Holographic Quantum Simulation of Entanglement Renormalization Circuits
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Solving Large‐Scale Linear Systems of Equations by a Quantum Hybrid Algorithm
Abstract Today's intermediate‐scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum‐enabled large‐scale solutions have been realized only for limited set of problems. Here a hybrid algorithm based on phase estimation and classical optimization of the circuit width and depth is employed for solving a specific class of large linear systems of equations ubiquitous to many areas of science and engineering. A classification of linear systems based on the entanglement properties of the associated phase‐estimation unitary operation is introduced, enabling a highly efficient search for solutions that is facilitated by a straightforward matrix‐to‐circuit map. A 2 17 ‐dimensional problem is implemented on several IBM quantum computer superconducting quantum processors, a record‐breaking result for a linear system solved by a quantum computer. Demonstrated realisation sets a clear benchmark in the quest for the future quantum speedup in the linear systems of equations solution.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum utility-scale error mitigation for quantum quench dynamics in Heisenberg spin chains
Here, we implement a quantum error mitigation method termed self-mitigation, which is comparable to zero-noise extrapolation, at large scales to achieve quantum utility on near-term, noisy quantum computers. We investigate the effectiveness of several quantum error mitigation strategies, including self-mitigation, by simulating quantum quench dynamics for Heisenberg spin chains with system sizes up to 104 qubits using IBM quantum processors. In particular, we discuss the limitations of zero-noise extrapolation and the advantages offered by self-mitigation at large scales. The self-mitigation method demonstrates stable accuracy with large systems of 104 qubits comprising more than 3,000 CNOT gates. Also, we combine the discussed quantum error mitigation methods with practical entanglement entropy measuring methods, and it shows a good agreement with the theoretical estimation. Our study illustrates the usefulness of near-term noisy quantum hardware in examining the quantum quench dynamics of many-body systems at large scales and lays the groundwork for surpassing classical simulations with quantum methods prior to the development of fault-tolerant quantum computers.
97 MATHEMATICS AND COMPUTING↗
Dynamical edge modes and entanglement in Maxwell theory
Abstract Previous work on black hole partition functions and entanglement entropy suggests the existence of “edge” degrees of freedom living on the (stretched) horizon. We identify a local and “shrinkable” boundary condition on the stretched horizon that gives rise to such degrees of freedom. They can be interpreted as the Goldstone bosons of gauge transformations supported on the boundary, with the electric field component normal to the boundary as their symplectic conjugate. Applying the covariant phase space formalism for manifolds with boundary, we show that both the symplectic form and Hamiltonian exhibit a bulk-edge split. We then show that the thermal edge partition function is that of a codimension-two ghost compact scalar living on the horizon. In the context of a de Sitter static patch, this agrees with the edge partition functions found by Anninos et al. in arbitrary dimensions. It also yields a 4D entanglement entropy consistent with the conformal anomaly. Generalizing to Proca theory, we find that the prescription of Donnelly and Wall reproduces existing results for its edge partition function, while its classical phase space does not exhibit a bulk-edge split.
Physics↗
Quantum computing and quantum information storage
Quantum storage, transmission, and processing is the future of information technology. Here, the promise of quantum hardware stems from the inherent complexity of an entangled quantum system—the size of the wave-function scales exponentially with the number of particles, whether represented in real space or in a parameter space. In contrast, a classical N-body system can be completely represented by only 6N variables (positions and momenta of all particles). This complexity of quantum systems creates a yet-unsolved challenge of modeling quantum systems by means of classical computing—the curse of dimensionality. Indeed, although we can easily write the Schrödinger equation for any system of interacting nuclei and electrons, we can only solve it exactly on classical computers for very small systems.
97 MATHEMATICS AND COMPUTING↗
Entropic lens on stabilizer states
The n-qubit stabilizer states are those left invariant by a 2 n -element subset of the Pauli group. The Clifford group is the group of unitaries which take stabilizer states to stabilizer states; a physically motivated generating set, the Hadamard, phase, and controlled-not (cnot) gates which comprise the Clifford gates, impose a graph structure on the set of stabilizers. We explicitly construct these structures, the “reachability graphs,” at n ≤ 5. When we consider only a subset of the Clifford gates, the reachability graphs separate into multiple, often complicated, connected components. Seeking an understanding of the entropic structure of the stabilizer states, which is ultimately built up by cnot gate applications on two qubits, we are motivated to consider the restricted subgraphs built from the Hadamard and cnot gates acting on only two of the n qubits. We show how the two subgraphs already present at two qubits are embedded into more complicated subgraphs at three and four qubits. We argue that no additional types of subgraph appear beyond four qubits, but that the entropic structures within the subgraphs can grow progressively more complicated as the qubit number increases. Starting at four qubits, some of the stabilizer states have entropy vectors which are not allowed by holographic entropy inequalities. Here, we comment on the nature of the transition between holographic and nonholographic states within the stabilizer reachability graphs.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Qudit Entanglers Using Quantum Optimal Control
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
Clifford circuits are insufficient for universal quantum computation or creating t t -designs with t\ge 4 t ≥ 4 . While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (\pi/8) ( π / 8 ) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Broadband polarization-entangled source for C+L-band flex-grid quantum networks
The rising demand for transmission capacity in optical networks has motivated steady interest in expansion beyond the standard C-band (1530–1565 nm) into the adjacent L-band (1565–1625 nm) for an approximate doubling of capacity in a single stroke. However, in the context of quantum networking, the L-band has yet to be fully leveraged with the suite of advanced tools for characterization and management available from classical lightwave communications. In this work, we demonstrate an ultrabroadband two-photon source integrating both C- and L-band wavelength-selective switches for complete control of spectral routing and allocation across 7.5 THz in a single setup. Polarization state tomography of all 150 pairs of 25-GHz-wide channels reveals an average fidelity of 0.98 and total distillable entanglement greater than 181 kebits/s. This source is explicitly designed for flex-grid optical networks and can facilitate optimal utilization of entanglement resources across the full C+L-band.
42 ENGINEERING↗
Quantum Computation: Entangling with the Future
Commercial applications of quantum computation have become viable due to the rapid progress of the field in the recent years. Efficient quantum algorithms are discovered to cope with the most challenging real-world problems that are too hard for classical computers. Manufactured quantum hardware has reached unprecedented precision and controllability, enabling fault-tolerant quantum computation. Here, I give a brief introduction on what principles in quantum mechanics promise its unparalleled computational power. I will discuss several important quantum algorithms that achieve exponential or polynomial speedup over any classical algorithm. Building a quantum computer is a daunting task, and I will talk about the criteria and various implementations of quantum computers. I conclude the talk with near-future commercial applications of a quantum computer.
Jiang, Zhang↗
Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer’s records. However, our “let quantum be quantum” approach poses questions absent in Bohr’s Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply “too relative”, and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born’s rule, p k =|ψ k | 2 , relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the ‘quantum theory of the classical’ one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born’s rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of p k =|ψ k | 2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Characterizing Topological Order with Matrix Product Operators
One of the most striking features of gapped quantum phases that exhibit topological order is the presence of long-range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a natural framework for the parameterization of gapped ground state wavefunctions which allows one to characterize topological order in terms of the virtual symmetries of the local tensors that encode the wavefunction. In their most general form, these symmetries are represented by matrix product operators acting on the virtual level, which leads to a set of algebraic rules characterizing states with topological quantum order. This construction generalizes the concepts of $\mathsf G$- and twisted injectivity; the corresponding matrix product operators encode all topological features of the theory and provide a complete picture of the ground state manifold on the torus. We show how the string-net models of Levin and Wen fit within this formalism and in doing so provide a particularly intuitive interpretation of the pentagon equation for F-symbols as the pulling of matrix product operators through the string-net tensor network. Our approach paves the way to finding novel topological phases beyond string nets and elucidates the description of topological phases in terms of entanglement Hamiltonians and edge theories.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Coupling Two Laser-Cooled Ions via a Room-Temperature Conductor
We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620 μm. Here, the ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Using Ultrafast Entangled Photon Correlations to Measure the Temporal Evolution of Optically Excited Molecular Entanglement (Final Technical Report)
The goal of this project is to build an ultrafast entangled photon spectrometer and use it to measure theoretical predictions that photoexcited states are enhanced by spin-photon interactions. Entanglement of two states describes a specific type of quantum superposition in which measuring one state gives information about a second state. While entanglement is well explored for quantum information and computing systems, its effects on photoexcited states are less understood, especially in the ultrafast domains of molecular vibronic coupling. The grant designs a frequency and temporally resolved entangled photon spectrometer and uses it to test theoretical predictions like enhanced two photon absorption, non-reciprocal Fourier relations, and coupling of photons to spin systems. The end goal of the project is an understanding of how, when, and where entanglement is useful for spectroscopy.
47 OTHER INSTRUMENTATION↗
Three-flavor collective neutrino oscillation simulations on a qubit quantum annealer
Neutrinos are unique among elementary particles in that their flavor-compositions oscillate over time. In extreme environments such as core-collapse supernovae, neutron-star mergers, and the early Universe, neutrinos are dense enough that their self-interactions significantly affect, if not dominate, these oscillations. This has implications for several phenomena within these environments, particularly nucleosynthesis. Simulations of these self-interactions have traditionally approximated neutrinos as having two flavors instead of the physical three. In order to develop techniques for characterizing the resulting quantum entanglement, I present the results of simulations of neutrino-neutrino interactions that include all three physical neutrino flavors and were performed on D-Wave Inc.’s Advantage 5000+ qubit quantum annealer. These results are checked against those from exact classical simulations, which are also used to compare the neutrino-neutrino interactions to neutrino-antineutrino and interactions between Majorana neutrinos, which are their own antiparticles. The D-Wave Advantage annealer is shown to be able to reproduce time evolution with the precision of a classical machine for small numbers of neutrinos and to do so without the Trotter errors present in most simulations of dynamics on quantum devices. Furthermore, it suffers from poor scaling in qubit-count with the number of neutrinos.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Universal Tripartite Entanglement in One-Dimensional Many-Body Systems
Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Space-Time Quantum Information from the Entangled States of Magnetic Molecule (STI Product)
This collaborative project combines synthesis, measurement, and theory by three faculty members at the Eddleman Quantum Institute of UC Irvine to effectively investigate the quantum properties of molecules in the space, time, and frequency domains. Through synthetic chemistry, molecules are tailored for their magnetic and coherent properties. By combining femtosecond (fs) terahertz (THz) light and a continuous wave (cw) THz laser with a low temperature scanning tunneling microscope (STM), quantum phenomena are probed with simultaneous femtosecond temporal and atomic-scale spatial resolution. In particular, the invention of the quantum superposition microscope (QSM) advances quantum sensing for enhanced spectroscopy and imaging capabilities. Coupling theory to the experimental efforts offers a deeper understanding and predictive power for the molecular systems. The phenomena of superposition, entanglement, and coherence is central to quantum information science and can be realized in qubit states. Many systems can be modeled by a double-well potential in which two levels are formed in the two lowest energy states interacting with the environment and external radiation. In focusing on molecules as two-level systems, the underlying expectation is that their tunable composition and structure allows an effective parameter space to optimize their use as qubits for quantum sensing and computing. The THz radiation induces the superposition between the two states, appearing as temporal oscillations that damp in amplitude. Enhanced spectroscopy and imaging in the time and frequency domains is achieved through the extreme sensitivity of the frequency and damping of coherence of two-level systems to its environment. A single hydrogen molecule trapped in the STM tunneling gap experiences a double-well potential and absorption of THz femtosecond pulses of light creates the superposition of its two levels, appearing as damped oscillations in the light induced direct current (DC). The oscillation frequency depends sensitively on the electric field distribution of the copper nitride (Cu 2 N) surface, through the Stark effect, and associated with the different charge distributions at the copper and nitrogen sites and in between. This QSM can resolve variation in the surface electric field with 0.02 nanometer resolution. In addition, the single hydrogen molecule entaes with nearby hydrogen molecules as seen in the avoided level crossings of energy (oscillation frequency) versus the voltage across the tunneling gap. Thus, the first application of the QSM senses and images the surface electric field at the atomic scale. Results from this project advance fundamental understanding of quantum phenomena, develop novel synthesis, measurement, and theory, provide the knowledge foundation for molecule-based qubits and sensing that enable the development of the QSM and emergent technologies. This project trained researchers in quantum information science, extended knowledge in classrooms, and outreached to the community.
47 OTHER INSTRUMENTATION↗
Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware
Teleporting physical quantities to remote locations remains a key challenge for quantum information science and technology. Quantum teleportation has enabled the transfer of quantum information, but teleportation of quantum physical quantities has not yet been realized. Here we report the realization and observation of quantum energy teleportation on real superconducting quantum hardware. We achieve this by using several IBM superconducting quantum computers. The results are consistent with the exact solution of the theory and are improved by the mitigation of measurement error. Quantum energy teleportation requires only local operations and classical communication. Furthermore, our results provide a realistic benchmark that is fully achievable with current quantum computing and communication technologies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗