Understanding fault-tolerant properties of quantum circuits is important for the design of large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the relationships between the noise model, encoding scheme, and threshold value. For general circuits and noise models, these simulations quickly become intractable in the size of the encoded circuit. We introduce methods for approximating a noise process by one which allows for efficient Monte Carlo simulation of properties of encoded circuits. The approximations are as close to the original process as possible without overestimating their ability to preserve quantum information, a key property for obtaining more honest estimates of threshold values. We numerically illustrate the method with various physically relevant noise models.Comment: 6 pages, 1 figur

In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those results by numerically studying the efficacy of this proposal as a tool for understanding the performance of an error-correction gadget implemented with fault models derived from physical simulations. Our approach is to approximate the arbitrary error maps that arise from realistic physical models with errors that are amenable to a particular classical simulation algorithm in an "honest" way; that is, such that we do not underestimate the faults introduced by our physical models. In all cases, our approximations provide an "honest representation" of the performance of the circuit composed of the original errors. This numerical evidence supports the use of our method as a way to understand the feasibility of an implementation of quantum information processing given a characterization of the underlying physical processes in experimentally accessible examples.

In the field of quantum control, effective Hamiltonian engineering is a powerful tool that utilizes perturbation theory to mitigate or enhance the effect that a variation in the Hamiltonian has on the evolution of the system. Here, we provide a general framework for computing arbitrary timedependent perturbation theory terms, as well as their gradients with respect to control variations, enabling the use of gradient methods for optimizing these terms. In particular, we show that effective Hamiltonian engineering is an instance of a bilinear control problem-the same general problem class as that of standard unitary design-and hence the same optimization algorithms apply. We demonstrate this method in various examples, including decoupling, recoupling, and robustness to control errors and stochastic errors. We also present a control engineering example that was used in experiment, demonstrating the practical feasibility of this approach.

Single-shot quantum channel discrimination is a fundamental task in quantum information theory. It is well known that entanglement with an ancillary system can help in this task, and furthermore that an ancilla with the same dimension as the input of the channels is always sufficient for optimal discrimination of two channels. A natural question to ask is whether the same holds true for the output dimension. That is, in cases when the output dimension of the channels is (possibly much) smaller than the input dimension, is an ancilla with dimension equal to the output dimension always sufficient for optimal discrimination? We show that the answer to this question is "no" by construction of a family of counterexamples. This family contains instances with arbitrary finite gap between the input and output dimensions, and still has the property that in every case, for optimal discrimination, it is necessary to use an ancilla with dimension equal to that of the input.The proof relies on a characterization of all operators on the trace norm unit sphere that maximize entanglement negativity. In the case of density operators we generalize this characterization to a broad class of entanglement measures, which we call weak entanglement measures. This characterization allows us to conclude that a quantum channel is reversible if and only if it preserves entanglement as measured by any weak entanglement measure, with the structure of maximally entangled states being equivalent to the structure of reversible maps via the Choi isomorphism. We also include alternate proofs of other known characterizations of channel reversibility.

We introduce a property of a matrix-valued linear map Φ that we call its "non-m-positive dimension" (or "non-mP dimension" for short), which measures how large a subspace can be if every quantum state supported on the subspace is non-positive under the action of I m ⊗ Φ. Equivalently, the non-mP dimension of Φ tells us the maximal number of negative eigenvalues that the adjoint map I m ⊗ Φ * can produce from a positive semidefinite input. We explore the basic properties of this quantity and show that it can be thought of as a measure of how good Φ is at detecting entanglement in quantum states. We derive nontrivial bounds for this quantity for some well-known positive maps of interest, including the transpose map, reduction map, Choi map, and Breuer-Hall map. We also extend some of our results to the case of higher Schmidt number as well as the multipartite case. In particular, we construct the largest possible multipartite subspace with the property that every state supported on that subspace has non-positive partial transpose across at least one bipartite cut, and we use our results to construct multipartite decomposable entanglement witnesses with the maximum number of negative eigenvalues.

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Given a linear map Φ : M n → M m , its multiplicity maps are defined as the family of linear maps Φ ⊗ id k : M n ⊗ M k → M m ⊗ M k , where id k denotes the identity on M k . Let · 1 denote the trace-norm on matrices, as well as the induced trace-norm on linear maps of matrices, i.e. Φ 1 = max{ Φ(X) 1 : X ∈ M n , X 1 = 1}. A fact of fundamental importance in both operator algebras and quantum information is that Φ ⊗ id k 1 can grow with k. In general, the rate of growth is bounded by Φ ⊗ id k 1 ≤ k Φ 1 , and matrix transposition is the canonical example of a map achieving this bound. We prove that, up to an equivalence, the transpose is the unique map achieving this bound. The equivalence is given in terms of complete trace-norm isometries, and the proof relies on a particular characterization of complete trace-norm isometries regarding preservation of certain multiplication relations.We use this result to characterize the set of single-shot quantum channel discrimination games satisfying a norm relation that, operationally, implies that the game can be won with certainty using entanglement, but is hard to win without entanglement. Specifically, we show that the well-known example of such a game, involving the Werner-Holevo channels, is essentially the unique game satisfying this norm relation. This constitutes a step towards a characterization of single-shot quantum channel discrimination games with maximal gap between optimal performance of entangled and unentangled strategies.

The implementation of Monte Carlo dose calculation algorithms in clinical radiotherapy treatment planning systems has been anticipated for many years however, its introduction into routine clinical practice has been delayed by the extent of calculation time required. With the advent of faster computers, Monte Carlo (MC) algorithms will become a standard calculation algorithm in clinical treatment planning systems. The purpose of this work was to develop a Monte Carlo based radiotherapy treatment planning research environment (MCTPRE) that uses patient‐specific computed tomography (CT) dataset. We have developed a windows based graphical user interface (GUI) that makes it very easy to import patient specific plans from a treatment planning system in either DICOM or RTOG format to a MC treatment planning research environment and can also be used to simulate simple patient specific treatment plans. The MCTPRE uses the BEAMnrcMP Monte Carlo code, which is based on the underlying ESGnrcMP particle transport code to simulate the Varian Clinac 21EX accelerator treatment head for 6 and 15MV photons and 6–20 MeV electron beams. The DOSXYZnrc Monte Carlo code is use for patient specific phantom dose calculations. We compared dose distributions from calculations done with a TPS and with the Monte Carlo code. The GUI incorporating the Monte Carlo code is a very useful research tool for benchmarking treatment planning systems (TPS), testing technique development, and dose verification. Future development will include a direct interface to a TPS.