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David P. DiVincenzo

Publications and source records attributed to David P. DiVincenzo.

At least 73 records · Page 4Linked to original sources
arXiv2007

The Complexity of Stoquastic Local Hamiltonian Problems

We study the complexity of the Local Hamiltonian Problem (denoted as LH-MIN) in the special case when a Hamiltonian obeys conditions of the Perron-Frobenius theorem: all off-diagonal matrix elements in the standard basis are real and non-positive. We will call such Hamiltonians, which are common in the natural world, stoquastic. An equivalent characterization of stoquastic Hamiltonians is that they have an entry-wise non-negative Gibbs density matrix for any temperature. We prove that LH-MIN for stoquastic Hamiltonians belongs to the complexity class AM -- a probabilistic version of NP with two rounds of communication between the prover and the verifier. We also show that 2-local stoquastic LH-MIN is hard for the class MA. With the additional promise of having a polynomial spectral gap, we show that stoquastic LH-MIN belongs to the class POSTBPP=BPPpath -- a generalization of BPP in which a post-selective readout is allowed. This last result also shows that any problem solved by adiabatic quantum computation using stoquastic Hamiltonians lies in PostBPP.

quant-ph↗
arXiv2007

Model for l/f Flux Noise in SQUIDs and Qubits

We propose a model for 1/f flux noise in superconducting devices (f is frequency). The noise is generated by the magnetic moments of electrons in defect states which they occupy for a wide distribution of times before escaping. A trapped electron occupies one of the two Kramers-degenerate ground states, between which the transition rate is negligible at low temperature. As a result, the magnetic moment orientation is locked. Simulations of the noise produced by randomly oriented defects with a density of 5*10^17 m^-2 yield 1/f noise magnitudes in good agreement with experiments.

cond-mat.supr-con↗
arXiv2006

Noise Threshold for a Fault-Tolerant Two-Dimensional Lattice Architecture

We consider a model of quantum computation in which the set of operations is limited to nearest-neighbor interactions on a 2D lattice. We model movement of qubits with noisy SWAP operations. For this architecture we design a fault-tolerant coding scheme using the concatenated [[7,1,3]] Steane code. Our scheme is potentially applicable to ion-trap and solid-state quantum technologies. We calculate a lower bound on the noise threshold for our local model using a detailed failure probability analysis. We obtain a threshold of 1.85 x 10^-5 for the local setting, where memory error rates are one-tenth of the failure rates of gates, measurement, and preparation steps. For the analogous nonlocal setting, we obtain a noise threshold of 3.61 x 10^-5. Our results thus show that the additional SWAP operations required to move qubits in the local model affect the noise threshold only moderately.

quant-ph↗
arXiv2006

Effective fault-tolerant quantum computation with slow measurements

How important is fast measurement for fault-tolerant quantum computation? Using a combination of existing and new ideas, we argue that measurement times as long as even 1,000 gate times or more have a very minimal effect on the quantum accuracy threshold. This shows that slow measurement, which appears to be unavoidable in many implementations of quantum computing, poses no essential obstacle to scalability.

quant-ph↗
arXiv2005

Efficient evaluation of decoherence rates in complex Josephson circuits

A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer and one small loop, and three Josephson junctions. The contributions to relaxation (T_1) and dephasing (T_ϕ) arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We use a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimensional. We develop a general Born-Oppenheimer approximation to reduce the effective dimensionality in the calculation to one. We explore T_1 and T_ϕalong an optimal line in the space of applied fluxes; along this "S line" we see significant and rapidly varying contributions to the decoherence parameters, primarily from the circuit coupling to the large loop.

cond-mat.mes-hall↗
arXiv2005

Local Fault-tolerant Quantum Computation

We analyze and study the effects of locality on the fault-tolerance threshold for quantum computation. We analytically estimate how the threshold will depend on a scale parameter r which estimates the scale-up in the size of the circuit due to encoding. We carry out a detailed semi-numerical threshold analysis for concatenated coding using the 7-qubit CSS code in the local and `nonlocal' setting. First, we find that the threshold in the local model for the [[7,1,3]] code has a 1/r dependence, which is in correspondence with our analytical estimate. Second, the threshold, beyond the 1/r dependence, does not depend too strongly on the noise levels for transporting qubits. Beyond these results, we find that it is important to look at more than one level of concatenation in order to estimate the threshold and that it may be beneficial in certain places, like in the transportation of qubits, to do error correction only infrequently.

quant-ph↗
arXiv2005

Asymmetry and decoherence in a double-layer persistent-current qubit

Superconducting circuits fabricated using the widely used shadow evaporation technique can contain unintended junctions which change their quantum dynamics. We discuss a superconducting flux qubit design that exploits the symmetries of a circuit to protect the qubit from unwanted coupling to the noisy environment, in which the unintended junctions can spoil the quantum coherence. We present a theoretical model based on a recently developed circuit theory for superconducting qubits and calculate relaxation and decoherence times that can be compared with existing experiments. Furthermore, the coupling of the qubit to a circuit resonance (plasmon mode) is explained in terms of the asymmetry of the circuit. Finally, possibilities for prolonging the relaxation and decoherence times of the studied superconducting qubit are proposed on the basis of the obtained results.

cond-mat.supr-con↗
arXiv2004

Multi-level quantum description of decoherence in superconducting qubits

We present a multi-level quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multi-level dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e. transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation (T_1) and decoherence (T_2) times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.

cond-mat.mes-hall↗
arXiv2003

Exact Born Approximation for the Spin-Boson Model

Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the Ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by $\sqrtα$, where $α$ is the coupling strength to the environment. These calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.

cond-mat.mes-hall↗
arXiv2002

Hiding Quantum Data

Recent work has shown how to use the laws of quantum mechanics to keep classical and quantum bits secret in a number of different circumstances. Among the examples are private quantum channels, quantum secret sharing and quantum data hiding. In this paper we show that a method for keeping two classical bits hidden in any such scenario can be used to construct a method for keeping one quantum bit hidden, and vice--versa. In the realm of quantum data hiding, this allows us to construct bipartite and multipartite hiding schemes for qubits from the previously known constructions for hiding bits. Our method also gives a simple proof that two bits of shared randomness are required to construct a private quantum channel hiding one qubit.

quant-ph↗
arXiv2002

The entanglement of purification

We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to the entanglement cost of creating a state $ρ$ asymptotically from maximally entangled states, with negligible communication. We prove that the classical mutual information and the quantum mutual information divided by two are lower bounds for the regularized entanglement of purification. We present numerical results of the entanglement of purification for Werner states in ${\cal H}_2 \otimes {\cal H}_2$.

quant-ph↗
arXiv2001

Classical simulation of noninteracting-fermion quantum circuits

We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits (quant-ph/0006088).

quant-ph↗
arXiv2001

Remote State Preparation

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit - half that of teleportation - and becomes even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.

quant-ph↗
arXiv2001

Quantum Data Hiding

We expand on our work on Quantum Data Hiding -- hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.

quant-ph↗
arXiv2001

Hiding bits in Bell states

We present a scheme for hiding bits in Bell states that is secure even when the sharers Alice and Bob are allowed to carry out local quantum operations and classical communication. We prove that the information that Alice and Bob can gain about a hidden bit is exponentially small in $n$, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits. We indicate an alternative efficient low-entanglement method for preparing the shared quantum states. We discuss how our scheme can be implemented using present-day quantum optics.

quant-ph↗
arXiv2000

Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.

quant-ph↗
arXiv2000

Evidence for Bound Entangled States with Negative Partial Transpose

We exhibit a two-parameter family of bipartite mixed states $ρ_{bc}$, in a $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in $2\otimes 2$ can be distilled by local quantum operations and classical communication (LQ+CC). Evidence for this undistillability is provided by the result that, for certain states in this family, we cannot extract entanglement from any arbitrarily large number of copies of $ρ_{bc}$ using a projection on $2\otimes 2$. These states are canonical NPT states in the sense that any bipartite mixed state in any dimension with NPT can be reduced by LQ+CC operations to an NPT state of the $ρ_{bc}$ form. We show that the main question about the distillability of mixed states can be formulated as an open mathematical question about the properties of composed positive linear maps.

quant-ph↗