# Todd A. BrunUniversity of Southern California | USC · Department of Electrical and Computer Engineering

Todd A. Brun

Ph.D. 1994 in Physics, California Institute of Technology

## About

197

Publications

19,088

Reads

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6,460

Citations

Introduction

Researcher in quantum information and quantum computation.

Additional affiliations

February 2014 - present

**University of Southern California**

Position

- Professor (Full)

April 2006 - February 2014

September 2003 - April 2006

Education

September 1989 - April 1994

September 1985 - June 1989

## Publications

Publications (197)

Classical random walks on finite graphs have an underrated property: a walk from any vertex can reach every other vertex in finite time, provided they are connected. Discrete-time quantum walks on finite connected graphs however, can have infinite hitting times. This phenomenon is related to graph symmetry, as previously characterized by the group...

Interest in building dedicated quantum information science and engineering (QISE) education programs has greatly expanded in recent years. These programs are inherently convergent, complex, often resource intensive and likely require collaboration with a broad variety of stakeholders. In order to address this combination of challenges, we have capt...

In the past decade or so, there has been a growing number of papers postulating a correspondence relating quantum cellular automata (QCAs) to quantum field theories (QFTs). If valid, this would relate two important but seemingly unconnected physical systems and offer the potential for a deeper understanding of both. For example, it could lead to al...

Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial dimension, the quantum walk can be “promoted” to a QCA that, in the long-wavelength limit, gives rise to the Di...

Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum cellular automata for distinguishable particles based on two different quantum walks, and show that by restricting...

Interest in building dedicated Quantum Information Science and Engineering (QISE) education programs has greatly expanded in recent years. These programs are inherently convergent, complex, often resource intensive and likely require collaboration with a broad variety of stakeholders. In order to address this combination of challenges, we have capt...

Quantum walks on lattices can give rise to one-particle relativistic wave equations in the long-wavelength limit. In going to multiple particles, quantum cellular automata (QCA) are natural generalizations of quantum walks. In one spatial dimension, the quantum walk can be "promoted" to a QCA that, in the long-wavelength limit, gives rise to the Di...

Performing measurements for high-weight operators has been a practical problem in quantum computation, especially for quantum codes in the stabilizer formalism. The conventional procedure of measuring a high-weight operator requires multiple pairwise unitary operations, which can be slow and prone to errors. We provide an alternative method to pass...

It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen in the multiparticle case. We construct a one-dimensional quantum cellular automaton (QCA) model, which match...

Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode k > 1 qubits in n physical qubits can potentially reduce the resource overhead to a great extent because of
their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually take...

It has been shown that certain quantum walks give rise to relativistic wave equations, such as the Dirac and Weyl equations, in their long-wavelength limits. This intriguing result raises the question of whether something similar can happen in the multi-particle case. We construct a one-dimensional quantum cellular automaton model which matches the...

Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for Alice to hide her secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy quantum chan...

Performing measurements for high-weight operators has been a practical problem in quantum computation, especially for quantum codes in the stabilizer formalism. The conventional procedure of measuring a high-weight operator requires multiple pairwise unitary operations, which can be slow and prone to errors. We provide an alternative method to pass...

Fault-tolerant quantum computation (FTQC) schemes using large block codes that encode $k>1$ qubits in $n$ physical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually ta...

Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of measured error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose syndrome measurement (SM) and quantum data-syndrome (DS) codes. SM codes protect syndrome with linearly dependent redundant stabi...

Quantum steganography is the art of secretly transmitting quantum information while disguising the fact that any secret communication is taking place. Like classical steganography, this involves embedding the hidden communication within a seemingly innocent “covertext,” which in the quantum case is a quantum state. The best-developed protocol for q...

Characterizing secret communication over noisy quantum channels is an interesting problem from both a practical and theoretical perspective. Suppose Alice and Bob wish to communicate secret information so that an eavesdropper Eve will not suspect any type of encoded communication between the two. Classical or quantum cryptography will not suffice s...

Quantum error correction is a set of methods to protect quantum information--that is, quantum states--from unwanted environmental interactions (decoherence) and other forms of noise. The information is stored in a quantum error-correcting code, which is a subspace in a larger Hilbert space. This code is designed so that the most common errors move...

Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea of quantum data-syndrome (DS) codes that are capable of correcting both data qubits and syndrome bits errors....

Many quantum measurements, such as photodetection, can be destructive. In photodetection, when the detector “clicks” a photon has been absorbed and destroyed. Yet the lack of a click also gives information about the presence or absence of a photon. In monitoring the emission of photons from a source, one decomposes the strong measurement into a ser...

The quantification and characterization of non-Markovian dynamics in quantum systems is an essential endeavor both for the theory of open quantum systems and for a deeper understanding of the effects of non-Markovian noise on quantum technologies. Here, we introduce the robustness of non-Markovianity, an operationally-motivated, \emph{optimization-...

We explore the use of a switchable single-photon detector (SPD) array scheme to reduce the effect of a detector's deadtime for a multi-bit/photon quantum link. The case of data encoding using M possible orbital-angular-momentum (OAM) states is specifically studied in this paper. Our method uses N SPDs with a controllable M×N optical switch and we u...

If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution. In particular, the lattice structure will be reflected in a modification of the free-particle dispersion relation. We show that these can pr...

Many quantum measurements, such as photodetection, can be destructive. In photodetection, when the detector clicks a photon has been absorbed and destroyed. Yet the lack of a click also gives information about the presence or absence of a photon. In monitoring the emission of photons from a source, one decomposes the strong measurement into a serie...

An easily solvable quantum master equation has long been sought that takes into account memory effects induced on the system by the bath, i.e., non-Markovian effects. We briefly review the post-Markovian master equation (PMME), which is relatively easy to solve, and analyze a simple example where solutions obtained exhibit non-Markovianity. We appl...

Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for a sender, Alice, to hide a secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy qua...

Clifford circuits play an important role in quantum computation. Gottesman and Chuang proposed a gate teleportation protocol so that a quantum circuit can be implemented by the teleportation circuit with specific ancillary qubits. In particular, an $n$-qubit Clifford circuit $U$ can be implemented by preparing an ancillary stabilizer state $(I\otim...

An easily solvable quantum master equation has long been sought that takes into account memory effects induced on the system by the bath, i.e., non-Markovian effects. We briefly review the Post-Markovian master equation (PMME), which is relatively easy to solve, and analyze a simple example where solutions obtained exhibit non-Markovianity. We appl...

Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for Alice to hide her secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy quantum chan...

It has been shown that any generalized measurement can be decomposed into a sequence of weak measurements corresponding to a stochastic process. However, the weak measurements may require almost arbitrary unitaries, which are unlikely to be realized by any real measurement device. Furthermore, many measurement processes are destructive, like photon...

Fault-tolerant quantum computation (FTQC) schemes that use multi-qubit large block codes can potentially reduce the resource overhead to a great extent. A major obstacle is the requirement of a large number of clean ancilla states of different types without correlated errors inside each block. These ancilla states are usually logical stabilizer sta...

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper we define the 3D walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin sp...

If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution that could in principle be experimentally detected. In particular, the lattice structure should be reflected in a modification of the free-pa...

A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we investigate the Markovianity of a qubit system coupled to a single-qubit bath with the qubit bath being contin...

Simulating high-weight Hamiltonians can convert local noise on the original Hamiltonian into undesirable nonlocal noise on the simulated Hamiltonian. Here we show how starting from two-local Hamiltonian in the presence of non-Markovian noise, a desired computation can be simulated as well as protected using fast pulses, while maintaining an energy...

Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly prepare arbitrary CSS stabilizer states for general CSS...

Proposed models of closed timelike curves (CTCs) have been shown to enable
powerful information-processing protocols. We examine the simulation of models
of CTCs both by other models of CTCs and by physical systems without access to
CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs)
are physically equivalent to postselec...

We present techniques that improve the performance of asymmetric stabilizer codes in the presence of unital channels with unknown parameters. Our method estimates the channel parameters using information recovered from syndrome measurements during standard stabilizer quantum error correction and adaptively realigns the codespace to minimize the unc...

Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this disturbance by measuring and correcting cumulative phase shifts in the wavefront. These shifts can be represented...

We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom to the internal vibrational degrees of freedom. For a composite system of bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between diff...

Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. Understanding the noise processes that affect photons is essential if we desire to protect them. In this paper we use the infinitesimal propagation equation of Roux to derive a di...

There is a rich variety of physics underlying the fundamental gating operations for quantum information processing (QIP). A key aspect of a QIP system is how noise may enter during quantum operations and how suppressing or correcting its effects can best be addressed. Quantum control techniques have been developed to specifically address this effor...

We provide a self-contained introduction for entanglement-assisted quantum error-correcting codes in this book chapter.

The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular “Chimera” physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the...

In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first order approximation of a small deviation in the probability distribution, and study the robustness of standard weak measurement and postselected weak meas...

DOI:http://dx.doi.org/10.1103/PhysRevA.93.059901

In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes (QECCs), including additive and nonadditive codes, based on the codeword stabilized (CWS) framework on subsystems. The CWS framework is a scheme to construct QECCs, including both additive and nonadditive codes, and gives a method to co...

Continuous-time quantum error correction (CTQEC) is a technique for protecting quantum information against decoherence, where both the decoherence and error correction processes are considered continuous in time. Given any [[$n,k,d$]] quantum stabilizer code, we formulate a class of protocols to implement CTQEC, involving weak coherent measurements...

Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose the idea of quantum data-syndrome (DS) codes that are capable of correcting both data qubits and syndrome bits errors....

We consider a composite system consisting of coupled particles, and
investigate decoherence due to coupling of the center-of-mass degree of freedom
with the internal degrees of freedom. For a simple model of two bound
particles, we show that in general such a decoherence effect exists, and leads
to suppression of interference between different path...

Postselected weak measurement has aroused broad interest for its distinctive
ability to amplify small physical quantities. However, the low postselection
efficiency to obtain a large weak value has been a big obstacle to its
application in practice, since it can waste resources, and reduce the
measurement precision. In this paper, we detail the ent...

A major goal for fault-tolerant quantum computation (FTQC) is to reduce the
overhead needed for error correction. One approach is to use block codes that
encode multiple qubits, which can achieve significantly higher rates for the
same code distance than single-qubit code blocks or topological codes. We
present a scheme for universal quantum comput...

We characterize the set of generalized quantum measurements that can be
decomposed into a continuous measurement process using a stream of probe qubits
and a tunable interaction Hamilto- nian. Each probe in the stream interacts
weakly with the target quantum system, then is measured projectively in a
standard basis. This measurement result is used...

Quantum walks can be defined in two quite distinct ways: discrete-time and
continuous-time quantum walks (DTQWs and CTQWs). For classical random walks,
there is a natural sense in which continuous-time walks are a limit of
discrete-time walks. Quantum mechanically, in the discrete-time case, an
additional "coin space" must be appended for the walk...

We show that universal holonomic quantum computation (HQC) can be achieved
fault-tolerantly by adiabatically deforming the gapped stabilizer Hamiltonian
of the surface code, where quantum information is encoded in the degenerate
ground space of the system Hamiltonian. We explicitly propose procedures to
perform each logical operation, including log...

We consider the discrimination of two pure quantum states with three allowed
outcomes: a correct guess, an incorrect guess, and a non-guess. To find an
optimum measurement procedure, we define a tunable cost that penalizes the
incorrect guess and non-guess outcomes. Minimizing this cost over all
projective measurements produces a rigorous cost boun...

Postselected weak measurement is a useful protocol to amplify weak physical
effects. However, there has recently been controversy over whether it gives any
advantage in precision. While it is now clear that retaining failed
postselections can yield more Fisher information than discarding them, the
advantage of postselecting weak measurement itself...

Quantum metrology enhances the precision of estimating a parameter using the
distinctive resources of quantum mechanics, such as entanglement or many-body
interactions. It has been shown that quantum resources can greatly increase the
precision of estimating an overall multiplicative factor of a Hamiltonian, yet
little is known about estimating a g...

Knill demonstrated a fault-tolerant quantum computation scheme based on concatenated error-detecting codes and postselection with a simulated error threshold of 3% over the depolarizing channel. We show how to use Knill’s postselection scheme in a practical two-dimensional quantum architecture that we designed with the goal to optimize the error co...

An important issue in the implementation of a quantum computer is to protect quantum information from decoherence. In fault-tolerant quantum computation, the circuits used to measure the error syndromes are themselves faulty; to minimize the effect of syndrome measurement errors, the syndromes are measured repeatedly. This paper introduces a scheme...

It is known that any two-outcome quantum measurement can be decomposed into a
continuous stochastic process using a feedback loop. In this article, we
characterize which of these decompositions are possible when each iteration of
the feedback loop consists of a weak measurement caused by an interaction with
a probe system. We restrict ourselves to...

The D-Wave quantum computer is designed to solve a specific class of problems - The Quadratic Unconstrained Binary Optimization (QUBO) problem. One of the key processes in this pathway to the solution consists in embedding the problem graph into a hardware graph. It is a nontrivial task to determine whether a problem graph is minor embeddable in a...

Large weak values have been used to amplify the sensitivity of a linear
response signal for detecting changes in a small parameter, which has also
enabled a simple method for precise parameter estimation. However, producing a
large weak value requires a low postselection probability for an ancilla degree
of freedom, which limits the utility of the...

We describe a method to perform any generalized purity-preserving measurement
of a qubit with techniques tailored to superconducting systems. We start with
considering two methods for realizing a two-outcome partial projection: using a
thresholded continuous measurement in the circuit QED setup and using an
indirect ancilla qubit measurement. Then...

In Chapter 16 it was shown how holonomic quantum computation (HQC) can be combined with the method of decoherence-free subspaces (DFSs), leading to passive protection against certain types of correlated errors. However, this is not enough for fault tolerance since other types of errors can accumulate detrimentally unless corrected. Scalability of H...

We show that it is possible to clone quantum states to arbitrary accuracy in the presence of a Deutschian closed timelike curve (D-CTC), with a fidelity converging to one in the limit as the dimension of the CTC system becomes large-thus resolving an open conjecture [Brun et al., Phys. Rev. Lett. 102, 210402 (2009)]. This result follows from a D-CT...

In this paper, we introduce a unified framework to construct
entanglement-assisted quantum error-correcting codes, including additive and
nonadditive codes, based on the codeword stabilized framework on subsystems.
The codeword stabilized (CWS) framework is a scheme to construct quantum
error-correcting codes (QECCs) including both additive and non...

We say that two (or more) state assignments for one and the same quantum
system are compatible if they could represent the assignments of observers with
differing information about the system. A criterion for compatibility was
proposed in [Phys. Rev. A 65, 032315 (2002)]; however, this leaves unanswered
the question of whether there are degrees of...

In this paper we lay out an argument that generically the psychological arrow
of time should align with the thermodynamic arrow of time where that arrow is
well-defined. This argument applies to any physical system that can act as a
memory, in the sense of preserving a record of the state of some other system.
This result follows from two principle...

We show an equivalence relation between fault-tolerant circuits for a
stabilizer code and fault-tolerant adiabatic processes for holonomic quantum
computation (HQC), in the case where quantum information is encoded in the
ground state of the system Hamiltonian. By this equivalence, we can
systematically construct a fault-tolerant HQC scheme, which...

One of the most important properties of orbital angular momentum (OAM) of photons is that the Hilbert space required to describe a general quantum state is infinite dimensional. In principle, this could allow for encoding arbitrarily large amounts of quantum information per photon, but in practice, this potential is limited by decoherence and error...

In this work, we solve the open problem of the amplification limit for a weak
measurement with post-selection. The pre- and post-selected states of the
system and the initial probe state are allowed to be arbitrary. We derive that
the maximal output of a weak measurement is the solution of an eigenvalue
equation, and reveal a remarkable property th...

Knill demonstrated a fault-tolerant quantum computation scheme based on concatenated error-detecting codes and postselection with a simulated error threshold of 3% over the depolarizing channel. We show how to use Knill's postselection scheme in a practical two-dimensional quantum architecture that we designed with the goal to optimize the error co...

We consider a quantum key expansion (QKE) protocol based on
entanglement-assisted quantum error-correcting codes (EAQECCs). In these
protocols, a seed of a previously shared secret key is used in the
post-processing stage of a standard quantum key distribution protocol like the
Bennett-Brassard 1984 protocol, in order to produce a larger secret key...

We present an all-geometric scheme for fault-tolerant holonomic quantum
computation with stabilizer codes, based on non-Abelian adiabatic
holonomies. This scheme implements a universal set of quantum gates by
adiabatic deformation of the stabilizer eigenspaces (both the code space
and error spaces) through the same closed path in the parameter spac...

An important issue in the implementation of a quantum computer is to
protect quantum information from decoherence. Concatenated quantum codes
and topological quantum codes are extensively studied for fault-tolerant
quantum computation. However, there is not much research on large block
codes in any fault-tolerant scheme. Here we propose a method fo...