V. Vyurkov, L. Gorelik, A. Orlikovsky
Fano resonances are proposed to perform a measurement of a spin state (whether it is up or down) of a single electron in a quantum dot via a spin-polarized current in an adjacent quantum wire. Rashba-like spin-orbit interaction in a quantum dot prohibits spin-flip events (Kondo-like phenomenon). That ensures the measurement to be non-demolishing.
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We propose a scheme to realize a quantum non-demolition (QND) measurement of a superconducting flux qubit by a Josephson bifurcation amplifier. Our scheme can implement a perfect QND measurement for a qubit subject to a variable magnetic bias. Measurement back-action induced qubit relaxation can be suppressed and hence the QND fidelity is expected to be high over a wide range of bias conditions.
We show that, for any n > 0, the Heisenberg interaction among 2n qubits (as spin-1/2 particles) can be used to exactly implement an n-qubit parity gate, which is equivalent in constant depth to an n-qubit fanout gate. Either isotropic or nonisotropic versions of the interaction can be used. We generalize our basic results by showing that any Hamiltonian (acting on suitably encoded logical qubits), whose eigenvalues depend quadratically on the Hamming weight of the logical qubit values, can be used to implement generalized Mod_q gates for any q > 1. This paper is a sequel to quant-ph/0309163, a…
Quantum Fanout and GHZ states using spin-exchange interactions
本文利用2n个物理量子比特间非均匀自旋交换相互作用，给出常数深度实现n量子比特扇出和任意Mod_q门的精确耦合条件，并据此制备广义GHZ态。
Quantum Fanout Gates in Constant Depth via Resonance Engineering
本文提出利用共振工程实现n量子比特扇出门，通过Jaynes-Cummings相互作用在系统层面实现扇出门，并在常数时间内证明了线性保真度衰减，同时通过排列对称性将模拟复杂度从指数级降低到多项式级，支持100量子比特的模拟，展示了该门在稳定子读取和多项式加速中的潜力。
While quantum information processing by nuclear magnetic resonance (NMR) with small number of qubits is well established, implementation of lengthy computations have proved to be difficult due to decoherence/relaxation. In such circumstances, shallow circuits (circuits using parallel computation) may prove to be realistic. Parity and fanout gates are essential to create shallow circuits. In this article we implement inversion-on-equality gate, followed by parity gate and fanout gate in 3-qubit systems by NMR, using evolution under indirect exchange coupling Hamiltonian.
Kinetic inductance coupling for circuit QED with spins
本研究实现了Cr₇Ni分子自旋量子比特系综与颗粒铝超导微波谐振器动电感的纵向耦合，验证了其宽磁场测量能力与较长弛豫时间，并提出单自旋与fluxonium量子比特纵向耦合的研究方向。
Implementing the quantum fanout operation with simple pairwise interactions
该研究推广了量子扇出门的实现方案，证明耦合不等的两两相互作用哈密顿量可对任意n实现恒定深度(n+1)量子比特扇出门，还给出了平方反比律耦合下的实现判据与5量子比特扇出的平面排布方案。
Given the symplectic polar space of type $W(5,2)$, let us call a set of five Fano planes sharing pairwise a single point a Fano pentad. Once 63 points of $W(5,2)$ are appropriately labeled by 63 non-trivial three-qubit observables, any such Fano pentad gives rise to a quantum contextual set known as Mermin pentagram. Here, it is shown that a Fano pentad also hosts another, closely related contextual set, which features 25 observables and 30 three-element contexts. Out of 25 observables, ten are such that each of them is on six contexts, while each of the remaining 15 observables belongs to two…
We prove several new lower bounds for constant depth quantum circuits. The main result is that parity (and hence fanout) requires log depth circuits, when the circuits are composed of single qubit and arbitrary size Toffoli gates, and when they use only constantly many ancillæ. Under this constraint, this bound is close to optimal. In the case of a non-constant number $a$ of ancillae, we give a tradeoff between $a$ and the required depth, that results in a non-trivial lower bound for fanout when $a = n^{1-o(1)}$.
Finite projective geometries, especially the Fano plane, have been observed to arise in the context of certain quantum gate operators. We use Clifford algebras to explain why these geometries, both planar and higher dimensional, appear in the context of multi-qubit composite systems.
Magneto-optical isolators and circulators have been widely used to safeguard quantum devices from reflections and noise in the readout stage. However, these devices have limited bandwidth, low tunability, are bulky, and suffer from high losses, making them incompatible with planar technologies such as circuit QED. To address these limitations, we propose a new approach to quantum non-reciprocity that utilizes the intrinsic nonlinearity of qubits and broken spatial symmetry. We show that a circuit containing Lorentz-type qubits can be transformed into Fano-type qubits with an asymmetric spectra…
The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this paper, we show that the diamond norm can be conveniently and in a physically transparent way computed by means of a Monte-Carlo algorithm based on the Fano representation of quantum states and quantum operations. The effectiveness of this algorithm is illustrated for several single-qubit quantum channels.
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…
A geometric Fano--Procrustes framework for purification-based distances and quantum channels analysis
本文提出了一种基于净化的几何框架，用于分析混合的双量子比特态和量子通道，通过Fano表示法将净化过程参数化为Bloch矢量、辅助系统Bloch矢量和相关矩阵，并将净化优化问题转化为在SO(3)李群上的正交Procrustes问题，从而得到最大净化重叠和最优旋转，定义了净化偏移角Θ，提供几何信息。
Quantum acoustic Fano interference of surface phonons
本研究在表面声波谐振器耦合超导量子比特的系统中，观测到共振压电表面声波模式与连续谱表面声子的Fano干涉，揭示了弱耦合机械模式的影响，明确了声子干涉对量子信息处理用量子声学架构的重要性。
Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. These invariants are explicitly calculated in the particular case of pure as well as mixed spin-1 state.
Given the facts that the three-qubit symplectic polar space features three different kinds of observables and each of its labeled Fano planes acquires a definite sign, we found that there are 45 distinct types of Mermin pentagrams in this space. A key element of our classification is the fact that any context of such pentagram is associated with a unique (positive or negative) Fano plane. Several intriguing relations between the character of pentagrams' three-qubit observables and `valuedness' of associated Fano planes are pointed out. In particular, we find two distinct kinds of negative cont…
We introduce a three qubit waveguide QED system to mimic the cavity-QED strong coupling regime of a probe qubit embedded in atom-like mirrors, which was realized in recent experiments. We then extend this system into the deep non-Markovian regime and demonstrate the profound role that retardation plays on the dressed resonances, allowing one to significantly improve the polariton lifetimes (by many orders of magnitude), tune the resonances, as well as realize Fano-like resonances and simultaneous coupling to multiple cavity modes. Exact Green function solutions are presented for the spectral r…
A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of physics, especially in today's field of quantum information, as the number of basic operators of two quantum spins ("qubits"). This affords a 1:1 correspondence that we exploit to use the well-known Pauli spin or Lie-Clifford algebra of those fifteen operators to provide specific constructions as posed in the recreational problem. An algorithm is set up that, wo…
Polylogarithmic-Weight Dicke States in QAC$^0$ and Arbitrary Symmetric States in QAC$^0_f$
本文提出用常深电路生成超常权重迪克态，无需FANOUT门，且证明任意对称态可由FANOUT_k门在常深内生成。
We formulate a model for the steady state response of a nonlinear quantum oscillator structure, such as those used in a variety of superconducting qubit experiments, when excited by a steady, but not necessarily small, ac tone. We show that this model can be derived directly from a circuit description of some recent qubit experiments in which the state of the qubit is read out directly, without a SQUID magnetometer. The excitation profile has a rich structure depending on the detuning of the tone from the small-signal resonant frequency, on the degree of damping, and on the excitation amplitud…
A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schrödinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano…
The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as $1/r^α$ in the distance $r$ provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm t…
Controlling periodic Fano resonances of quantum acoustic waves with a giant atom coupled to microwave waveguide
本文提出利用超导量子比特与微波波导及叉指换能器耦合实现量子声波周期性Fano共振，并通过调节时间延迟和耦合强度精确控制共振形状，为量子信息处理与传感提供新途径。
The power of constant-depth quantum circuits of unbounded size
本文研究无界规模常数深度量子电路的能力，给出任意置换、对角酉和纯态制备的精确常数深度构造，并利用端口隐形传态实现任意酉的近似，深度为$O(\sqrt d)$。
We show that the quantum parity gate on $n > 3$ qubits cannot be cleanly simulated by a quantum circuit with two layers of arbitrary C-SIGN gates of any arity and arbitrary 1-qubit unitary gates, regardless of the number of allowed ancilla qubits. This is the best known and first nontrivial separation between the parity gate and circuits of this form. The same bounds also apply to the quantum fanout gate. Our results are incomparable with those of Fang et al. [3], which apply to any constant depth but require a sublinear number of ancilla qubits on the simulating circuit.
We show that the Fano representation leads to a particularly simple and appealing form of the quantum process tomography matrix $χ_{_F}$, in that the matrix $χ_{_F}$ is real, the number of matrix elements is exactly equal to the number of free parameters required for the complete characterization of a quantum operation, and these matrix elements are directly related to evolution of the expectation values of the system's polarization measurements. These facts are illustrated in the examples of one- and two-qubit quantum noise channels.
There is a intriguing relation between quantum information theory and super gravity, discovered by M.J. Duff and S. Ferrara. It relates entanglement measures for qubits to black hole entropy, which in a certain case involves the quartic invariant on the 56-dimensional representation of the Lie group E7. In this paper we recall the relatively straightforward manner in which three-qubits lead to E7, or at least to the Weyl group of E7. We also show how the Fano plane emerges in this context.
Mid-circuit measurements and feedforward implement every unitary exactly in constant depth
本文提出一种利用中间测量与前馈的确定性构造，将精确n量子比特酉合成的量子深度从Θ(n)降至O(1)，并给出深度-宽度权衡，在恒定深度内实现任意酉变换。
Operating semiconductor qubits without individual barrier gates
本文提出一种无需独立势垒栅极即可调谐半导体自旋量子比特间交换相互作用的方法，通过改变柱塞栅极电压实现两量子比特操作，简化制造并保持通用量子计算所需控制。
In this paper we use the Fano representation of two-qubit states from which we can identify a correlation matrix containing the information about the classical and quantum correlations present in the bipartite quantum state. To illustrate the use of this matrix, we analyze the behavior of the correlations under non-dissipative decoherence in two-qubit states with maximally mixed marginals. From the behavior of the elements of the correlation matrix before and after making measurements on one of the subsystems, we identify the classical and quantum correlations present in the Bell-diagonal stat…
We review some recently established connections between the mathematics of black hole entropy in string theory and that of multipartite entanglement in quantum information theory. In the case of N=2 black holes and the entanglement of three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant, provides both the black hole entropy and the measure of tripartite entanglement. In the case of N=8 black holes and the entanglement of seven qubits, the quartic E_7 invariant of Cartan provides both the black hole entropy and the measure of a particular tripartite entanglement encoded in t…
Quantum formulas, defined by Yao [FOCS '93], are the quantum analogs of classical formulas, i.e., classical circuits in which all gates have fanout one. We show that any read-once quantum formula over a gate set that contains all single-qubit gates is equivalent to a read-once classical formula of the same size and depth over an analogous classical gate set. For example, any read-once quantum formula over Toffoli and single-qubit gates is equivalent to a read-once classical formula over Toffoli and NOT gates. We then show that the equivalence does not hold if the read-once restriction is remov…
Small spin-qubit registers defined by single electrons confined in Si/SiGe quantum dots operate successfully and connecting these would permit scalable quantum computation. Shuttling the qubit carrying electrons between registers is a natural choice for high-fidelity coherent links provided the overhead of control signals stays moderate. Our proof-of-principle demonstrates shuttling of a single electron by a propagating wave-potential in an electrostatically defined 420 nm long Si/SiGe quantum-channel. This conveyor-mode shuttling approach requires independent from its length only four sinusoi…
Query and Depth Upper Bounds for Quantum Unitaries via Grover Search
本文通过Grover搜索证明了n量子比特单位元可近似在时间~O(2^{n/2})内实现，且可精确用深度~O(2^{n/2})的电路实现，同时给出了对应的下界。
Non-classical photon statistics in frequency-modulated double quantum dot cavity systems
研究频率调制双量子点腔系统的量子动力学，在特定条件下，通过法诺因子行为等证明输出腔电磁场由单光子通量构成，服从亚泊松量子光子统计，还探讨了声子等对光子量子特性的影响。
Crossover from Fast Scrambling to Operator Confinement Tuned by an Auxiliary Qubit
该研究提出含辅助量子比特的混合场伊辛链模型，通过调控无量纲参数 λ 实现快速 scrambling 与算符 confinement 的 crossover，揭示相关隐藏对称性，调和了星型几何两种 scrambling 行为的矛盾。
Random Unitaries in Constant (Quantum) Time
本文在多种常数时间量子计算模型中高效构造酉设计和伪随机酉变换，证明其可在比先前认为更弱的电路模型中实现，并由此推出在密码学假设下QAC^0电路类无多项式时间学习算法，为证明PARITY不在QAC^0中提供新思路。
Previous studies of photon-assisted tunneling through normal-metal-insulator-superconductor junctions have exhibited potential for providing a convenient tool to control the dissipation of quantum-electric circuits in-situ. However, the current literature on such a quantum-circuit refrigerator (QCR) does not present a detailed description for the charge dynamics of the tunneling processes or the phase coherence of the open quantum system. Here we derive a master equation describing both quantum-electric and charge degrees of freedom, and discover that typical experimental parameters of low tem…
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group $G$ with relations. A valid subgroup $H$ of index $d$ in $G$ leads to a 'magic' state $\left|ψ\right\rangle$ in $d$-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite 'contextual' geometry. In the present work, we choose $G$ as the fundamental group $π_1(V)$ of an exotic $4$-manifold $V$, more precisely a 'small exotic' (space-time) $R^4$ (that is homeomorphic and isometric, but no…
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