skip to main content


Search for: All records

Award ID contains: 1908730

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Abstract

    For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal “joint-detection receiver” that acts collectively on long codeword-blocks of modulated pulses; an effect often termed “superadditive capacity”. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of “belief-propagation with quantum messages” (BPQM). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best “classical” approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.

     
    more » « less
  2. This paper considers the design and decoding of polar codes for general classical-quantum (CQ) channels. It focuses on decoding via belief-propagation with quantum messages (BPQM) and, in particular, the idea of paired-measurement BPQM (PM-BPQM) decoding. Since the PM-BPQM decoder admits a classical density evolution (DE) analysis, one can use DE to design a polar code for any CQ channel and then efficiently compute the trade-off between code rate and error probability. We have also implemented and tested a classical simulation of our PM-BPQM decoder for polar codes. While the decoder can be implemented efficiently on a quantum computer, simulating the decoder on a classical computer actually has exponential complexity. Thus, simulation results for the decoder are somewhat limited and are included primarily to validate our theoretical results. 
    more » « less
  3. Belief propagation (BP) is a classical algorithm that approximates the marginal distribution associated with a factor graph by passing messages between adjacent nodes in the graph. It gained popularity in the 1990’s as a powerful decoding algorithm for LDPC codes. In 2016, Renes introduced a belief propagation with quantum messages (BPQM) and described how it could be used to decode classical codes defined by tree factor graphs that are sent over the classical-quantum pure-state channel. In this work, we propose an extension of BPQM to general binary-input symmetric classical-quantum (BSCQ) channels based on the implementation of a symmetric "paired measurement". While this new paired-measurement BPQM (PMBPQM) approach is suboptimal in general, it provides a concrete BPQM decoder that can be implemented with local operations. Finally, we demonstrate that density evolution can be used to analyze the performance of PMBPQM on tree factor graphs. As an application, we compute noise thresholds of some LDPC codes with BPQM decoding for a class of BSCQ channels. 
    more » « less
  4. The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal T gate play an important role in implementing a universal set of quantum operations. This paper introduces a framework that describes the process of preparing a code state, applying a diagonal physical gate, measuring a code syndrome, and applying a Pauli correction that may depend on the measured syndrome (the average logical channel induced by an arbitrary diagonal gate). It focuses on CSS codes, and describes the interaction of code states and physical gates in terms of generator coefficients determined by the induced logical operator. The interaction of code states and diagonal gates depends very strongly on the signs of Z -stabilizers in the CSS code, and the proposed generator coefficient framework explicitly includes this degree of freedom. The paper derives necessary and sufficient conditions for an arbitrary diagonal gate to preserve the code space of a stabilizer code, and provides an explicit expression of the induced logical operator. When the diagonal gate is a quadratic form diagonal gate (introduced by Rengaswamy et al.), the conditions can be expressed in terms of divisibility of weights in the two classical codes that determine the CSS code. These codes find application in magic state distillation and elsewhere. When all the signs are positive, the paper characterizes all possible CSS codes, invariant under transversal Z -rotation through π / 2 l , that are constructed from classical Reed-Muller codes by deriving the necessary and sufficient constraints on l . The generator coefficient framework extends to arbitrary stabilizer codes but there is nothing to be gained by considering the more general class of non-degenerate stabilizer codes. 
    more » « less
  5. A diagonal physical gate U has 2^n diagonal entries, each indexed by a binary vector v of length n. A CSS codespace C on n qubits is specified by two classical code C1 and C2, where C2 provides the X-stabilizers and the dual of C1 provides the Z-stabilizers. We proved U preserves C if and only if entries indexed by the same coset of C2 in C1 (same X-logical) are identical. 
    more » « less
  6. Binary Chirps (BCs) are 2^m dimensional complex vectors employed in deterministic compressed sensing and in random/unsourced multiple access in wireless networks. The vectors are obtained by exponentiating codewords from a 2nd order Reed-Muller code defined over Z4, the ring of integers modulo 4. We doubled the size of the BC codebook, without compromising performance in wireless multiple access. 
    more » « less