 2 or more mutually unbiased bases or a set of $n$-qubit ($n\geq2$) entangled states of a particular form are usually used to form a verification string which is subsequently used to detect traces of eavesdropping. The qubits that form a verification string are referred to as decoy qubits, and there exists a large set of different quantum states that can be used as decoy qubits. In the absence of noise, any choice of decoy qubits provides equivalent security. In this paper, we examine such equivalence for noisy env…
It has been suggested that reality works like a quantum computer, but such claims are just words if they are not backed up by sound mathematics. In pursuit of the fundamental equations I look to string theory where physicists led by Mike Duff have noticed useful connections between the quantum gravity of black holes and quantum information theory. By building on my earlier work on universal symmetry in string theory and using links between elliptic curves and hyperdeterminants, I find intriguing clues that these connections may be deep as well as useful. Ultimately any theory of the foundation…
Quantum memory assisted observable estimation
针对 Pauli 字符串测量中散粒噪声累积的问题，提出 CPS 方法，利用单量子比特量子存储器相干累积信息，使给定方差所需测量次数随 Pauli 字符串数量线性减少。
The scheduling problem consists of finding a common 1 in two remotely located N bit strings. Denote the number of 1s in the string with the fewer 1s by epsilon*N. Classically, it needs at least O(epsilon*N) bits of communication to find the common 1 (ignoring logarithmic factors). The best known quantum algorithm would require O(sqrt(N)) qubits of communication. This paper gives a modified quantum algorithm to find the common 1 with only O(sqrt(epsilon*N)) qubits of communication.
We study quantum information properties of a seven-level system realized by a particle in an one-dimensional square-well trap. Features of encodings of seven-level systems in a form of three-qubit or qubit-qutrit systems are discussed. We use the three-qubit encoding of the system in order to investigate subadditivity and strong subadditivity conditions for the thermal state of the particle. The qubit-qutrit encoding is employed to suggest a single qudit algorithm for calculation of parity of a bit string. Obtained results indicate on the potential resource of multilevel systems for realizatio…
The first achievement of quantum supremacy has been claimed recently by Google for the random quantum circuit benchmark with 53 superconducting qubits. Here, we analyze the randomness of Google's quantum random-bit sampling. The heat maps of Google's random bit-strings show stripe patterns at specific qubits in contrast to the Haar-measure or classical random-bit strings. Google's data contains more bit 0 than bit 1, i.e., about 2.8\% difference, and fail to pass the NIST random number tests, while the Haar-measure or classical random-bit samples pass. Their difference is also illustrated by t…
We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of quantum computation with magic states on qubits that satisfy three simple postulates. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.
Decomposition of multi-qutrit gates generated by Weyl-Heisenberg strings
本文针对量子三态系统，开发将外尔-海森堡算子张量积指数分解的算法，并扩展到盖尔曼串生成的酉运算，用于分解多量子三态门，应用于图k着色问题的量子近似优化算法，还解决了路由挑战。
The theory of quantum trajectories is applied to simulate the effects of quantum noise sources induced by the environment on quantum information protocols. We study two models that generalize single qubit noise channels like amplitude damping and phase flip to the many-qubit situation. We calculate the fidelity of quantum information transmission through a chaotic channel using the teleportation scheme with different environments. In this example, we analyze the role played by the kind of collective noise suffered by the quantum processor during its operation. We also investigate the stability…
We present a bit-string quantum oblivious transfer protocol based on single-qubit rotations. Our protocol is built upon a previously proposed quantum public-key protocol and its practical security relies on the laws of Quantum Mechanics. Practical security is reflected in the fact that, due to technological limitations, the receiver (Bob) of the transferred bit-string is restricted to performing only "few-qubit" coherent measurements. We also present a single-bit oblivious transfer based on the proposed bit-string protocol. The protocol can be implemented with current technology based on optic…
A quantum random access memory (QRAM) using a polynomial encoding of binary strings
本文提出基于比特串多项式编码的QRAM设计$\text{QRAM}_{poly}$，通过Clifford+T电路优化T深度与T计数，并在T深度上实现指数级改进，同时结合两个QRAM设计了双重指数级改进T深度的量子查找表$\text{qLUT}_{poly}$。
Random quantum sampling, a task to sample bit-strings from a random quantum circuit, is considered one of suitable benchmark tasks to demonstrate the outperformance of quantum computers even with noisy qubits. Recently, random quantum sampling was performed on the Sycamore quantum processor with 53 qubits [Nature 574, 505 (2019)] and on the Zuchongzhi quantum processor with 56 qubits [Phys. Rev. Lett. 127, 180501 (2021)]. Here, we analyze and compare statistical properties of the outputs of random quantum sampling by Sycamore and Zuchongzhi. Using the Marchenko-Pastur law and the Wasssertein d…
Floquet symmetry protected topological (FSPT) phases are non-equilibrium topological phases enabled by time-periodic driving. FSPT phases of 1d chains of bosons, spins, or qubits host dynamically protected edge states that can store quantum information without decoherence, making them promising for use as quantum memories. While FSPT order cannot be detected by any local measurement, here we construct non-local string order parameters that directly measure general 1d FSPT order. We propose a superconducting-qubit array based realization of the simplest Ising-FSPT, which can be implemented with…
Efficiently manipulating Pauli strings with PauliArray
本文介绍PauliArray库，基于NumPy高效表示和操作泡利字符串数组，支持广播，加速费米子映射、期望值估计和对易子计算。
Any unitary transformation can be decomposed into a product of a group of near-trivial transformations. We investigate in details the construction of universal quantum circuit of near trivial transformations. We first construct two universal quantum circuits which can implement any single-qubit rotation $R_y(θ)$ and $R_z(θ)$ within any given precision, and then we construct universal quantum circuit implementing any single-qubit transformation within any given precision. Finally, a universal quantum circuit implementing any $n$-qubit near-trivial transformation is constructed using the univers…
PACOX: A FPGA-based Pauli Composer Accelerator for Pauli String Computation
PACOX是一种基于FPGA的Pauli编译器加速器，通过紧凑编码和并行架构高效计算Pauli字符串，实现高速度和低功耗。
In this work we study several models of decoherence and how different quantum maps and algorithms react when perturbed by them. Following closely Ref. [1], generalizations of the three paradigmatic one single qubit quantum channels (these are the depolarizing channel, the phase damping channel and the amplitude damping channel) for the case of an arbitrarily-sized finite-dimensional Hilbert space are presented, as well as other types of noise in phase space. More specifically, Grover's search algorithm's response to decoherence is analyzed; together with those of a family of quantum versions o…
Qubit-efficient quantum combinatorial optimization solver
本文提出一种量子比特效率更高的算法，通过将候选位串映射到更少量子比特的纠缠波函数，克服了当前量子计算机量子比特数量不足的问题，并为Sherrington-Kirkpatrick自旋玻璃问题提供了性能保证。
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the Intercept/Resend attack), …
Sufficient conditions for quantum advantage in random access code protocols with two-qubit states
该研究针对单比特通信、共享两量子比特态的量子随机存取码协议，推导了n=2、3时实现量子优势的充分条件，发现可分态可作为量子优势资源，同时证明n≥4时单份量子态辅助的RAC无量子优势。
An explicit algorithm for performing Schumacher's noiseless compression of quantum bits is given. This algorithm is based on a combinatorial expression for a particular bijection among binary strings. The algorithm, which adheres to the rules of reversible programming, is expressed in a high-level pseudocode language. It is implemented using $O(n^3)$ two- and three-bit primitive reversible operations, where $n$ is the length of the qubit strings to be compressed. Also, the algorithm makes use of $O(n)$ auxiliary qubits; however, space-saving techniques based on those proposed by Bennett are de…
We find multiple relations between extremal black holes in string theory and 2- and 3-qubit systems in quantum information theory. We show that the entropy of the axion-dilaton extremal black hole is related to the concurrence of a 2-qubit state, whereas the entropy of the STU black holes, BPS as well as non-BPS, is related to the 3-tangle of a 3-qubit state. We relate the 3-qubit states with the string theory states with some number of D-branes. We identify a set of "large" black holes with the maximally entangled GHZ-class of states and "small" black holes with separable, bipartite and W sta…
Ultralow-power coherent qubit control using AQFP logic at millikelvin temperatures
本文提出一种超低功耗量子比特控制器，利用Adiabatic量子-通量-参数顿（AQFP）逻辑在毫开尔文温度下实现多频微波脉冲生成，通过微波和时间分片复用技术实现多个量子比特的X和虚拟Z门并行操作，且无相干退相干。
All existing quantum oblivious transfer protocols are to realize the oblivious transfer of bit or bit-string. In this paper, p-Rabin quantum oblivious transfer of a qubit (abbr. p-Rabin qubit-OT) is achieved by using a probabilistic teleportation (abbr. PT) protocol. Here, this is the first time that the concept of qubit-OT is presented. As the PT protocol is able to transfer an (un)known pure state with a certain probability, this feature makes the PT protocol well fit for Rabin OT. Furthermore, the PT protocol can be used for OT of a bit by encoding classical bit with two pre-agreed orthogon…
Simulating fermionic lattice models with qubits requires mapping fermionic degrees of freedom to qubits. The simplest method for this task, the Jordan-Wigner transformation, yields strings of Pauli operators acting on an extensive number of qubits. This overhead can be a hindrance to implementation of qubit-based quantum simulators, especially in the analog context. Here we thus review and analyze alternative fermion-to-qubit mappings, including the two approaches by Bravyi and Kitaev and the Auxiliary Fermion transformation. The Bravyi-Kitaev transform is reformulated in terms of a classical …
The universality theorem in quantum computing states that any quantum computational task can be decomposed into a finite set of logic gates operating on one and two qubits. However, the process of such decomposition is generally inefficient, often leading to exponentially many gates to realize an arbitrary computational task. Practical processor designs benefit greatly from availability of multi-qubit gates that operate on more than two qubits to implement the desired circuit. In 1995, Cirac and Zoller proposed a method to realize native multi-qubit controlled-$Z$ gates in trapped ion systems,…
The realization of novel phases of matter on quantum simulators is a topic of intense interest. Digital quantum computers offer a route to prepare topological phases with interactions that do not naturally arise in analog quantum simulators. Here, we report the realization of symmetry-protected topological (SPT) phases of a spin-{1/2} Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor. We observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string order parameters. …
High-fidelity two-qubit gates in a 7-qubit register for quantum networks
在基于金刚石氮空位中心的7量子比特寄存器中，通过优化串扰和门层析表征，实现了平均99.18%的双量子比特门保真度，达到分布式量子计算阈值，并演示了VQE分子模拟。
Qubit-based distributed frame synchronization for quantum key distribution
针对QKD中经典基于量子比特的同步在连续和高损耗系统中表现不佳的问题，提出一种基于量子比特的分布式帧同步方法，能在连续运行系统中实现时间恢复并抵抗更高损耗，性能优于Qubit4Sync，适用于无人机QKD和量子网络构建等场景。
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