We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with polynomial efficiency, certain diagonal matrix elements of an observable. This sub-algorithm is performed on a quantum computer, using quantum phase estimation and tomography. The second sub-algorithm is for sampling a probability distribution. This sub-algorithm is not polynomially efficient. It can be performed either on a classical or a quantum computer, but a quantum computer can perform it quadratically faster.
In quantum Darwinism, the pointer observable of a system leaves redundant imprints in its environment after decoherence. Each imprint is recorded in a fraction of the environment, which identifies a particular partition of the environment. An ambiguity situation may occur when another observable noncommuting to the pointer observable also leaves redundant imprints with respect to another partition of the environment. We study this problem based on a uniqueness theorem we proved. We find that within a particular subset of all possible partitions of the environment, the observable of the system …
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean logic of complementary features may also apply to classical systems, if their states and observables are defined by partitions of a classical state space. If these partitions do not satisfy certain stability criteria, complementary observables and non-Boolean propositional lattices may be the consequence. This is especially the case for non-generating partitio…
The Gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. There are several proposals to calculate the partition functions on near-team quantum computers. However, the existing schemes require many copies of the Gibbs states to perform an extrapolation for the calculation of the partition function, and these could be costly performed on the near-term quantum computers. Here, we propose an efficient scheme to calculate the Gibbs function with the imaginary time evolution. To calculate the Gibbs function of $N$ qubits, on…
In this paper, we consider a continuous-time quantum walk based search algorithm. We introduce equitable partition of the graph and perfect state transfer on it. By these two methods, we can calculate the success probability and the finding time of the search algorithm. In addition, we gave some examples of graphs that we can calculate the success probability and the finding time.
We consider the effective Gibbs state for averaged observables. In particular, we perturbatively calculate the correspondent effective Hamiltonian. We show that there are a lot of similarities between this effective Hamiltonian and the mean force Hamiltonian. We also discuss a thermodynamic role of the information loss due to restriction of our measurement capabilities to such averaged observables.
We propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there is an associated average energy. The sampling is done through an accept/reject Metropolis-style algorithm on the quantum gates of the circuit itself. Observables calculated under the canonical ensemble from these samples of circuits are extrapolated from higher-energies to the ground state.
We present the quantum computation of nuclear observables where the operators of interest are first decomposed in terms of the linear combination of unitaries. Then we utilise the Hadamard test and the linear combination of unitaries (LCU) based methods to compute the expectation values. We apply these methods to calculate the electric quadrupole moment of deuteron. The results are compared for the Jordan-Wigner transformation and Gray code encoding. We discuss the versatility of our approach that can be utilized in general to calculate several observables on a quantum computer.
We present an experimental scheme to measure the full distribution of many-body observables in spin systems, both in and out of equilibrium, using an auxiliary qubit as a probe. We focus on the determination of the magnetization and the kink-number statistics at thermal equilibrium. The corresponding characteristic functions are related to the analytically-continued partition function. Thus, both distributions can be directly extracted from experimental measurements of the coherence of a probe qubit that is coupled to an Ising-type bath, as reported in [X. Peng et al., Phys. Rev. Lett. 114, 01…
