Quantum simulation of partially distinguishable boson sampling

Boson Sampling is the problem of sampling from the same output probability distribution as a collection of indistinguishable single photons input into a linear interferometer. It has been shown that, subject to certain computational complexity conjectures, in general the problem is difficult to solve classically, motivating optical experiments aimed at demonstrating quantum computational "supremacy". There are a number of challenges faced by such experiments, including the generation of indistinguishable single photons. We provide a quantum circuit that simulates bosonic sampling with arbitrarily distinguishable particles. This makes clear how distinguishabililty leads to decoherence in the standard quantum circuit model, allowing insight to be gained. At the heart of the circuit is the quantum Schur transform, which follows from a representation theoretic approach to the physics of distinguishable particles in first quantisation. The techniques are quite general and have application beyond boson sampling.Comment: 25 pages, 4 figures, 2 algorithms, comments welcom

Randomized benchmarking in measurement-based quantum computing

Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.Comment: 10 pages, 4 figures, comments welcome; v2 published versio

Generating entanglement with linear optics

Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only 3 photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing 4 photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.Comment: 13 pages, 10 figures, 1 table, comments welcom

Phase-random states: ensembles of states with fixed amplitudes and uniformly distributed phases in a fixed basis

Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that canonical states typically appear in subsystems of phase-random states. We then investigate the simulatability of phase-random states, which is directly related to that of time evolution in closed systems, by studying their entanglement properties. We find that starting from a separable state, time evolutions under Hamiltonians composed of only separable eigenstates generate extremely high entanglement and are difficult to simulate with matrix product states. We also show that random quantum circuits consisting of only two-qubit diagonal unitaries can generate an ensemble with the same average entanglement as phase-random states.Comment: Revised, 12 pages, 4 figur

A coherent middle Pliocene magnetostratigraphy, Wanganui Basin, New Zealand

We document magnetostratigraphies for three river sections (Turakina, Rangitikei, Wanganui) in Wanganui Basin and interpret them as corresponding to the Upper Gilbert, the Gauss and lower Matuyama Chrons of the Geomagnetic Polarity Timescale, in agreement with foraminiferal biostratigraphic datums. The Gauss-Gilbert transition (3.58 Ma) is located in both the Turakina and Wanganui River sections, while the Gauss-Matuyama transition (2.58 Ma) is located in all three sections, as are the lower and upper boundaries of the Mammoth (3.33–3.22 Ma) and Kaena (3.11–3.04 Ma) Subchrons. Our interpretations are based in part on the re-analysis of existing datasets and in part on the acquisition and analysis of new data, particularly for the Wanganui River section. The palaeomagnetic dates of these six horizons provide the only numerical age control for a thick (up to 2000 m) mudstone succession (Tangahoe Mudstone) that accumulated chiefly in upper bathyal and outer neritic palaeoenvironments. In the Wanganui River section the mean sediment accumulation rate is estimated to have been about 1.8 m/k.y., in the Turakina section it was about 1.5 m/k.y., and in the Rangitikei section, the mean rate from the beginning of the Mammoth Subchron to the Hautawa Shellbed was about 1.1 m/k.y. The high rates may be associated with the progradation of slope clinoforms northward through the basin. This new palaeomagnetic timescale allows revised correlations to be made between cyclothems in the Rangitikei River section and the global Oxygen Isotope Stages (OIS) as represented in Ocean Drilling Program (ODP) Site 846. The 16 depositional sequences between the end of the Mammoth Subchron and the Gauss-Matuyama Boundary are correlated with OIS MG2 to 100. The cyclothems average 39 k.y. in duration in our age model, which is close to the 41 k.y. duration of the orbital obliquity cycles. We support the arguments advanced recently in defence of the need for local New Zealand stages as a means of classifying New Zealand sedimentary successions, and strongly oppose the proposal to move stage boundaries to selected geomagnetic polarity transitions. The primary magnetisation of New Zealand mudstone is frequently overprinted with secondary components of diagenetic origin, and hence it is often difficult to obtain reliable magnetostratigraphic records. We suggest specific approaches, analytical methods, and criteria to help ensure robustness and coherency in the palaeomagnetic identification of chron boundaries in typical New Zealand Cenozoic mudstone successions

Time-reversal frameness and superselection

We show that appropriate superpositions of motional states are a reference frame resource that enables breaking of time -reversal superselection so that two parties lacking knowledge about the other's direction of time can still communicate. We identify the time-reversal reference frame resource states and determine the corresponding frameness monotone, which connects time-reversal frameness to entanglement. In contradistinction to other studies of reference frame quantum resources, this is the first analysis that involves an antiunitary rather than unitary representation.Comment: 10 p