We introduce a novel bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the SLOCC protocols familiar in quantum information. Although the mathematical methods are the same the meaning of the gauge group will be different. The measure we introduce, `twist', is constructed as a Wilson loop from a correlation induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state globally using local operations, the twistedness is given by a non-trivial element of the Lorentz group, the correlation induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary non-trivial loop one can imagine.
We investigate the spontaneous emission spectrum of a qubit in a lossy resonant cavity. We use neither the rotating-wave approximation nor the Markov approximation. The qubit-cavity coupling strength is varied from weak, to strong, even to lower bound of the ultra-strong. For the weak-coupling case, the spontaneous emission spectrum of the qubit is a single peak, with its location depending on the spectral density of the qubit environment. Increasing the qubit-cavity coupling increases the asymmetry (the positions about the qubit energy spacing and heights of the two peaks) of the two spontane…
Controlled-NOT (CNOT) gates are commonly included in the standard gate set of quantum processors and provide an important way to entangle qubits. For fixed-frequency qubits using the cross-resonance entangling technique, using the higher-frequency qubit to control the lower-frequency qubit enables much shorter entangling times than using the lower-frequency qubit as the control. Consequently, when implementing a CNOT gate where logical control by the lower-frequency qubit is needed, compilers may implement this functionality by using an equivalent circuit such as placing Hadamard gates on both…
Superconducting circuits fabricated using the widely used shadow evaporation technique can contain unintended junctions which change their quantum dynamics. We discuss a superconducting flux qubit design that exploits the symmetries of a circuit to protect the qubit from unwanted coupling to the noisy environment, in which the unintended junctions can spoil the quantum coherence. We present a theoretical model based on a recently developed circuit theory for superconducting qubits and calculate relaxation and decoherence times that can be compared with existing experiments. Furthermore, the co…
We demonstrate that charge-qubit cluster state generation by capacitive coupling is anisotropic. Specifically, horizontal vs vertical nearest-neighbor inter-qubit coupling differs in a rectangular lattice. We show how to ameliorate this anisotropy by applying potential biases to the array of double dots.
We study the quantum simulation of Z2 lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e., with two temporal Wilson lines. Some results obtained by the simulator (with no hardware noise) and the real device (with sizable hardware noise) of a quantum computer are shown.
A conceptually simple model for strongly interacting compact U(1) lattice gauge theory is expressed as operators acting on qubits. The number of independent gauge links is reduced to its minimum through the use of Gauss's law. The model can be implemented with any number of qubits per gauge link, and a choice as small as two is shown to be useful. Real-time propagation and real-time collisions are observed on lattices in two spatial dimensions. The extension to three spatial dimensions is also developed, and a first look at 3-dimensional real-time dynamics is presented.
We extend recent work on a leakage-protected, adiabatic entangling gate for exchange-only spin qubits [Doherty and Wardrop, PRL 111, 050503 (2013)] by adapting to a setting where single spins are not assumed to be polarized on preparation. Previous gate constructions do not function correctly when "gauge spins" are uninitialized, because the entangling gate has different, non-trivial action in different gauge subspaces. Our construction inherits many of the desirable features of the previous work while addressing the gauge-dependent behavior. Using numerical simulation, we show that the result…
For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed minimal error probability (i.e., the minimal error distinguishability time). For the case of unitary dynamics generated by a time-independent Hamiltonian, we derive a necessary and sufficient condition on two asymmetry monotones that guarantees that an arbitrary state of a two-level quantum system or a separable state of $N$ two-level quantum systems will unitar…
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the…
We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite systems under local (gauge) transformations. This new formalism yields observable effects arising from the gauge geometry of the bipartite system. In particular, we propose a non-Abelian gauge theory realized via two separated spatial modes of the quantized electromagnetic field manipulated by linear optics. In this linear optical realization, a bi-partite st…
We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic quantum information theory. We then use this formulation to consider the transformation properties of qubits and density matrices under space-time and gauge transformations. Finally we use our results to understand the behaviour of entanglement between different partitions of quantum systems. Our approach not only clarifies the notation, but provides a more intui…
We propose to periodically modulate the onsite energy via two-tone drives, which can be furthermore used to engineer artificial gauge potential. As an example, we show that the fermionic ladder model penetrated with effective magnetic flux can be constructed by superconducting flux qubits using such two-tone-drive-engineered artificial gauge potential. In this superconducting system, the single-particle ground state can range from vortex phase to Meissner phase due to the competition between the interleg coupling strength and the effective magnetic flux. We also present the method to experimen…
We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (arXiv:1912.06133) as a basis for digital quantum computation easily solves an important problem of fundamental interest: implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in $d$ spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,'"so we decompose circuits that flag gauge invariant wavefunctions. We then analyze the logical qubi…
We consider a classical pure SU(2) gauge theory, and make an ansatz, which separates the space-temporal degrees of freedom from the internal ones. This ansatz is gauge-invariant but not Lorentz invariant. In a limit case of the ansatz, obtained through a contraction map, and corresponding to a vacuum solution, the SU(2) gauge field reduces to an operator, which is the product of the generator of a global U(1) group times a Pauli matrix. We give a geometrical interpretation of the ansatz and of the contraction map in the framework of principal fiber bundles. Then, we identify the internal degre…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance. Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarising noise from $0.67\%$ to $0.81\%$. The threshold increases further under a circuit-level noise model with small finite bias, up to $2.22…
We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli spin operators such that the simulation can be performed on a quantum computer using only one and two qubit manipulations. We examine three models, the U(1), SU(2), and SU(3) lattice gauge theories which are transcribed into a spin Hamiltonian up to a cutoff in the Hilbert space of the gauge fields on the lattice. The number of qubits required for storing a p…
Real-Time Observation of Aharonov-Bohm Interference in a $\mathbb{Z}_2$ Lattice Gauge Theory on a Hybrid Qubit-Oscillator Quantum Computer
Department of Physics, University of Oxford（牛津大学物理系）；Instituto de Física Teorica, UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学-西班牙国家科学研究委员会理论物理研究所）
We explore a geometric approach to generating local SU(2) and $SL(2,\mathbb{C})$ invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or 'gauge' invariant is associated to a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters and the gauge invariant observable associated to a particular closed path is given by the Wilson loop. In our approach the points of the lattice…
Z2 Lattice Gauge Theory on Non-trivial Topology and Its Quantum Simulation
Tsinghua University（清华大学）；Fudan University（复旦大学）；Southern University of Science and Technology（南方科技大学）；International Quantum Academy, Shenzhen（深圳国际量子研究院）；Shanghai Institute for Advanced Studies, University of Science and Technology of China（中国科学院上海高等研究院）
An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto qubit degrees of freedom is presented. This new mapping allows for a reduced unphysical Hilbert space. Insensitivity to interactions within this unphysical space is exploited to design more efficient quantum circuits. Local gauge symmetry is used to analytically incorporate the angular momentum alignment, leading to qubit registers encoding the total angular momentum on each link. The results of a multi-plaquette calculation on IBM's quantum hardware are presented.
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can always be globally distinguished. We establish the necessary and sufficient conditions for a general set of 2x2 quantum states to be locally distinguishable, and for a general set of 2xn quantum states to be distinguished given an initial measurement of the qubit. These results reveal a fundamental asymmetry to nonlocality, which is the origin of ``nonlocali…
We study the interaction of a two-level atom with a single-mode nonlinear electromagnetic resonator, considering coupling strengths ranging from zero to the so-called deep strong coupling regime. When the qubit-resonator coupling is very strong, the standard Kerr model for the resonator becomes questionable. Moreover, recently, it has been shown that extra care is needed when constructing gauge-independent theories in the presence of approximations as the truncation of the Hilbert space of the matter system. Such a truncation can ruin gauge invariance leading to non-physical results, especiall…
The state disturbance induced by locally measuring a quantum system yields a signature of nonclassical correlations beyond entanglement. Here we present a detailed study of such correlations for two-qubit mixed states. To overcome the asymmetry of quantum discord and the unfaithfulness of measurement-induced disturbance (severely overestimating quantum correlations), we propose an ameliorated measurement-induced disturbance as nonclassicality indicator, optimized over joint local measurements, and we derive its closed expression for relevant two-qubit states. We study its analytical relation w…
In circuit QED, a Rabi model can be derived by truncating the Hilbert space of the anharmonic qubit coupled to a linear, reactive environment. This truncation breaks the gauge invariance present in the full Hamiltonian. We analyze the determination of an optimal gauge such that the differences between the truncated and the full Hamiltonian are minimized. Here, we derive a simple criterion for the optimal gauge. We find that it is determined by the ratio of the anharmonicity of the qubit to an averaged environmental frequency. We demonstrate that the usual choices of flux and charge gauge are n…
Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests in quantum simulations. Here we experimentally investigate the emergent $\mathbb{Z}_2$ gauge invariance in a 1D superconducting circuit with 10 transmon qubits. By precisely adjusting staggered longitudinal and transverse fields to each qubit, we construct an effective Hamiltonian containing an LGT and gauge-broken terms. The corresponding matter sector can exhibit a localization, and there also exists a 3-qubit operator, of which the expectati…
Confinement-Tunable Synthetic Gauge Fields and Floquet Topological Phenomena in a Driven Quantum Wire Qubit
University of Abomey-Calavi（阿博梅-卡利维大学）；University of Dschang（德尚大学）；Quantum Materials and Computing Group - QMaCG（量子材料与计算群 - QMaCG）；Instituteur principal de l’enseignement général, Délégation Régionale de l’Ouest, Délégation Départementale de la Menoua, Arrondissement de Nkong-Ni, École Publique de Batsing’la Chefferie, Bafou, Cameroun（喀麦隆巴富，班辛拉酋长国公立学校，孔克尼区，梅努瓦省教育厅，西部大区教育厅，普通教育首席教师）；University of Yaoundé I（雅温得第一大学）
Gauge field is essential for exploring novel phenomena in modern physics. However, it has not been realized in the recent breakthrough experiment about two-leg superconducting circuits with transmon qubits [Phys. Rev. Lett. 123, 050502 (2019)]. Here we present an experimentally-feasible method to achieve the synthetic gauge field by introducing ac microwave driving in each qubit. In particular, the effective magnetic flux per plaquette achieved can be tuned independently by properly choosing the driving phases. Moreover, the ground-state chiral currents for the single- and two-qubit excitation…
James Franck Institute, University of Chicago（芝加哥大学詹姆斯·弗兰克研究所）；Department of Physics, University of Chicago（芝加哥大学物理系）；Department of Physics and Astronomy, Purdue University（普渡大学物理与天文学系）；Purdue Quantum Science and Engineering Institute, Purdue University（普渡大学普渡量子科学与工程研究所）；Department of Physics, Boston University（波士顿大学物理系）；AppliedTQC；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普利兹克分子工程学院）
In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The schemes consist of coupled transmons whose flux are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the fixed phase offset of each site on the complex coupling rate between coupled qubits. These configurations can be directly realised in a superconducting circuit and is easily extendable to a scalable lattice. Due to the intrinsic non-linearity of the transmon qubits such lattices would be an ideal…
Most works on open quantum systems generally focus on the reduced physical system by tracing out the environment degrees of freedom. Here we show that the qubit distributions with the environment are essential for a thorough analysis, and demonstrate that the way that quantum correlations are distributed in a quantum register is constrained by the way in which each subsystem gets correlated with the environment. For a two-qubit system coupled to a common dissipative environment $\mathcal{E}$, we show how to optimise interqubit correlations and entanglement via a quantification of the qubit-env…
We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the underlying physical system and the available means to manipulate it. The final goal is to obtain optimal decompositions of QEC codes into elementary operations which can be realized with high experimental fidelities. In the first part of this paper, this subject is studied in a general fashion, while in the second part, a system of trapped ions is treated as a conc…
We describe a lattice of asymmetrical qubit pairs in one or two dimensions, with couplings arranged so that the motion of single-qubit excited states mimics the behavior of charged lattice bosons hopping in a magnetic field. We show in particular that one can choose the parameters of the many-body circuit to reach a regime where the complex hopping phase between any two elements can be tuned to any value by simply adjusting the relative phases of two applied oscillating voltage signals. We also propose a specific realization of our model using coupled three junction flux qubits, in which one c…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the Harper-Hofstadter, the Haldane models, demonstrating one-way waveguides and topologically protected edge states. Central to these discoveries is the chirality induced by time-symmetry breaking. In quantum walk algorithms, recent work has discovered implications time-reversal symmetry breaking has on the transport of quantum states which has enabled a host of new ex…
