Parity-time (PT) symmetric quantum theory can broaden the scope of quantum dynamics beyond unitary evolution which may lead to numerous counter-intuitive phenomena, including single-shot discrimination of non-orthogonal states, faster evolution of state than the standard quantum speed limit, and violation of no-signaling principle. On the other hand, PT-symmetric evolution can be realized as reduced dynamics of a subsystem in real experiments within the scope of standard quantum theory. In this experimental setup, if one side of a composite system is evolved according to a PT-symmetric way, a non-trivial information transfer can happen, i.e., the operation performed at one side can be gathered by the other side. By considering an arbitrary shared state between two parties situated in two distant locations and arbitrary measurements, we show that the PT-symmetric evolution of the reduced subsystem at one side is not sufficient for this information transfer to occur. Specifically, we prove that the information transfer can only happen when the density matrix and the corresponding measurements contain complex numbers. Moreover, we connect the entanglement content of the shared state with the efficacy of information transfer. We find evidence that the task becomes more efficient with the increase of dimension.
We propose a physical implementation of time and spatial parity transformations, as well as Galilean boosts, in a trapped-ion quantum simulator. By embedding the simulated model into an enlarged simulating Hilbert space, these fundamental symmetry operations can be fully realized and measured with ion traps. We illustrate our proposal with analytical and numerical techniques of prototypical examples with state-of-the-art trapped-ion platforms. These results pave the way for the realization of time and spatial parity transformations in other models and quantum platforms.
Zitterbewegung (ZB), the trembling of free relativistic electrons in a vacuum could be simulated by a single trapped ion. We focus on the variations of ZB under different parity conditions and find no ZB in the case of odd or even parity. ZB occurs only for admixture of the odd and even parity states. We also show the similar role played by the parity operator for the trapped ion in Fock-state representation and the space inversion operator for a realistic relativistic electron. Although the ZB effect is invisible in a relativistic electron, preparation of the trapped ion in different parity s…
We analyze a direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected/transmitted microwave radiation and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these condition…
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 propose the effective simulation of light-matter ultrastrong-coupling phenomena with strong-coupling systems. Recent theory and experiments have shown that the quantum Rabi Hamiltonian can be simulated by a Jaynes--Cummings system with the addition of two classical drives. This allows to implement nonlinear processes that do not conserve the total number of excitations. However, parity is still a conserved quantity in the quantum Rabi Hamiltonian, which forbids a wide family of processes involving virtual transitions that break this conservation. Here, we show that these parity-non-conservi…
Quantum phase transition in the spin-boson model was claimed on the basis of various numerical studies, but not strictly proven. Here by using a unitary transformation to decompose the Hamiltonian into two branches of odd and even parity we obtained the necessary and sufficient condition for degeneracy to occur between states of opposite parity in the spin-boson model, and the analytical expression for such degenerate energies. It can be strictly proven that the ground state of spin-boson model with non-vanishing tunneling amplitude must have an energy lower than the lowest possible such degen…
Parity Mapping for Quantum Optimization on Frustrated Ising Rings
SISSA（的里雅斯特国际高等研究学校）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Parity Quantum Computing GmbH（Parity量子计算有限公司）；Parity Quantum Computing Germany GmbH（Parity量子计算德国有限公司）；International Centre for Theoretical Physics (ICTP)（国际理论物理中心）
Measurements provide a novel mechanism for generating the entanglement resource necessary for performing scalable quantum computation. Recently, we proposed a method for performing parity measurements in a coupled quantum dot system. In this paper we generalise this scheme and perform a comprehensive analytic and numerical study of environmental factors. We calculate the effects of possible error sources including non-ideal photon detectors, ineffective spin-selective excitation and dot distinguishability (both spatial and spectral). Furthermore, we present an experimental approach for verifyi…
Parity measurements on qubits can generate the entanglement resource necessary for scalable quantum computation. Here we describe a method for fast optical parity measurements on electron spin qubits within coupled quantum dots. The measurement scheme, which can be realised with existing technology, consists of the optical excitation of excitonic states followed by monitored relaxation. Conditional on the observation of a photon, the system is projected into the odd/even parity subspaces. Our model incorporates all the primary sources of error, including detector inefficiency, effects of spati…
We introduce the concept of parity symmetry in restricted spatial domains -- local parity -- and explore its impact on the stationary transport properties of generic, one-dimensional aperiodic potentials of compact support. It is shown that, in each domain of local parity symmetry of the potential, there exists an invariant quantity in the form of a non-local current, in addition to the globally invariant probability current. For symmetrically incoming states, both invariant currents vanish if weak commutation of the total local parity operator with the Hamiltonian is established, leading to l…
For many optimization algorithms the time-to-solution depends not only on the problem size but also on the specific problem instance and may vary by many orders of magnitude. It is then necessary to investigate the full distribution and especially its tail. Here we analyze the distributions of annealing times for simulated annealing and simulated quantum annealing (by path integral quantum Monte Carlo) for random Ising spin glass instances. We find power-law distributions with very heavy tails, corresponding to extremely hard instances, but far broader distributions - and thus worse performanc…
As in classical coding theory, quantum analogues of low-density parity-check (LDPC) codes have offered good error correction performance and low decoding complexity by employing the Calderbank-Shor-Steane (CSS) construction. However, special requirements in the quantum setting severely limit the structures such quantum codes can have. While the entanglement-assisted stabilizer formalism overcomes this limitation by exploiting maximally entangled states (ebits), excessive reliance on ebits is a substantial obstacle to implementation. This paper gives necessary and sufficient conditions for the …
Exceptional points (EPs), the degeneracy point of non-Hermitian systems, have recently attracted great attention after its ability to greatly enhance the sensitivity of micro-cavities is demonstrated experimentally. Unlike the usual degeneracies in Hermitian systems, at EPs, both the eigenenergies and eigenvectors coalesce. Although some of the exotic properties and potential applications of EPs are explored, the range of EPs studied is largely limited by the experimental capability. Some of the systems, e.g. with higher-order EPs, are hard to achieve with conventional simulations. Here we pro…
Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard random $k$-SAT problems. This paper compares simulated annealing, simulated quantum annealing and walkSAT, an open-source SAT solver, in terms of their ability to find such solutions. The results indicate that solutions found by simulated quantum annealing are generally less disparate than solutions found by the other solvers and therefore less useful for th…
Optimizing QAOA circuit transpilation with parity twine and SWAP network encodings
Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich（于利希研究中心先进模拟研究所超级计算中心）；Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich（于利希研究中心量子计算分析研究所）；Department of Mechanical Engineering, Virginia Tech（弗吉尼亚理工大学机械工程系）；Davidson School of Chemical Engineering, Purdue University（普渡大学戴维森化学工程学院）；AIDAS；RWTH Aachen University（亚琛工业大学）
Utilizing present and futuristic Quantum Computers to solve difficult problems in different domains has become one of the main endeavors at this moment. Of course, in arriving at the requisite solution both quantum and classical computers work in conjunction. With the continued popularity of Low Density Parity Check (LDPC) codes and hence their decoding, this paper looks into the latter as a Quadratic Unconstrained Binary Optimization (QUBO) and utilized D-Wave 2000Q Quantum Annealer to solve it. The outputs from the Annealer are classically post-processed using simple minimum distance decodin…
We present a concept for performing direct parity measurements on three or more qubits in microwave structures with superconducting resonators coupled to Josephson-junction qubits. We write the quantum-eraser conditions that must be fulfilled for the parity measurements as requirements for the scattering phase shift of our microwave structure. We show that these conditions can be fulfilled with present-day devices. We present one particular scheme, implemented with two-dimensional cavity techniques, in which each qubit should be coupled equally to two different microwave cavities. The magnitud…
Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return incorrect outcomes or inject additional faults into the qubits. To achieve fault-tolerant error correction, Shor proposed to repeat the sequence of parity check measurements until the same outcome is observed sufficiently many times. Then, one can use this information to perform error correction. A basic implementation of this fault tolerance strategy requires $Ω(…
When independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement, with two possible results $\pm1$. With two interferometers and two BEC's, the parity (product of all results obtained at each interferometer) has all the features of an Einstein-Podolsky-Rosen quantity, with perfect correlations predicted by quantum mechanics when the settings (phase shifts of the interferometers) are the same. When they are different, signif…
The effects induced by the quantum vacuum fluctuations of one massless real scalar field on a configuration of two partially transparent plates are investigated. The physical properties of the infinitely thin plates are simulated by means of Dirac-$δ-δ^\prime$ point interactions. It is shown that the distortion caused on the fluctuations by this external background gives rise to a generalization of Robin boundary conditions. The $T$-operator for potentials concentrated on points with non defined parity is computed with total generality. The quantum vacuum interaction energy between the two pla…
Quantum transition probabilities and quantum entanglement for two-qubit states of a four level trapped ion quantum system are computed for time-evolving ionic states driven by Jaynes-Cummings Hamiltonians with interactions mapped onto a $\mbox{SU}(2)\otimes \mbox{SU}(2)$ group structure. Using the correspondence of the method of simulating a $3+1$ dimensional Dirac-like Hamiltonian for bi-spinor particles into a single trapped ion, one preliminarily obtains the analytical tools for describing ionic state transition probabilities as a typical quantum oscillation feature. For Dirac-like structur…
We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $\langle W \rangle \le 3$ for a…
